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necessity of the leaderboard

mute-god

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better inadequate than never

the solutions to tempuss problems require more thought than people are willing to bear, myself included
jump community suffers from the same phenomena ive observed in the spy communitys controversy over movement methodology, lack of scientific method


the paradigm of tempus i hear parroted throughout the community is a fundamentally anticompetitive one, where players reject points & leaderboards identical to jumping offline. admins believe the point rework will never come yet act as if it has already, employing an undiscriminating map pool dooming competition, community

why did jump centralise online? the source of competition, leaderboard, the framework which coordinates & validates achievement in jump

the point system articulates a competence-predicated hierarchy as a leaderboard. players objective is determined by the criteria of point designation, chief criterion being map completion. maps are an assemblage of levels which variably limit & obstruct movement; ergo, the map is the predicate of competency and embodies desired ability. control over the map is enough to rework the leaderboard, the solution is to curate the map pool


two examples
? remove bad maps. bad maps embody undesirable movement which axiomatically distort competence & leaderboard
? remove duplicate maps. maps with undifferentiated movement (eg triple pre) are just decentralised leaderboards that obscure standards

what maps are desirable, or atleast undesirable? i dont have a complete answer but believe there is one & it should dictate map approval criteria

offclass is an irrelevant classification in maps
gimmick or unconvention in the way that jumping & airpogo were once unconventional
tempus records most viewed demo maps are virtuoso (airpogo), when (pogo) & miner (speedrun / maximum optimisation)

« Last Edit: July 18, 2021, 09:40:43 PM by mute-god »




John

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i agree, wallpogo maps and players should all be banned for the sake of everyone's mental health


Zike

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better inadequate than never

the solutions to tempuss problems require more thought than people are willing to bear, myself included
jump community suffers from the same phenomena ive observed in the spy communitys controversy over movement methodology, lack of scientific method


the paradigm of tempus i hear parroted throughout the community is a fundamentally anticompetitive one, where players reject points & leaderboards identical to jumping offline. admins believe the point rework will never come yet act as if it has already, employing an undiscriminating map pool dooming competition, community

why did jump centralise online? the source of competition, leaderboard, the framework which coordinates & validates achievement in jump

the point system articulates a competence-predicated hierarchy as a leaderboard. players objective is determined by the criteria of point designation, chief criterion being map completion. maps are an assemblage of levels which variably limit & obstruct movement; ergo, the map is the predicate of competency and embodies desired ability. control over the map is enough to rework the leaderboard, the solution is to curate the map pool


two examples
? remove bad maps. bad maps embody undesirable movement which axiomatically distort competence & leaderboard
? remove duplicate maps. maps with undifferentiated movement (eg triple pre) are just decentralised leaderboards that obscure standards

what maps are desirable, or atleast undesirable? i dont have a complete answer but believe there is one & it should dictate map approval criteria

offclass maps should not be a pejorative
gimmick or unconvention in the way that jumping & airpogo were once unconventional
tempus records most viewed demo maps are virtuoso (airpogo), when (pogo) & miner (speedrun / maximum optimisation)


It's just so problematic. I make it sound too simple. I introduce some new concepts here again.
Numbers of completions say something about popularity, but in which way it drives competition is immensely complex.

Let's look at something.

For example, completionists play any map. And dedicated surfers in general play any map. It might be argued that the most interesting completions are actually from that part of the population that is least dedicated to surf or who spent the least time on surf because they will naturally be most picky with their time; economize their time and spend it on the actual most popular maps.

But this will fuck up the simplicity that I assumed actually. For simplicity, for the example (obv. this is not how it exactly works in the real world lol, but you need to understand the concepts), let's assume, that dedicated surfers complete any map they can afford because they are no-lifers (xd); that will mean that inside each tier map pool, all maps have the same number of completions among dedicated surfers. If we now include the non-dedicated surfers, the number of completions will start to vary (especially depending on how long the time map has been out ofc)

Let's say the population consists of 80 % dedicated surfers, and 20 % non-dedicated surfers (in reality surfers will be dedicated and non-dedicated to different degree ofc.)

So an average t3 map may have 500 completions, 400 completions from dedicated surfers, 100 from non-dedicated.
A t3 map with 600 completions will then also have 400 completions from the dedicated! (because the dedicated surfers complete whatever they can as I assumed!), so it is the non-dedicated surfers that get it to 600. And their population increase x2!!! So the popularity has increased x2???

I don't know. What does popularity even mean for competition, etc., it's very confusing. This also shows how using the number of completions to measure competitivity will be vary depending on the mix of dedicated and non-dedicated surfers in the population (well, if you were nerds, you could try to compensate for that lol)

I personally believe (though with my very shallow knowledge) that the statistical knowledge required in order to use number of completions accurately and without biases (biases we prob. won't even understand, etc.) is absolutely immensely!!! I think you should look at how close times are in the top10. Yeah, like KSF. But KSF's model had some problems which I have pointed out as well.

e: I'm not sure if this is relevant or not, but in case someone puts up a counter-argument that somehow exploits it and refuse to look at the large picture which I'm trying ... then I just mention: All the completions from the dedicated players that complete whatever they can afford, do not imply competition (like that they will equally contest all the maps they can afford to beat, obv. that's bullshit). They will in general contest what is most popular which will be suggested by the non-dedicated players as they will mainly drive the differences in numbers of completions cross maps (among other factors).

I now try to list up everything that will affect number of completions.

vertical tier
horizontal tier
the time limit (a tight time limit with a lenghty map will make the lenght and horizontal tier add to the vertical tier)
rng difficulty (fake tier)
length
complexity (information load, e.g., bhop maps with many bhop blocks. length and complexity have a connection ofc.)
the proportion of completionists and non-completionists in the population
time map has been out
popularity.

as you see, it is immensely complex!!!

e2:
You could also say. You can indeed look at dedicated surfer's completions as well. Just at the dedicated surfers that don't have completions everywhere, but have been picky. I mean you can be a dedicated surfer and be picky but then grind the few maps you have picked.

So maybe. It is rather just the "completionists" that blur the pictures, and it is the non-completionists that suggest the popularity. But some non-completionists can actually be dedicated as well. So maybe that's a better way to word it. I'm not sure.

e3: I hope that's my last message on this subject for a while ..................................

e4: In KZ there is a lot of rng difficulty. When I say RNG, I don't mean RNG in its most strict sense.
But, e.g., when you have to get the perfect offset from a block for a LJ. This kind of difficulty is partly related to low competition because you just have to be accurate "for one point" which everyone can be if they just consume enough time (so it's inappropriate as means for the pro's to differentiate them from those who are worse). Continuous accuracy is great. "one point accuracy" is ok for competition IN TOURNAMENTS; for infinite time running ... It's bad. I believe RNG difficulty is a bigger factor in many other games than surf. So perhaps that's why many people are not as outrageous as me.

But well, this isn't an argument for my opponents case (HAHA, you apply your narrow-minded surf knowledge to all other games! xD). No, this just shows how biased this stupid # completion is; it depends on so many factors and even depends on the specific game in question which wasn't even added to my list xD top10 time distributions are far more neutral.

e5: It's also funny because I have heard many times you guys speaking good of surfers playing a big variety of maps. Especially you have the XP system that encourages this and through which you can earn coins etc. to buy cosmetics. You have plans about making a tournament for every new map! (which I isolatively think is a good idea) How more you are going to encourage completionist tendencies, how smaller become the sample of non-completionist tendencies - how higher inaccuracy (even if you knew how to adjust for all these things!) ... This is not well-concieved ...............


cowboyana

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why did jump centralise online? the source of competition, leaderboard, the framework which coordinates & validates achievement in jump

the point system articulates a competence-predicated hierarchy as a leaderboard. players objective is determined by the criteria of point designation, chief criterion being map completion. maps are an assemblage of levels which variably limit & obstruct movement; ergo, the map is the predicate of competency and embodies desired ability. control over the map is enough to rework the leaderboard, the solution is to curate the map pool[/size]

two examples
? remove bad maps. bad maps embody undesirable movement which axiomatically distort competence & leaderboard
? remove duplicate maps. maps with undifferentiated movement (eg triple pre) are just decentralised leaderboards that obscure standards

what maps are desirable, or atleast undesirable? i dont have a complete answer but believe there is one & it should dictate map approval criteria

offclass maps should not be a pejorative
gimmick or unconvention in the way that jumping & airpogo were once unconventional
tempus records most viewed demo maps are virtuoso (airpogo), when (pogo) & miner (speedrun / maximum optimisation)

[/center]

It's just so problematic. I make it sound too simple. I introduce some new concepts here again.
Numbers of completions say something about popularity, but in which way it drives competition is immensely complex.

Let's look at something.

For example, completionists play any map. And dedicated surfers in general play any map. It might be argued that the most interesting completions are actually from that part of the population that is least dedicated to surf or who spent the least time on surf because they will naturally be most picky with their time; economize their time and spend it on the actual most popular maps.


i think this explains why it is still necessary to rework the point system, it serves as a proxy for the underlying mechanic of map design

if no map is complete, then it is impossible to play the point system & we can continue to play the leaderboard as we would if there were no point system

but jump leaderboards are a proxy for a mechanic we reject, the point system itself still remains

i agree completely, i just think the solution is easier than some people make out. the problem is that you would need to change the point system, but that would destroy the leaderboard, so you would need to preserve both.

that's why i see the point system as the foundation of the leaderboard & the leaderboard as a kind of meta-layer or overlay. because you cannot change the point system without changing the leaderboard or leaderboard without changing the point system

as far as map design is concerned, it's entirely possible to put in an obstacle, and if you remove all the waypoints as you're running, there's nothing to guide you other than sound, your own judgement, & experience.

but if you make a jump leaderboard, you're artificially restricting your map play from the beginning. so the point system still exists, it's just much more limited

I think this whole thing is just an interesting observation from a new player.

You would be making things a lot more complicated than they have to be.

Map design and playstyle is all about learning the game as it is at the time. Just have a look at some of the best maps - their style is entirely different to what is now.

I can imagine how you'd need to put more obstacles on the map to encourage the kind of playstyle you'd want. And it'd still be possible to play it like any other type of map if you wanted to, so you're not going to get everything.

If you made a jump leaderboard it would likely give people some kind of unfair advantage that wasn't there before. At least, that's how I see it.

the leaderboard has an effect on the map because it's what determines the point system.

i could remove the obstacles & leave a plain, open map that has no points in it, but as you pointed out, there's no real way to distinguish between the two styles of map. the only difference is that one of them has more obstacles, because otherwise, they're both completely the same.

as i said before, this was a thought experiment, but this whole post was a little too much for me to digest, and i have school to go back to

i just wanted to say that it's cool to see this conversation be moved over to this forum, because it's really nice to see that kind of feedback in a respectful way. thanks for bringing it up!

The map might also lose some replayability if it's really difficult to play to certain kinds of styles. I'm not even sure if it'd be that fun.

Originally posted by ZirconianIf you made a jump leaderboard it would likely give people some kind of unfair advantage that wasn't there before. At least, that's how I see it.

That's kinda how it works.

There's no problem with a map being a little difficult, but even if there is, the people who don't need it are playing the map as intended and the people who don't know they can go over a wall to get ahead are getting a game over.

I agree with this, they should have something in the middle like a cross, or something that's easy to remember but easy to jump over. Something that encourages all styles, not just one kind. That way the map could still be enjoyable and there wouldn't be much unfair advantages.

better inadequate than never

the solutions to tempuss problems require more thought than people are willing to bear, myself included
jump community suffers from the same phenomena ive observed in the spy communitys controversy over movement methodology, lack of scientific method


the paradigm of tempus i hear parroted throughout the community is a fundamentally anticompetitive one, where players reject points & leaderboards identical to jumping offline. admins believe the point rework will never come yet act as if it has already, employing an undiscriminating map pool dooming competition, community

why did jump centralise online? the source of competition, leaderboard, the framework which coordinates & validates achievement in jump

the point system articulates a competence-predicated hierarchy as a leaderboard. players objective is determined by the criteria of point designation, chief criterion being map completion. maps are an assemblage of levels which variably limit & obstruct movement; ergo, the map is the predicate of competency and embodies desired ability. control over the map is enough to rework the leaderboard, the solution is to curate the map pool


two examples
? remove bad maps. bad maps embody undesirable movement which axiomatically distort competence & leaderboard
? remove duplicate maps. maps with undifferentiated movement (eg triple pre) are just decentralised leaderboards that obscure standards

what maps are desirable, or atleast undesirable? i dont have a complete answer but believe there is one & it should dictate map approval criteria

offclass maps should not be a pejorative
gimmick or unconvention in the way that jumping & airpogo were once unconventional
tempus records most viewed demo maps are virtuoso (airpogo), when (pogo) & miner (speedrun / maximum optimisation)


You are the one that speaks against completionist tendencies for surf - so this shows in your own game that you need to adapt your game more and more for people.

Also, I haven't heard of a single person saying that you can't play the other surf maps in tournaments (of course some surf maps are not well-balanced - just look at some other online game to see this).

The only thing that is lacking in your game is replay value. The game-world is limited and so every level is the same. So if you want a challenge, you have to just stay with one of the maps. I believe you had an idea with the XP and in terms of level distribution the maps are still balanced, but the problem is - if you have all maps in you'll probably stay on the same map for most of the time (because the XP and the level distribution) and play maps you already know.

If you want surf to be more like Mario Kart, i suggest you to make the game more open. Not only should be the game more balanced, but a more fun game to play. I like to play more and more to surf and that's why i'm still playing in the online tournaments. So don't focus on the completionist part - that will just frustrate your users (a bad idea) How more you are going to encourage completionist tendencies, how smaller become the sample of non-completionist tendencies - how higher inaccuracy (even if you knew how to adjust for all these things!) ... This is not well-concieved ............... ^_^

You are the one that speaks against completionist tendencies for surf - so this shows in your own game that you need to adapt your game more and more for people.

what?

I'd suggest looking at more maps which try to follow the principle of using tiles where it makes sense to do so, using an appropriate number of them, and not forcing specific themes on the player using the map, e.g. not having too large regions which are either all forest or all desert, or using the same tiles for water in the water tileset you use.

And there is the map-theme issue.
As you have a map pool with only a few different themes, you have to find ways to make them work together, either by having several maps which just use a different theme.
Or by using tilesets which are used together to make a consistent feeling, which still doesn't help with the player using the map.

So you will still get a lot of maps which are just horrible to play on, and players will still be unhappy with not having been given tools that are good for the game.

I think the most appropriate tool here is that you have to be a player before you can use a tool.
You can't just create a new game for yourself to explore the mechanics without understanding the system.

It's like when you start learning programming, you don't write for yourself but to actually make your code useful to you, you have to learn how to use the programming tool, not the other way around.

The best design, by the way, isn't something you design when nobody knows what the map is going to be.
It's something you design in collaboration with other people you've tried to bring to the table, to bring them in the right mindset,
with the right knowledge of the game, and with the right understanding of the other players.
There are a lot of people with excellent skills and knowledge, but very little experience in design or in making games.

That's another of my major pet peeves of being self-taught,
I'll give you an example,

I made a game, and after the release I got positive comments about it.
Some people wrote:

"There were some things I liked, some things I didn't, it was overall really good, but I've never done this before so I might have missed some things in how I wanted to do something. I would have done this differently, it could do with some polish."

So I didn't do that, I didn't think that I had any polish, or any other players' feedback, and went on.
But some time later, I noticed people writing reviews on Steam about it saying:

"Wow, I didn't realize you put points on a map. I thought you were just moving them like with a board game."

That was a very good feedback!
I wasn't aware of that, that points were a mechanic in a game,
and I hadn't thought of how that would influence the map design in some of the earlier maps, so I had to re-work it.

When I think about people who have skills but haven't yet built a game design portfolio,
if you want to work in game development, and be very good at it,
then you should do it with all the skills you have.

That means if you're creative in a certain way, if you're good at programming, if you're good at art,
if you're good at sound, if you're good at mechanics, and so on.
You should also do it with other people you work with, you should build a portfolio.

If you don't, then you'll likely only work in one area, or maybe just one type of game design, and you'll be limited.
You won't know how other people do things, you won't know the right questions to ask.

People also make games without any of the skills, without any of the abilities they have.

I recently had a conversation with a developer about a very interesting thing.
He's making this puzzle game, and he wanted to know, should he do all the programming himself, or should he find a programmer?

That's a really important question. The programming guy you hire could be anyone.
You can hire someone who already knows programming, or you can find someone you know who wants to make games.

This is really easy to miss. The people who are the best designers of game mechanics,
of game systems, of game concepts, of game design are people who know programming, who know art, who know games,
because game designers are all that.

If you make a concept document that says this is what we're trying to do,
and if you have the programming skills to make it, that's all that matters.
If you don't have all the other skills, you'll be in trouble.

:o

But that is a matter of opinion. I believe length hinders competition. It is not the length as such, it is just that it is a very, very, very difficult task to play in such a very, very, very short time, when you have no clue what the other player is doing or even whether he is moving or not. It's a different time scale, where players do not react fast enough, and in such a short time as in a 3sec or even a 5sec long bonus it becomes impossible to react to what is going on. And it becomes a whole different game of its own.

That is why I also prefer the 5sec long bonus for the game, but for a game in which you are able to see your opponents moves, as well as to know when the other person is in the air. Such as in a 5-6sec long bonus is fine.

A different perspective on length and short track.

Quote

In chess, the game is too short and I can see two moves ahead.

I am not a chess player (yet), but I am also not a big computer chess fan. In computer chess all that is visible on the board usually becomes known by the time the next "turn" is played. And, as already mentioned, it is too short and it is also very difficult to play well, when you don't know what the other player does. You are also playing in a 5-6sec long time scale, where your reaction time is slower than with human opponents, and which again is very, very, very slow. Also, the players know what the other player's moves are and the moves themselves have a very big impact, for their own game.

Quote

In a 5-6 sec long bonus, the game is too long and not interesting enough.

But it is a game in which you can see all your moves! Or at least for you all the moves that are part of your own game. All other moves are invisible. If you make a mistake in one of the moves which is played by your opponent, it might be a hard move, but you are still completely able to see what happened.

Quote

In a 5-6 sec long bonus, I play a lot of it but I don't learn very much from it, as the opponent is too unpredictable and too much of a wild card. I like to see what my opponent will do with the same moves that I made.

But then you do not actually play the game that you are supposed to be playing. And for that game you have to play the same moves, all the time. So, the real thing to play is the game that you would play, if you were actually playing this very long bonus time game. This game is completely different from the game that you actually play. But people are always playing the real game, not the game that they should be playing. So, they don't see much of anything. In their "game" they never see what their opponent did.

Quote

To make a long story short, I think if this game is used for learning the rules of the game, you are totally wrong. It is not really a good game for learning the rules.

But in my mind this is a very good game for learning the rules of the game. It is the ultimate game that teaches you the rules. I've played it dozens of times to learn the rules of the game. I don't play it for real. It is the real thing.

Quote

I know it is not a very clever thing to say, but the game for learning the rules should be the same thing that is played in the official games.

Exactly. The board game is the ultimate game to learn the rules.

Quote
« Last Edit: July 15, 2021, 03:54:10 PM by cowboyana »


879m

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this begs the question, what will be the one triple pre and off-class map that is allowed on tempus


hex

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this begs the question, what will be the one triple pre and off-class map that is allowed on tempus

jump_prism the first intended soldier map for demo


Resistance

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better inadequate than never

the solutions to tempuss problems require more thought than people are willing to bear, myself included
jump community suffers from the same phenomena ive observed in the spy communitys controversy over movement methodology, lack of scientific method


the paradigm of tempus i hear parroted throughout the community is a fundamentally anticompetitive one, where players reject points & leaderboards identical to jumping offline. admins believe the point rework will never come yet act as if it has already, employing an undiscriminating map pool dooming competition, community

why did jump centralise online? the source of competition, leaderboard, the framework which coordinates & validates achievement in jump

the point system articulates a competence-predicated hierarchy as a leaderboard. players objective is determined by the criteria of point designation, chief criterion being map completion. maps are an assemblage of levels which variably limit & obstruct movement; ergo, the map is the predicate of competency and embodies desired ability. control over the map is enough to rework the leaderboard, the solution is to curate the map pool


two examples
? remove bad maps. bad maps embody undesirable movement which axiomatically distort competence & leaderboard
? remove duplicate maps. maps with undifferentiated movement (eg triple pre) are just decentralised leaderboards that obscure standards

what maps are desirable, or atleast undesirable? i dont have a complete answer but believe there is one & it should dictate map approval criteria

offclass maps should not be a pejorative
gimmick or unconvention in the way that jumping & airpogo were once unconventional
tempus records most viewed demo maps are virtuoso (airpogo), when (pogo) & miner (speedrun / maximum optimisation)


Chapter 1

In my younger and more vulnerable years my father gave me some advice that I've been turning over in my mind ever since.

"Whenever you feel like criticizing any one," he told me, "just remember that all the people in this world haven't had the advantages that you've had."

He didn't say any more but we've always been unusually communicative in a reserved way, and I understood that he meant a great deal more than that. In consequence I'm inclined to reserve all judgments, a habit that has opened up many curious natures to me and also made me the victim of not a few veteran bores. The abnormal mind is quick to detect and attach itself to this quality when it appears in a normal person, and so it came about that in college I was unjustly accused of being a politician, because I was privy to the secret griefs of wild, unknown men. Most of the confidences were unsought?frequently I have feigned sleep, preoccupation, or a hostile levity when I realized by some unmistakable sign that an intimate revelation was quivering on the horizon?for the intimate revelations of young men or at least the terms in which they express them are usually plagiaristic and marred by obvious suppressions. Reserving judgments is a matter of infinite hope. I am still a little afraid of missing something if I forget that, as my father snobbishly suggested, and I snobbishly repeat, a sense of the fundamental decencies is parcelled out unequally at birth.

And, after boasting this way of my tolerance, I come to the admission that it has a limit. Conduct may be founded on the hard rock or the wet marshes but after a certain point I don't care what it's founded on. When I came back from the East last autumn I felt that I wanted the world to be in uniform and at a sort of moral attention forever; I wanted no more riotous excursions with privileged glimpses into the human heart. Only Gatsby, the man who gives his name to this book, was exempt from my reaction?Gatsby who represented everything for which I have an unaffected scorn. If personality is an unbroken series of successful gestures, then there was something gorgeous about him, some heightened sensitivity to the promises of life, as if he were related to one of those intricate machines that register earthquakes ten thousand miles away. This responsiveness had nothing to do with that flabby impressionability which is dignified under the name of the "creative temperament"?it was an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again. No?Gatsby turned out all right at the end; it is what preyed on Gatsby, what foul dust floated in the wake of his dreams that temporarily closed out my interest in the abortive sorrows and short-winded elations of men.


My family have been prominent, well-to-do people in this middle-western city for three generations. The Carraways are something of a clan and we have a tradition that we're descended from the Dukes of Buccleuch, but the actual founder of my line was my grandfather's brother who came here in fifty-one, sent a substitute to the Civil War and started the wholesale hardware business that my father carries on today.

I never saw this great-uncle but I'm supposed to look like him?with special reference to the rather hard-boiled painting that hangs in Father's office. I graduated from New Haven in 1915, just a quarter of a century after my father, and a little later I participated in that delayed Teutonic migration known as the Great War. I enjoyed the counter-raid so thoroughly that I came back restless. Instead of being the warm center of the world the middle-west now seemed like the ragged edge of the universe?so I decided to go east and learn the bond business. Everybody I knew was in the bond business so I supposed it could support one more single man. All my aunts and uncles talked it over as if they were choosing a prep-school for me and finally said, "Why?ye-es" with very grave, hesitant faces. Father agreed to finance me for a year and after various delays I came east, permanently, I thought, in the spring of twenty-two.

The practical thing was to find rooms in the city but it was a warm season and I had just left a country of wide lawns and friendly trees, so when a young man at the office suggested that we take a house together in a commuting town it sounded like a great idea. He found the house, a weather beaten cardboard bungalow at eighty a month, but at the last minute the firm ordered him to Washington and I went out to the country alone. I had a dog, at least I had him for a few days until he ran away, and an old Dodge and a Finnish woman who made my bed and cooked breakfast and muttered Finnish wisdom to herself over the electric stove.

It was lonely for a day or so until one morning some man, more recently arrived than I, stopped me on the road.

"How do you get to West Egg village?" he asked helplessly.

I told him. And as I walked on I was lonely no longer. I was a guide, a pathfinder, an original settler. He had casually conferred on me the freedom of the neighborhood.

And so with the sunshine and the great bursts of leaves growing on the trees?just as things grow in fast movies?I had that familiar conviction that life was beginning over again with the summer.

There was so much to read for one thing and so much fine health to be pulled down out of the young breath-giving air. I bought a dozen volumes on banking and credit and investment securities and they stood on my shelf in red and gold like new money from the mint, promising to unfold the shining secrets that only Midas and Morgan and Maecenas knew. And I had the high intention of reading many other books besides. I was rather literary in college?one year I wrote a series of very solemn and obvious editorials for the "Yale News"?and now I was going to bring back all such things into my life and become again that most limited of all specialists, the "well-rounded man." This isn't just an epigram?life is much more successfully looked at from a single window, after all.

It was a matter of chance that I should have rented a house in one of the strangest communities in North America. It was on that slender riotous island which extends itself due east of New York and where there are, among other natural curiosities, two unusual formations of land. Twenty miles from the city a pair of enormous eggs, identical in contour and separated only by a courtesy bay, jut out into the most domesticated body of salt water in the Western Hemisphere, the great wet barnyard of Long Island Sound. They are not perfect ovals?like the egg in the Columbus story they are both crushed flat at the contact end?but their physical resemblance must be a source of perpetual confusion to the gulls that fly overhead. To the wingless a more arresting phenomenon is their dissimilarity in every particular except shape and size.

I lived at West Egg, the?well, the less fashionable of the two, though this is a most superficial tag to express the bizarre and not a little sinister contrast between them. My house was at the very tip of the egg, only fifty yards from the Sound, and squeezed between two huge places that rented for twelve or fifteen thousand a season. The one on my right was a colossal affair by any standard?it was a factual imitation of some H?tel de Ville in Normandy, with a tower on one side, spanking new under a thin beard of raw ivy, and a marble swimming pool and more than forty acres of lawn and garden. It was Gatsby's mansion. Or rather, as I didn't know Mr. Gatsby it was a mansion inhabited by a gentleman of that name. My own house was an eye-sore, but it was a small eye-sore, and it had been overlooked, so I had a view of the water, a partial view of my neighbor's lawn, and the consoling proximity of millionaires?all for eighty dollars a month.

Across the courtesy bay the white palaces of fashionable East Egg glittered along the water, and the history of the summer really begins on the evening I drove over there to have dinner with the Tom Buchanans. Daisy was my second cousin once removed and I'd known Tom in college. And just after the war I spent two days with them in Chicago.

Her husband, among various physical accomplishments, had been one of the most powerful ends that ever played football at New Haven?a national figure in a way, one of those men who reach such an acute limited excellence at twenty-one that everything afterward savors of anti-climax. His family were enormously wealthy?even in college his freedom with money was a matter for reproach?but now he'd left Chicago and come east in a fashion that rather took your breath away: for instance he'd brought down a string of polo ponies from Lake Forest. It was hard to realize that a man in my own generation was wealthy enough to do that.

Why they came east I don't know. They had spent a year in France, for no particular reason, and then drifted here and there unrestfully wherever people played polo and were rich together. This was a permanent move, said Daisy over the telephone, but I didn't believe it?I had no sight into Daisy's heart but I felt that Tom would drift on forever seeking a little wistfully for the dramatic turbulence of some irrecoverable football game.

And so it happened that on a warm windy evening I drove over to East Egg to see two old friends whom I scarcely knew at all. Their house was even more elaborate than I expected, a cheerful red and white Georgian Colonial mansion overlooking the bay. The lawn started at the beach and ran toward the front door for a quarter of a mile, jumping over sun-dials and brick walks and burning gardens?finally when it reached the house drifting up the side in bright vines as though from the momentum of its run. The front was broken by a line of French windows, glowing now with reflected gold, and wide open to the warm windy afternoon, and Tom Buchanan in riding clothes was standing with his legs apart on the front porch.

He had changed since his New Haven years. Now he was a sturdy, straw haired man of thirty with a rather hard mouth and a supercilious manner. Two shining, arrogant eyes had established dominance over his face and gave him the appearance of always leaning aggressively forward. Not even the effeminate swank of his riding clothes could hide the enormous power of that body?he seemed to fill those glistening boots until he strained the top lacing and you could see a great pack of muscle shifting when his shoulder moved under his thin coat. It was a body capable of enormous leverage?a cruel body.

His speaking voice, a gruff husky tenor, added to the impression of fractiousness he conveyed. There was a touch of paternal contempt in it, even toward people he liked?and there were men at New Haven who had hated his guts.

"Now, don't think my opinion on these matters is final," he seemed to say, "just because I'm stronger and more of a man than you are." We were in the same Senior Society, and while we were never intimate I always had the impression that he approved of me and wanted me to like him with some harsh, defiant wistfulness of his own.

We talked for a few minutes on the sunny porch.

"I've got a nice place here," he said, his eyes flashing about restlessly.

Turning me around by one arm he moved a broad flat hand along the front vista, including in its sweep a sunken Italian garden, a half acre of deep pungent roses and a snub-nosed motor boat that bumped the tide off shore.

"It belonged to Demaine the oil man." He turned me around again, politely and abruptly. "We'll go inside."

We walked through a high hallway into a bright rosy-colored space, fragilely bound into the house by French windows at either end. The windows were ajar and gleaming white against the fresh grass outside that seemed to grow a little way into the house. A breeze blew through the room, blew curtains in at one end and out the other like pale flags, twisting them up toward the frosted wedding cake of the ceiling?and then rippled over the wine-colored rug, making a shadow on it as wind does on the sea.

The only completely stationary object in the room was an enormous couch on which two young women were buoyed up as though upon an anchored balloon. They were both in white and their dresses were rippling and fluttering as if they had just been blown back in after a short flight around the house. I must have stood for a few moments listening to the whip and snap of the curtains and the groan of a picture on the wall. Then there was a boom as Tom Buchanan shut the rear windows and the caught wind died out about the room and the curtains and the rugs and the two young women ballooned slowly to the floor.

The younger of the two was a stranger to me. She was extended full length at her end of the divan, completely motionless and with her chin raised a little as if she were balancing something on it which was quite likely to fall. If she saw me out of the corner of her eyes she gave no hint of it?indeed, I was almost surprised into murmuring an apology for having disturbed her by coming in.

The other girl, Daisy, made an attempt to rise?she leaned slightly forward with a conscientious expression?then she laughed, an absurd, charming little laugh, and I laughed too and came forward into the room.

"I'm p-paralyzed with happiness."

She laughed again, as if she said something very witty, and held my hand for a moment, looking up into my face, promising that there was no one in the world she so much wanted to see. That was a way she had. She hinted in a murmur that the surname of the balancing girl was Baker. (I've heard it said that Daisy's murmur was only to make people lean toward her; an irrelevant criticism that made it no less charming.)

At any rate Miss Baker's lips fluttered, she nodded at me almost imperceptibly and then quickly tipped her head back again?the object she was balancing had obviously tottered a little and given her something of a fright. Again a sort of apology arose to my lips. Almost any exhibition of complete self sufficiency draws a stunned tribute from me.

I looked back at my cousin who began to ask me questions in her low, thrilling voice. It was the kind of voice that the ear follows up and down as if each speech is an arrangement of notes that will never be played again. Her face was sad and lovely with bright things in it, bright eyes and a bright passionate mouth?but there was an excitement in her voice that men who had cared for her found difficult to forget: a singing compulsion, a whispered "Listen," a promise that she had done gay, exciting things just a while since and that there were gay, exciting things hovering in the next hour.

I told her how I had stopped off in Chicago for a day on my way east and how a dozen people had sent their love through me.

"Do they miss me?" she cried ecstatically.

"The whole town is desolate. All the cars have the left rear wheel painted black as a mourning wreath and there's a persistent wail all night along the North Shore."

"How gorgeous! Let's go back, Tom. Tomorrow!" Then she added irrelevantly, "You ought to see the baby."

"I'd like to."

"She's asleep. She's two years old. Haven't you ever seen her?"

"Never."

"Well, you ought to see her. She's?"

Tom Buchanan who had been hovering restlessly about the room stopped and rested his hand on my shoulder.

"What you doing, Nick?"

"I'm a bond man."

"Who with?"

I told him.

"Never heard of them," he remarked decisively.

This annoyed me.

"You will," I answered shortly. "You will if you stay in the East."

"Oh, I'll stay in the East, don't you worry," he said, glancing at Daisy and then back at me, as if he were alert for something more. "I'd be a God Damned fool to live anywhere else."

At this point Miss Baker said "Absolutely!" with such suddenness that I started?it was the first word she uttered since I came into the room. Evidently it surprised her as much as it did me, for she yawned and with a series of rapid, deft movements stood up into the room.

"I'm stiff," she complained, "I've been lying on that sofa for as long as I can remember."

"Don't look at me," Daisy retorted. "I've been trying to get you to New York all afternoon."

"No, thanks," said Miss Baker to the four cocktails just in from the pantry, "I'm absolutely in training."

Her host looked at her incredulously.

"You are!" He took down his drink as if it were a drop in the bottom of a glass. "How you ever get anything done is beyond me."

I looked at Miss Baker wondering what it was she "got done." I enjoyed looking at her. She was a slender, small-breasted girl, with an erect carriage which she accentuated by throwing her body backward at the shoulders like a young cadet. Her grey sun-strained eyes looked back at me with polite reciprocal curiosity out of a wan, charming discontented face. It occurred to me now that I had seen her, or a picture of her, somewhere before.

"You live in West Egg," she remarked contemptuously. "I know somebody there."

"I don't know a single?"

"You must know Gatsby."

"Gatsby?" demanded Daisy. "What Gatsby?"

Before I could reply that he was my neighbor dinner was announced; wedging his tense arm imperatively under mine Tom Buchanan compelled me from the room as though he were moving a checker to another square.

Slenderly, languidly, their hands set lightly on their hips the two young women preceded us out onto a rosy-colored porch open toward the sunset where four candles flickered on the table in the diminished wind.

"Why candles?" objected Daisy, frowning. She snapped them out with her fingers. "In two weeks it'll be the longest day in the year." She looked at us all radiantly. "Do you always watch for the longest day of the year and then miss it? I always watch for the longest day in the year and then miss it."

"We ought to plan something," yawned Miss Baker, sitting down at the table as if she were getting into bed.

"All right," said Daisy. "What'll we plan?" She turned to me helplessly. "What do people plan?"

Before I could answer her eyes fastened with an awed expression on her little finger.

"Look!" she complained. "I hurt it."

We all looked?the knuckle was black and blue.

"You did it, Tom," she said accusingly. "I know you didn't mean to but you did do it. That's what I get for marrying a brute of a man, a great big hulking physical specimen of a?"

"I hate that word hulking," objected Tom crossly, "even in kidding."

"Hulking," insisted Daisy.

Sometimes she and Miss Baker talked at once, unobtrusively and with a bantering inconsequence that was never quite chatter, that was as cool as their white dresses and their impersonal eyes in the absence of all desire. They were here?and they accepted Tom and me, making only a polite pleasant effort to entertain or to be entertained. They knew that presently dinner would be over and a little later the evening too would be over and casually put away. It was sharply different from the West where an evening was hurried from phase to phase toward its close in a continually disappointed anticipation or else in sheer nervous dread of the moment itself.

"You make me feel uncivilized, Daisy," I confessed on my second glass of corky but rather impressive claret. "Can't you talk about crops or something?"

I meant nothing in particular by this remark but it was taken up in an unexpected way.

"Civilization's going to pieces," broke out Tom violently. "I've gotten to be a terrible pessimist about things. Have you read 'The Rise of the Coloured Empires' by this man Goddard?"

"Why, no," I answered, rather surprised by his tone.

"Well, it's a fine book, and everybody ought to read it. The idea is if we don't look out the white race will be?will be utterly submerged. It's all scientific stuff; it's been proved."

"Tom's getting very profound," said Daisy with an expression of unthoughtful sadness. "He reads deep books with long words in them. What was that word we?"

"Well, these books are all scientific," insisted Tom, glancing at her impatiently. "This fellow has worked out the whole thing. It's up to us who are the dominant race to watch out or these other races will have control of things."

"We've got to beat them down," whispered Daisy, winking ferociously toward the fervent sun.

"You ought to live in California?" began Miss Baker but Tom interrupted her by shifting heavily in his chair.

"This idea is that we're Nordics. I am, and you are and you are and?" After an infinitesimal hesitation he included Daisy with a slight nod and she winked at me again. "?and we've produced all the things that go to make civilization?oh, science and art and all that. Do you see?"

There was something pathetic in his concentration as if his complacency, more acute than of old, was not enough to him any more. When, almost immediately, the telephone rang inside and the butler left the porch Daisy seized upon the momentary interruption and leaned toward me.

"I'll tell you a family secret," she whispered enthusiastically. "It's about the butler's nose. Do you want to hear about the butler's nose?"

"That's why I came over tonight."

"Well, he wasn't always a butler; he used to be the silver polisher for some people in New York that had a silver service for two hundred people. He had to polish it from morning till night until finally it began to affect his nose?"

"Things went from bad to worse," suggested Miss Baker.

"Yes. Things went from bad to worse until finally he had to give up his position."

For a moment the last sunshine fell with romantic affection upon her glowing face; her voice compelled me forward breathlessly as I listened?then the glow faded, each light deserting her with lingering regret like children leaving a pleasant street at dusk.

The butler came back and murmured something close to Tom's ear whereupon Tom frowned, pushed back his chair and without a word went inside. As if his absence quickened something within her Daisy leaned forward again, her voice glowing and singing.

"I love to see you at my table, Nick. You remind me of a?of a rose, an absolute rose. Doesn't he?" She turned to Miss Baker for confirmation. "An absolute rose?"

This was untrue. I am not even faintly like a rose. She was only extemporizing but a stirring warmth flowed from her as if her heart was trying to come out to you concealed in one of those breathless, thrilling words. Then suddenly she threw her napkin on the table and excused herself and went into the house.

Miss Baker and I exchanged a short glance consciously devoid of meaning. I was about to speak when she sat up alertly and said "Sh!" in a warning voice. A subdued impassioned murmur was audible in the room beyond and Miss Baker leaned forward, unashamed, trying to hear. The murmur trembled on the verge of coherence, sank down, mounted excitedly, and then ceased altogether.

"This Mr. Gatsby you spoke of is my neighbor?" I said.

"Don't talk. I want to hear what happens."

"Is something happening?" I inquired innocently.

"You mean to say you don't know?" said Miss Baker, honestly surprised. "I thought everybody knew."

"I don't."

"Why?" she said hesitantly, "Tom's got some woman in New York."

"Got some woman?" I repeated blankly.

Miss Baker nodded.

"She might have the decency not to telephone him at dinner-time. Don't you think?"

Almost before I had grasped her meaning there was the flutter of a dress and the crunch of leather boots and Tom and Daisy were back at the table.

"It couldn't be helped!" cried Daisy with tense gayety.

She sat down, glanced searchingly at Miss Baker and then at me and continued: "I looked outdoors for a minute and it's very romantic outdoors. There's a bird on the lawn that I think must be a nightingale come over on the Cunard or White Star Line. He's singing away?" her voice sang "?It's romantic, isn't it, Tom?"

"Very romantic," he said, and then miserably to me: "If it's light enough after dinner I want to take you down to the stables."

The telephone rang inside, startlingly, and as Daisy shook her head decisively at Tom the subject of the stables, in fact all subjects, vanished into air. Among the broken fragments of the last five minutes at table I remember the candles being lit again, pointlessly, and I was conscious of wanting to look squarely at every one and yet to avoid all eyes. I couldn't guess what Daisy and Tom were thinking but I doubt if even Miss Baker who seemed to have mastered a certain hardy skepticism was able utterly to put this fifth guest's shrill metallic urgency out of mind. To a certain temperament the situation might have seemed intriguing?my own instinct was to telephone immediately for the police.

The horses, needless to say, were not mentioned again. Tom and Miss Baker, with several feet of twilight between them strolled back into the library, as if to a vigil beside a perfectly tangible body, while trying to look pleasantly interested and a little deaf I followed Daisy around a chain of connecting verandas to the porch in front. In its deep gloom we sat down side by side on a wicker settee.

Daisy took her face in her hands, as if feeling its lovely shape, and her eyes moved gradually out into the velvet dusk. I saw that turbulent emotions possessed her, so I asked what I thought would be some sedative questions about her little girl.

"We don't know each other very well, Nick," she said suddenly. "Even if we are cousins. You didn't come to my wedding."

"I wasn't back from the war."

"That's true." She hesitated. "Well, I've had a very bad time, Nick, and I'm pretty cynical about everything."

Evidently she had reason to be. I waited but she didn't say any more, and after a moment I returned rather feebly to the subject of her daughter.

"I suppose she talks, and?eats, and everything."

"Oh, yes." She looked at me absently. "Listen, Nick; let me tell you what I said when she was born. Would you like to hear?"

"Very much."

"It'll show you how I've gotten to feel about?things. Well, she was less than an hour old and Tom was God knows where. I woke up out of the ether with an utterly abandoned feeling and asked the nurse right away if it was a boy or a girl. She told me it was a girl, and so I turned my head away and wept. 'All right,' I said, 'I'm glad it's a girl. And I hope she'll be a fool?that's the best thing a girl can be in this world, a beautiful little fool."

"You see I think everything's terrible anyhow," she went on in a convinced way. "Everybody thinks so?the most advanced people. And I know. I've been everywhere and seen everything and done everything." Her eyes flashed around her in a defiant way, rather like Tom's, and she laughed with thrilling scorn. "Sophisticated?God, I'm sophisticated!"

The instant her voice broke off, ceasing to compel my attention, my belief, I felt the basic insincerity of what she had said. It made me uneasy, as though the whole evening had been a trick of some sort to exact a contributory emotion from me. I waited, and sure enough, in a moment she looked at me with an absolute smirk on her lovely face as if she had asserted her membership in a rather distinguished secret society to which she and Tom belonged.


Inside, the crimson room bloomed with light. Tom and Miss Baker sat at either end of the long couch and she read aloud to him from the "Saturday Evening Post"?the words, murmurous and uninflected, running together in a soothing tune. The lamp-light, bright on his boots and dull on the autumn-leaf yellow of her hair, glinted along the paper as she turned a page with a flutter of slender muscles in her arms.

When we came in she held us silent for a moment with a lifted hand.

"To be continued," she said, tossing the magazine on the table, "in our very next issue."

Her body asserted itself with a restless movement of her knee, and she stood up.

"Ten o'clock," she remarked, apparently finding the time on the ceiling. "Time for this good girl to go to bed."

"Jordan's going to play in the tournament tomorrow," explained Daisy, "over at Westchester."

"Oh,?you're Jordan Baker."

I knew now why her face was familiar?its pleasing contemptuous expression had looked out at me from many rotogravure pictures of the sporting life at Asheville and Hot Springs and Palm Beach. I had heard some story of her too, a critical, unpleasant story, but what it was I had forgotten long ago.

"Good night," she said softly. "Wake me at eight, won't you."

"If you'll get up."

"I will. Good night, Mr. Carraway. See you anon."

"Of course you will," confirmed Daisy. "In fact I think I'll arrange a marriage. Come over often, Nick, and I'll sort of?oh?fling you together. You know?lock you up accidentally in linen closets and push you out to sea in a boat, and all that sort of thing?"

"Good night," called Miss Baker from the stairs. "I haven't heard a word."

"She's a nice girl," said Tom after a moment. "They oughtn't to let her run around the country this way."

"Who oughtn't to?" inquired Daisy coldly.

"Her family."

"Her family is one aunt about a thousand years old. Besides, Nick's going to look after her, aren't you, Nick? She's going to spend lots of week-ends out here this summer. I think the home influence will be very good for her."

Daisy and Tom looked at each other for a moment in silence.

"Is she from New York?" I asked quickly.

"From Louisville. Our white girlhood was passed together there. Our beautiful white?"

"Did you give Nick a little heart to heart talk on the veranda?" demanded Tom suddenly.

"Did I?" She looked at me. "I can't seem to remember, but I think we talked about the Nordic race. Yes, I'm sure we did. It sort of crept up on us and first thing you know?"

"Don't believe everything you hear, Nick," he advised me.

I said lightly that I had heard nothing at all, and a few minutes later I got up to go home. They came to the door with me and stood side by side in a cheerful square of light. As I started my motor Daisy peremptorily called "Wait!

"I forgot to ask you something, and it's important. We heard you were engaged to a girl out West."

"That's right," corroborated Tom kindly. "We heard that you were engaged."

"It's libel. I'm too poor."

"But we heard it," insisted Daisy, surprising me by opening up again in a flower-like way. "We heard it from three people so it must be true."

Of course I knew what they were referring to, but I wasn't even vaguely engaged. The fact that gossip had published the banns was one of the reasons I had come east. You can't stop going with an old friend on account of rumors and on the other hand I had no intention of being rumored into marriage.

Their interest rather touched me and made them less remotely rich?nevertheless, I was confused and a little disgusted as I drove away. It seemed to me that the thing for Daisy to do was to rush out of the house, child in arms?but apparently there were no such intentions in her head. As for Tom, the fact that he "had some woman in New York" was really less surprising than that he had been depressed by a book. Something was making him nibble at the edge of stale ideas as if his sturdy physical egotism no longer nourished his peremptory heart.

Already it was deep summer on roadhouse roofs and in front of wayside garages, where new red gas-pumps sat out in pools of light, and when I reached my estate at West Egg I ran the car under its shed and sat for a while on an abandoned grass roller in the yard. The wind had blown off, leaving a loud bright night with wings beating in the trees and a persistent organ sound as the full bellows of the earth blew the frogs full of life. The silhouette of a moving cat wavered across the moonlight and turning my head to watch it I saw that I was not alone?fifty feet away a figure had emerged from the shadow of my neighbor's mansion and was standing with his hands in his pockets regarding the silver pepper of the stars. Something in his leisurely movements and the secure position of his feet upon the lawn suggested that it was Mr. Gatsby himself, come out to determine what share was his of our local heavens.

I decided to call to him. Miss Baker had mentioned him at dinner, and that would do for an introduction. But I didn't call to him for he gave a sudden intimation that he was content to be alone?he stretched out his arms toward the dark water in a curious way, and far as I was from him I could have sworn he was trembling. Involuntarily I glanced seaward?and distinguished nothing except a single green light, minute and far away, that might have been the end of a dock. When I looked once more for Gatsby he had vanished, and I was alone again in the unquiet darkness.



Waldo

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Supersingular isogeny key exchange
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Supersingular isogeny Diffie?Hellman key exchange (SIDH) is a post-quantum cryptographic algorithm used to establish a secret key between two parties over an otherwise insecure communications channel. It is analogous to the Diffie?Hellman key exchange, but is based on walks in a supersingular isogeny graph and is designed to resist cryptanalytic attack by an adversary in possession of a quantum computer. SIDH boasts one of the smallest key sizes of all post-quantum key exchanges; with compression, SIDH uses 2688-bit[1] public keys at a 128-bit quantum security level. SIDH also distinguishes itself from similar systems such as NTRU and Ring-LWE by supporting perfect forward secrecy, a property that prevents compromised long-term keys from compromising the confidentiality of old communication sessions. These properties make SIDH a natural candidate to replace Diffie?Hellman (DHE) and elliptic curve Diffie?Hellman (ECDHE), which are widely used in Internet communication.
Contents

    1 Introduction
    2 Background
    3 Security
    4 Efficiency
    5 The supersingular isogeny Diffie-Hellman method
        5.1 Setup
        5.2 Key exchange
    6 Sample parameters
    7 Similar systems, signatures, and uses
    8 References

Introduction

For certain classes of problems, algorithms running on quantum computers are naturally capable of achieving lower time complexity than on classical computers. That is, quantum algorithms can solve certain problems faster than the most efficient algorithm running on a traditional computer. For example, Shor's algorithm can factor an integer N in polynomial time, while the best-known factoring classic algorithm, the general number field sieve, operates in sub-exponential time. This is significant to public key cryptography because the security of RSA is dependent on the infeasibility of factoring integers, the integer factorization problem. Shor's algorithm can also efficiently solve the discrete logarithm problem, which is the basis for the security of Diffie?Hellman, elliptic curve Diffie?Hellman, elliptic curve DSA, Curve25519, ed25519, and ElGamal. Although quantum computers are currently in their infancy, the ongoing development of quantum computers and their theoretical ability to compromise modern cryptographic protocols (such as TLS/SSL) has prompted the development of post-quantum cryptography.[2]

SIDH was created in 2011 by De Feo, Jao, and Plut.[3] It uses conventional elliptic curve operations and is not patented. SIDH provides perfect forward secrecy and thus does not rely on the security of long-term private keys. Forward secrecy improves the long-term security of encrypted communications, helps defend against mass surveillance, and reduces the impact of vulnerabilities like Heartbleed.[4][5]
Background

The j-invariant of an elliptic curve given by the Weierstrass equation y 2 = x 3 + a x + b {\displaystyle y^{2}=x^{3}+ax+b} y^{2}=x^{3}+ax+b is given by the formula:

    j ( E ) = 1728 4 a 3 4 a 3 + 27 b 2 {\displaystyle j(E)=1728{\frac {4a^{3}}{4a^{3}+27b^{2}}}} {\displaystyle j(E)=1728{\frac {4a^{3}}{4a^{3}+27b^{2}}}}.

Isomorphic curves have the same j-invariant; over an algebraically closed field, two curves with the same j-invariant are isomorphic.

The supersingular isogeny Diffie-Hellman protocol (SIDH) works with the graph whose vertices are (isomorphism classes of) supersingular elliptic curves and whose edges are isogenies between those curves. An isogeny ϕ : E → E ′ {\displaystyle \phi :E\to E'} {\displaystyle \phi :E\to E'} between elliptic curves E {\displaystyle E} E and E ′ {\displaystyle E'} E' is a rational map which is also a group homomorphism. If separable, ϕ {\displaystyle \phi } \phi is determined by its kernel up to an isomorphism of target curve E ′ {\displaystyle E'} E'.

The setup for SIDH is a prime of the form p = l A e A ⋅ l B e B ⋅ f ∓ 1 {\displaystyle p=l_{A}^{e_{A}}\cdot l_{B}^{e_{B}}\cdot f\mp 1} {\displaystyle p=l_{A}^{e_{A}}\cdot l_{B}^{e_{B}}\cdot f\mp 1}, for different (small) primes l A {\displaystyle l_{A}} l_{A} and l B {\displaystyle l_{B}} l_{B}, (large) exponents e A {\displaystyle e_{A}} e_{A} and e B {\displaystyle e_{B}} {\displaystyle e_{B}}, and small cofactor f {\displaystyle f} f, together with a supersingular elliptic curve E {\displaystyle E} E defined over F p 2 {\displaystyle \mathbb {F} _{p^{2}}} {\mathbb {F}}_{{p^{2}}}. Such a curve has two large torsion subgroups, E [ l A e A ] {\displaystyle E[l_{A}^{e_{A}}]} {\displaystyle E[l_{A}^{e_{A}}]} and E [ l B e B ] {\displaystyle E[l_{B}^{e_{B}}]} {\displaystyle E[l_{B}^{e_{B}}]}, which are assigned to Alice and Bob, respectively, as indicated by the subscripts. Each party starts the protocol by selecting a (secret) random cyclic subgroup of their respective torsion subgroup and computing the corresponding (secret) isogeny. They then publish, or otherwise provide the other party with, the equation for the target curve of their isogeny along with information about the image of the other party's torsion subgroup under that isogeny. This allows them both to privately compute new isogenies from E {\displaystyle E} E whose kernels are jointly generated by the two secret cyclic subgroups. Since the kernels of these two new isogenies agree, their target curves are isomorphic. The common j-invariant of these target curves may then be taken as the required shared secret.

Since the security of the scheme depends on the smaller torsion subgroup, it is recommended to choose l A e A ≈ l B e B {\displaystyle l_{A}^{e_{A}}\approx l_{B}^{e_{B}}} {\displaystyle l_{A}^{e_{A}}\approx l_{B}^{e_{B}}}.

An excellent reference for this subject is De Feo's article "Mathematics of Isogeny Based Cryptography."[6]
Security

The security of SIDH is closely related to the problem of finding the isogeny mapping between two supersingular elliptic curves with the same number of points. De Feo, Jao and Plut suggest that the best attack against SIDH is solving the related claw finding problem, hence of complexity O(p1/4) for classical computers and O(p1/6) for quantum computers. This suggests that SIDH with a 768-bit prime (p) will have a 128-bit security level.[3] A 2014 study of the isogeny mapping problem by Delfs and Galbraith confirmed the O(p1/4) security analysis for classical computers.[7] The classical security, O(p1/4), of the SIDH was confirmed in the work of Biasse, Jao and Sankar as well as Galbraith, Petit, Shani and Ti.[8][9]
Efficiency

During a key exchange entities A and B will each transmit information of 2 coefficients (mod p2) defining an elliptic curve and 2 elliptic curve points. Each elliptic curve coefficient requires log2p2 bits. Each elliptic curve point can be transmitted in log2p2+1 bits, hence the transmission is 4log2p2 + 4 bits. This is 6144 bits for a 768-bit modulus p (128-bit security). However, this can be reduced by over half to 2640 bits (330 bytes) using key-compression techniques, the latest of which appears in recent work by authors Costello, Jao, Longa, Naehrig, Renes and Urbanik.[10] With these compression techniques, SIDH has a similar bandwidth requirement to traditional 3072-bit RSA signatures or Diffie-Hellman key exchanges. This small space requirement makes SIDH applicable to context that have a strict space requirement, such as Bitcoin or Tor. Tor's data cells must be less than 517 bytes in length, so they can hold 330-byte SIDH keys. By contrast, NTRUEncrypt must exchange approximately 600 bytes to achieve a 128-bit security and cannot be used within Tor without increasing the cell size.[11]

In 2014, researchers at the University of Waterloo developed a software implementation of SIDH. They ran their partially optimized code on an x86-64 processor running at 2.4 GHz. For a 768-bit modulus they were able to complete the key exchange computations in 200 milliseconds thus demonstrating that the SIDH is computationally practical.[12]

In 2016, researchers from Microsoft posted software for the SIDH which runs in constant time (thus protecting against timing attacks) and is the most efficient implementation to date. They write: "The size of public keys is only 564 bytes, which is significantly smaller than most of the popular post-quantum key exchange alternatives. Ultimately, the size and speed of our software illustrates the strong potential of SIDH as a post-quantum key exchange candidate and we hope that these results encourage a wider cryptanalytic effort."[13] Their software is downloadable from Microsoft Research.

In 2016, researchers from Florida Atlantic University developed efficient ARM implementations of SIDH and provided a comparison of affine and projective coordinates.[14][15] In 2017, researchers from Florida Atlantic University developed the first FPGA implementations of SIDH.[16]
The supersingular isogeny Diffie-Hellman method

While several steps of SIDH involve complex isogeny calculations, the overall flow of SIDH for parties A and B is straightforward for those familiar with a Diffie-Hellman key exchange or its elliptic curve variant.
Setup

These are public parameters that can be shared by everyone in the network, or they can be negotiated by parties A and B at the beginning of a session.

    A prime of the form p = w A e A ⋅ w B e B ⋅ f ? 1. {\displaystyle p=w_{A}^{e_{A}}\cdot w_{B}^{e_{B}}\cdot f\pm 1.} p=w_{A}^{{e_{A}}}\cdot w_{B}^{{e_{B}}}\cdot f\pm 1.
    A supersingular elliptic curve E {\displaystyle E} E over F p 2 {\displaystyle \mathbb {F} _{p^{2}}} {\mathbb {F}}_{{p^{2}}}.
    Fixed elliptic points P A , Q A , P B , Q B {\displaystyle P_{A},Q_{A},P_{B},Q_{B}} {\displaystyle P_{A},Q_{A},P_{B},Q_{B}} on E {\displaystyle E} E.
    The order of P A {\displaystyle P_{A}} P_{A} and Q A {\displaystyle Q_{A}} Q_{A} is ( w A ) e A {\displaystyle (w_{A})^{e_{A}}} {\displaystyle (w_{A})^{e_{A}}}. The order of P B {\displaystyle P_{B}} P_B and Q B {\displaystyle Q_{B}} Q_{B} is ( w B ) e B {\displaystyle (w_{B})^{e_{B}}} (w_{B})^{{e_{B}}}.

Key exchange

In the key exchange, parties A and B will each create an isogeny from a common elliptic curve E. They each will do this by creating a random point in what will be the kernel of their isogeny. The kernel of their isogeny will be spanned by R A {\displaystyle R_{A}} R_{A} and R B {\displaystyle R_{B}} R_{B} respectively. The different pairs of points used ensure that parties A and B create different, non-commuting, isogenies. A random point ( R A {\displaystyle R_{A}} R_{A}, or R B {\displaystyle R_{B}} R_{B}) in the kernel of the isogenies is created as a random linear combination of the points P A {\displaystyle P_{A}} P_{A}, Q A {\displaystyle Q_{A}} Q_{A} and P B {\displaystyle P_{B}} P_B, Q B {\displaystyle Q_{B}} Q_{B}.

Using R A {\displaystyle R_{A}} R_{A}, or R B {\displaystyle R_{B}} R_{B}, parties A and B then use Velu's formulas for creating isogenies ϕ A {\displaystyle \phi _{A}} \phi _{A} and ϕ B {\displaystyle \phi _{B}} \phi _{B} respectively. From this they compute the image of the pairs of points P A {\displaystyle P_{A}} P_{A}, Q A {\displaystyle Q_{A}} Q_{A} or P B {\displaystyle P_{B}} P_B, Q B {\displaystyle Q_{B}} Q_{B} under the ϕ B {\displaystyle \phi _{B}} \phi _{B} and ϕ A {\displaystyle \phi _{A}} \phi _{A} isogenies respectively.

As a result, A and B will now have two pairs of points ϕ B ( P A ) {\displaystyle \phi _{B}(P_{A})} \phi _{B}(P_{A}), ϕ B ( Q A ) {\displaystyle \phi _{B}(Q_{A})} \phi _{B}(Q_{A}) and ϕ A ( P B ) {\displaystyle \phi _{A}(P_{B})} \phi _{A}(P_{B}), ϕ A ( Q B ) {\displaystyle \phi _{A}(Q_{B})} \phi _{A}(Q_{B}) respectively. A and B now exchange these pairs of points over a communications channel.

A and B now use the pair of points they receive as the basis for the kernel of a new isogeny. They use the same linear coefficients they used above with the points they received to form a point in the kernel of an isogeny that they will create. They each compute points S B A {\displaystyle S_{BA}} S_{{BA}} and S A B {\displaystyle S_{AB}} S_{{AB}} and use Velu's formulas to construct new isogenies.

To complete the key exchange, A and B compute the coefficients of two new elliptic curves under these two new isogenies. They then compute the j-invariant of these curves. Unless there were errors in transmission, the j-invariant of the curve created by A will equal to the j-invariant of the curve created by B.

Notationally, the SIDH key exchange between parties A and B works as follows:

1A. A generates two random integers m A , n A < ( w A ) e A . {\displaystyle m_{A},n_{A}<(w_{A})^{e_{A}}.} {\displaystyle m_{A},n_{A}<(w_{A})^{e_{A}}.}

2A. A generates R A := m A ⋅ ( P A ) + n A ⋅ ( Q A ) . {\displaystyle R_{A}:=m_{A}\cdot (P_{A})+n_{A}\cdot (Q_{A}).} R_{A}:=m_{A}\cdot (P_{A})+n_{A}\cdot (Q_{A}).

3A. A uses the point R A {\displaystyle R_{A}} R_{A} to create an isogeny mapping ϕ A : E → E A {\displaystyle \phi _{A}:E\rightarrow E_{A}} \phi _{A}:E\rightarrow E_{A} and curve E A {\displaystyle E_{A}} E_{A} isogenous to E . {\displaystyle E.} E.

4A. A applies ϕ A {\displaystyle \phi _{A}} \phi _{A} to P B {\displaystyle P_{B}} P_B and Q B {\displaystyle Q_{B}} Q_{B} to form two points on E A : ϕ A ( P B ) {\displaystyle E_{A}:\phi _{A}(P_{B})} E_{A}:\phi _{A}(P_{B}) and ϕ A ( Q B ) . {\displaystyle \phi _{A}(Q_{B}).} \phi _{A}(Q_{B}).

5A. A sends to B E A , ϕ A ( P B ) {\displaystyle E_{A},\phi _{A}(P_{B})} E_{A},\phi _{A}(P_{B}), and ϕ A ( Q B ) . {\displaystyle \phi _{A}(Q_{B}).} \phi _{A}(Q_{B}).

1B - 4B: Same as A1 through A4, but with A and B subscripts swapped.

5B. B sends to A E B , ϕ B ( P A ) {\displaystyle E_{B},\phi _{B}(P_{A})} E_{B},\phi _{B}(P_{A}), and ϕ B ( Q A ) . {\displaystyle \phi _{B}(Q_{A}).} \phi _{B}(Q_{A}).

6A. A has m A , n A , ϕ B ( P A ) {\displaystyle m_{A},n_{A},\phi _{B}(P_{A})} m_{A},n_{A},\phi _{B}(P_{A}), and ϕ B ( Q A ) {\displaystyle \phi _{B}(Q_{A})} \phi _{B}(Q_{A}) and forms S B A := m A ( ϕ B ( P A ) ) + n A ( ϕ B ( Q A ) ) . {\displaystyle S_{BA}:=m_{A}(\phi _{B}(P_{A}))+n_{A}(\phi _{B}(Q_{A})).} S_{{BA}}:=m_{A}(\phi _{B}(P_{A}))+n_{A}(\phi _{B}(Q_{A})).

7A. A uses S B A {\displaystyle S_{BA}} S_{{BA}} to create an isogeny mapping ψ B A {\displaystyle \psi _{BA}} \psi _{{BA}}.

8A. A uses ψ B A {\displaystyle \psi _{BA}} \psi _{{BA}} to create an elliptic curve E B A {\displaystyle E_{BA}} E_{{BA}} which is isogenous to E {\displaystyle E} E.

9A. A computes K :=  j-invariant  ( j B A ) {\displaystyle K:={\text{ j-invariant }}(j_{BA})} K:={\text{ j-invariant }}(j_{{BA}}) of the curve E B A {\displaystyle E_{BA}} E_{{BA}}.

6B. Similarly, B has m B , n B , ϕ A ( P B ) {\displaystyle m_{B},n_{B},\phi _{A}(P_{B})} m_{B},n_{B},\phi _{A}(P_{B}), and ϕ A ( Q B ) {\displaystyle \phi _{A}(Q_{B})} \phi _{A}(Q_{B}) and forms S A B = m B ( ϕ A ( P B ) ) + n B ( ϕ A ( Q B ) ) {\displaystyle S_{AB}=m_{B}(\phi _{A}(P_{B}))+n_{B}(\phi _{A}(Q_{B}))} S_{{AB}}=m_{B}(\phi _{A}(P_{B}))+n_{B}(\phi _{A}(Q_{B})).

7B. B uses S A B {\displaystyle S_{AB}} S_{{AB}} to create an isogeny mapping ψ A B {\displaystyle \psi _{AB}} \psi _{{AB}}.

8B. B uses ψ A B {\displaystyle \psi _{AB}} \psi _{{AB}} to create an elliptic curve E A B {\displaystyle E_{AB}} E_{{AB}} which is isogenous to E {\displaystyle E} E.

9B. B computes K :=  j-invariant  ( j A B ) {\displaystyle K:={\text{ j-invariant }}(j_{AB})} {\displaystyle K:={\text{ j-invariant }}(j_{AB})} of the curve E A B {\displaystyle E_{AB}} E_{{AB}}.

The curves E A B {\displaystyle E_{AB}} E_{{AB}} and E B A {\displaystyle E_{BA}} E_{{BA}} are guaranteed to have the same j-invariant. A function of K {\displaystyle K} K is used as the shared key.[3]
Sample parameters

The following parameters were taken as an example by De Feo et al.:[3]

p = prime for the key exchange with wA = 2, wB = 3, eA = 63, eB = 41, and f = 11. Thus p = (263?341?11) - 1.

E0 = the base (starting) curve for the key exchange = y2 = x3 + x

Luca De Feo, one of the authors of the paper defining the key exchange has posted software that implements the key exchange for these and other parameters.[17]
Similar systems, signatures, and uses

A predecessor to the SIDH was published in 2006 by Rostovtsev and Stolbunov. They created the first Diffie-Hellman replacement based on elliptic curve isogenies. Unlike the method of De Feo, Jao, and Plut, the method of Rostovtsev and Stolbunov used ordinary elliptic curves[18] and was found to have a subexponential quantum attack.[19]

In March 2014, researchers at the Chinese State Key Lab for Integrated Service Networks and Xidian University extended the security of the SIDH to a form of digital signature with strong designated verifier.[20] In October 2014, Jao and Soukharev from the University of Waterloo presented an alternative method of creating undeniable signatures with designated verifier using elliptic curve isogenies.[21]
References

Costello, Craig; Jao, David; Longa, Patrick; Naehrig, Michael; Renes, Joost; Urbanik, David (2016-10-04). "Efficient compression of SIDH public keys".
Utsler, Jim (2013). "Quantum Computing Might Be Closer Than Previously Thought". IBM. Retrieved 27 May 2013.
De Feo, Luca; Jao, Plut. "Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies" (PDF). PQCrypto 2011. Springer. Retrieved 4 May 2014.
Higgins, Parker (2011-11-30). "Long Term Privacy with Forward Secrecy". Electronic Frontier Foundation. Retrieved 4 May 2014.
Zhu, Yan (2014-04-08). "Why the Web Needs Perfect Forward Secrecy More Than Ever". Electronic Frontier Foundation. Retrieved 4 May 2014.
De Feo, Luca (2017). "Mathematics of Isogeny Based Cryptography". arXiv:1711.04062 [cs.CR].
Delfs, Christina; Galbraith (29 Oct 2013). "Computing isogenies between supersingular elliptic curves over F_p". arXiv:1310.7789 [math.NT].
biasse. "A quantum algorithm for computing isogenies between supersingular elliptic curves" (PDF). CACR. Retrieved 11 December 2016.
Galbraith (2016). "ON THE SECURITY OF SUPERSINGULAR ISOGENY CRYPTOSYSTEMS" (PDF). IACR.
Costello, Craig; Jao, David; Longa, Patrick; Naehrig, Michael; Renes, Joost; Urbanik, David. "Efficient Compression of SIDH public keys". Retrieved 8 October 2016.
Azarderakhsh; Jao; Kalach; Koziel; Leonardi. "Key Compression for Isogeny-Based Cryptosystems". eprint.iacr.org. Retrieved 2016-03-02.
Fishbein, Dieter (30 April 2014). "Machine-Level Software Optimization of Cryptographic Protocols". University of Waterloo Library - Electronic Theses. University of Waterloo. Retrieved 21 June 2014.


reero

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H, or h, is the eighth letter in the ISO basic Latin alphabet. Its name in English is aitch (pronounced /ˈeɪtʃ/, plural aitches), or regionally haitch /ˈheɪtʃ/.[1]


Contents
1   History
2   Name in English
3   Use in writing systems
3.1   English
3.2   Other languages
3.3   Other systems
4   Related characters
4.1   Descendants and related characters in the Latin alphabet
4.2   Ancestors, siblings and descendants in other alphabets
4.3   Derived signs, symbols and abbreviations
5   Computing codes
6   Other representations
7   See also
8   References
9   External links
History
Egyptian hieroglyph
fence   Old Semitic
ħ   Phoenician
heth   Greek
heta   Etruscan
H |   Latin
H
N24
Proto-semiticH-01.svg   PhoenicianH-01.svg   PhoenicianH-01.svgGreek Eta 2-bars.svg
Greek Eta square-2-bars.svgGreek Eta diagonal.svg   PhoenicianH-01.svg   Capitalis monumentalis H.svg
The original Semitic letter Heth most likely represented the voiceless pharyngeal fricative (ħ). The form of the letter probably stood for a fence or posts.

The Greek eta 'Η' in Archaic Greek alphabets, before coming to represent a long vowel, /ɛː/, still represented a similar sound, the voiceless glottal fricative /h/. In this context, the letter eta is also known as heta to underline this fact. Thus, in the Old Italic alphabets, the letter heta of the Euboean alphabet was adopted with its original sound value /h/.

While Etruscan and Latin had /h/ as a phoneme, almost all Romance languages lost the sound?Romanian later re-borrowed the /h/ phoneme from its neighbouring Slavic languages, and Spanish developed a secondary /h/ from /f/, before losing it again; various Spanish dialects have developed [h] as an allophone of /s/ or /x/ in most Spanish-speaking countries, and various dialects of Portuguese use it as an allophone of /ʀ/. 'H' is also used in many spelling systems in digraphs and trigraphs, such as 'ch', which represents /tʃ/ in Spanish, Galician, Old Portuguese and English, /ʃ/ in French and modern Portuguese, /k/ in Italian, French and English, /x/ in German, Czech, Polish, Slovak, one native word of English and a few loanwords into English, and /?/ in German.

Name in English
For most English speakers, the name for the letter is pronounced as /eɪtʃ/ and spelled "aitch"[1] or occasionally "eitch". The pronunciation /heɪtʃ/ and the associated spelling "haitch" is often considered to be h-adding and is considered nonstandard in England.[2] It is, however, a feature of Hiberno-English,[3] as well as scattered varieties of Edinburgh, England, and Welsh English,[4] and in Australia and Nova Scotia.

The perceived name of the letter affects the choice of indefinite article before initialisms beginning with H: for example "an H-bomb" or "a H-bomb". The pronunciation /heɪtʃ/ may be a hypercorrection formed by analogy with the names of the other letters of the alphabet, most of which include the sound they represent.[5]

The haitch pronunciation of h has spread in England, being used by approximately 24% of English people born since 1982,[6] and polls continue to show this pronunciation becoming more common among younger native speakers. Despite this increasing number, the pronunciation without the /h/ sound is still considered to be standard in England, although the pronunciation with /h/ is also attested as a legitimate variant.[2]

Authorities disagree about the history of the letter's name. The Oxford English Dictionary says the original name of the letter was [ˈaha] in Latin; this became [ˈaka] in Vulgar Latin, passed into English via Old French [atʃ], and by Middle English was pronounced [aːtʃ]. The American Heritage Dictionary of the English Language derives it from French hache from Latin haca or hic. Anatoly Liberman suggests a conflation of two obsolete orderings of the alphabet, one with H immediately followed by K and the other without any K: reciting the former's ..., H, K, L,... as [...(h)a ka el ...] when reinterpreted for the latter ..., H, L,... would imply a pronunciation [(h)a ka] for H.[7]

Use in writing systems
English
In English, ⟨h⟩ occurs as a single-letter grapheme (being either silent or representing the voiceless glottal fricative (/h/) and in various digraphs, such as ⟨ch⟩ /tʃ/, /ʃ/, /k/, or /x/), ⟨gh⟩ (silent, /ɡ/, /k/, /p/, or /f/), ⟨ph⟩ (/f/), ⟨rh⟩ (/r/), ⟨sh⟩ (/ʃ/), ⟨th⟩ (/θ/ or /?/), ⟨wh⟩ (/hw/[8]). The letter is silent in a syllable rime, as in ah, ohm, dahlia, cheetah, pooh-poohed, as well as in certain other words (mostly of French origin) such as hour, honest, herb (in American but not British English) and vehicle (in certain varieties of English). Initial /h/ is often not pronounced in the weak form of some function words including had, has, have, he, her, him, his, and in some varieties of English (including most regional dialects of England and Wales) it is often omitted in all words (see '⟨h⟩'-dropping). It was formerly common for an rather than a to be used as the indefinite article before a word beginning with /h/ in an unstressed syllable, as in "an historian", but use of a is now more usual (see English articles ? Indefinite article). In English, The pronunciation of ⟨h⟩ as /h/ can be analyzed as a voiceless vowel. That is, when the phoneme /h/ precedes a vowel, /h/ may be realized as a voiceless version of the subsequent vowel. For example the word ⟨hit⟩, /hɪt/ is realized as [ɪ̥ɪt].[9] H is the eighth most frequently used letter in the English language (after S, N, I, O, A, T, and E), with a frequency of about 4.2% in words.[citation needed] When h is placed after certain other consonants, it modifies their pronunciation in various ways, e.g. for ch, gh, ph, sh and th.

Other languages
In the German language, the name of the letter is pronounced /haː/. Following a vowel, it often silently indicates that the vowel is long: In the word erh?hen ('heighten'), the second ⟨h⟩ is mute for most speakers outside of Switzerland. In 1901, a spelling reform eliminated the silent ⟨h⟩ in nearly all instances of ⟨th⟩ in native German words such as thun ('to do') or Th?r ('door'). It has been left unchanged in words derived from Greek, such as Theater ('theater') and Thron ('throne'), which continue to be spelled with ⟨th⟩ even after the last German spelling reform.

In Spanish and Portuguese, ⟨h⟩ ("hache" in Spanish, pronounced ['atʃe], or ag? in Portuguese, pronounced [aˈɣa] or [ɐˈɡa]) is a silent letter with no pronunciation, as in hijo [ˈixo] ('son') and h?ngaro [ˈũɡaɾu] ('Hungarian'). The spelling reflects an earlier pronunciation of the sound /h/. It is sometimes pronounced with the value [h], in some regions of Andalusia, Extremadura, Canarias, Cantabria and the Americas in the beginning of some words. ⟨h⟩ also appears in the digraph ⟨ch⟩, which represents /tʃ/ in Spanish and northern Portugal, and /ʃ/ in oral traditions that merged both sounds (the latter originarily represented by ⟨x⟩ instead) e.g. in most of the Portuguese language and some Spanish-speaking places, prominently Chile, as well as ⟨nh⟩ /ɲ/ and ⟨lh⟩ /ʎ/ in Portuguese, whose spelling is inherited from Occitan.

In French, the name of the letter is written as "ache" and pronounced /aʃ/. The French orthography classifies words that begin with this letter in two ways, one of which can affect the pronunciation, even though it is a silent letter either way. The H muet, or "mute" ⟨h⟩, is considered as though the letter were not there at all, so for example the singular definite article le or la, which is elided to l' before a vowel, elides before an H muet followed by a vowel. For example, le + h?bergement becomes l'h?bergement ('the accommodation'). The other kind of ⟨h⟩ is called h aspir? ("aspirated '⟨h⟩'", though it is not normally aspirated phonetically), and does not allow elision or liaison. For example in le homard ('the lobster') the article le remains unelided, and may be separated from the noun with a bit of a glottal stop. Most words that begin with an H muet come from Latin (honneur, homme) or from Greek through Latin (h?catombe), whereas most words beginning with an H aspir? come from Germanic (harpe, hareng) or non-Indo-European languages (harem, hamac, haricot); in some cases, an orthographic ⟨h⟩ was added to disambiguate the [v] and semivowel [ɥ] pronunciations before the introduction of the distinction between the letters ⟨v⟩ and ⟨u⟩: huit (from uit, ultimately from Latin octo), hu?tre (from uistre, ultimately from Greek through Latin ostrea).

In Italian, ⟨h⟩ has no phonological value. Its most important uses are in the digraphs 'ch' /k/ and 'gh' /ɡ/, as well as to differentiate the spellings of certain short words that are homophones, for example some present tense forms of the verb avere ('to have') (such as hanno, 'they have', vs. anno, 'year'), and in short interjections (oh, ehi).

Some languages, including Czech, Slovak, Hungarian, and Finnish, and Estonian use ⟨h⟩ as a breathy voiced glottal fricative [ɦ], often as an allophone of otherwise voiceless /h/ in a voiced environment.

In Hungarian, the letter has no fewer than five pronunciations, with three additional uses as a productive and non-productive element of digraphs. The letter h may represent /h/ as in the name of the Sz?kely town Hargita; intervocalically it represents /ɦ/ as in teh?n; it represents /x/ in the word doh; it represents /?/ in ihlet; and it is silent in cseh. As part of a digraph, it represents, in archaic spelling, /t͡ʃ/ with the letter c as in the name Sz?chenyi; it represents, again, with the letter c, /x/ in pech (which is pronounced [pɛxː]); in certain environments it breaks palatalization of a consonant, as in the name Be?thy which is pronounced [b?ːti] (without the intervening h, the name Be?ty could be pronounced [b?ːc]); and finally, it acts as a silent component of a digraph, as in the name Vargha, pronounced [vɒrgɒ].

In Ukrainian and Belarusian, when written in the Latin alphabet, ⟨h⟩ is also commonly used for /ɦ/, which is otherwise written with the Cyrillic letter ⟨г⟩.

In Irish, ⟨h⟩ is not considered an independent letter, except for a very few non-native words, however ⟨h⟩ placed after a consonant is known as a "s?imhi?" and indicates lenition of that consonant; ⟨h⟩ began to replace the original form of a s?imhi?, a dot placed above the consonant, after the introduction of typewriters.

In most dialects of Polish, both ⟨h⟩ and the digraph ⟨ch⟩ always represent /x/.

In Basque, during the 20th century it was not used in the orthography of the Basque dialects in Spain but it marked an aspiration in the North-Eastern dialects. During the standardization of Basque in the 1970s, the compromise was reached that h would be accepted if it were the first consonant in a syllable. Hence, herri ("people") and etorri ("to come") were accepted instead of erri (Biscayan) and ethorri (Souletin). Speakers could pronounce the h or not. For the dialects lacking the aspiration, this meant a complication added to the standardized spelling.

Other systems
As a phonetic symbol in the International Phonetic Alphabet (IPA), it is used mainly for the so-called aspirations (fricative or trills), and variations of the plain letter are used to represent two sounds: the lowercase form ⟨h⟩ represents the voiceless glottal fricative, and the small capital form ⟨ʜ⟩ represents the voiceless epiglottal fricative (or trill). With a bar, minuscule ⟨ħ⟩ is used for a voiceless pharyngeal fricative. Specific to the IPA, a hooked ⟨ɦ⟩ is used for a voiced glottal fricative, and a superscript ⟨ʰ⟩ is used to represent aspiration.

Related characters
Descendants and related characters in the Latin alphabet
H with diacritics: Ĥ ĥ Ȟ ȟ Ħ ħ Ḩ ḩ Ⱨ ⱨ ẖ ẖ Ḥ ḥ Ḣ ḣ Ḧ ḧ Ḫ ḫ ꞕ
IPA-specific symbols related to H: ʜ ꟸ ɦ ʰ ʱ ɥ ᶣ[10]
ᴴ : Modifier letter H is used in the Uralic Phonetic Alphabet[11]
ₕ : Subscript small h was used in the Uralic Phonetic Alphabet prior to its formal standardization in 1902[12]
ʰ : Modifier letter small h is used in Indo-European studies[13]
ʮ and ʯ : Turned H with fishhook and turned H with fishhook and tail are used in Sino-Tibetanist linguistics[14]
Ƕ ƕ : Latin letter hwair, derived from a ligature of the digraph hv, and used to transliterate the Gothic letter 𐍈 (which represented the sound [hʷ])
Ⱶ ⱶ : Claudian letters[15]
Ꟶ ꟶ : Reversed half h used in Roman inscriptions from the Roman provinces of Gaul[16]
Ancestors, siblings and descendants in other alphabets
𐤇 : Semitic letter Heth, from which the following symbols derive
Η η : Greek letter Eta, from which the following symbols derive
𐌇 : Old Italic H, the ancestor of modern Latin H
ᚺ, ᚻ : Runic letter haglaz, which is probably a descendant of Old Italic H
Һ һ : Cyrillic letter Shha, which derives from Latin H
𐌷 : Gothic letter haal
Derived signs, symbols and abbreviations
h : Planck constant
ℏ : reduced Planck constant
{\displaystyle \mathbb {H} }\mathbb {H} : Blackboard bold capital H used in quaternion notation




Shunix

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this place really fell off since -tt stopped running the streets