@0xninicha @TrustlessState @ArthurB @danrobinson Multiplication is a function.

@0xninicha @TrustlessState @ArthurB @danrobinson 乘法是一个函数。

@TrustlessState @ArthurB @danrobinson But even if you're not willing to use "+" for GT multiplication, you can still use additive notation for elliptic curve crypto (and I do). But then, you want to use e(A, B) instead of A * B for pairings to avoid confusing people.

@TrustlessState @ArthurB @danrobinson 但是即使你不愿意使用“”来进行 GT 乘法，你仍然可以对椭圆曲线加密使用加法表示法（我也这样做）。但是，您想使用 e(A, B) 而不是 A * B 进行配对以避免混淆。

@TrustlessState @ArthurB @danrobinson And so this is the debate. Do we make the black-box view cleaner, or do we make it more accurately describe what's going on "under the hood"?

@TrustlessState @ArthurB @danrobinson 这就是辩论。我们是让黑盒视图更清晰，还是让它更准确地描述“幕后”发生的事情？

@TrustlessState @ArthurB @danrobinson This makes a lot of pedantically inclined people's brains explode. Noooo, you can't just pretend that it's addition, it literally is multiplication! And yet if you pretend it's addition, it just makes describing cryptographic protocols soooo much easier.

@TrustlessState @ArthurB @danrobinson 这让很多学究式的人的大脑爆炸了。不，你不能假装它是加法，它实际上是乘法！然而，如果你假装它是加法，它只会让描述加密协议变得非常容易。

@TrustlessState @ArthurB @danrobinson But, and here's the fun part, from a mathematical perspective, the ⚬ operation between GT elements *literally is multiplication*. And so if we want the math to look clean when treating A, B and X as a black box, we have to pretend that multiplication in GT is addition.

@TrustlessState @ArthurB @danrobinson 但是，从数学的角度来看，这是有趣的部分，GT 元素之间的 ⚬ 运算*字面意思是乘法*。因此，如果我们希望在将 A、B 和 X 视为黑盒时数学看起来干净，我们必须假设 GT 中的乘法是加法。

@TrustlessState @ArthurB @danrobinson And the fun question. What do we call the ⚬ operation above? From a "black box" perspective, it seems correct to just call it addition. After all, if you plug in numbers instead of curve points to the equation, and `A * B = X`, then `(3A) * B = A * (3B) = X + X + X` is correct.

@TrustlessState @ArthurB @danrobinson 还有一个有趣的问题。我们把上面的⚬操作叫做什么？从“黑匣子”的角度来看，将其称为加法似乎是正确的。毕竟，如果你在方程中插入数字而不是曲线点，并且“A * B = X”，那么“(3A) * B = A * (3B) = X X X”是正确的。

@TrustlessState @ArthurB @danrobinson Now, we get to pairings. Described in additive notation, pairings let you "multiply" two elliptic curve points *by each other* (the result is not a curve point, but a different thing called a "GT element")
A * B = X
(3A) * B = A * (3B) = X⚬X⚬X
(A + C) * B = A * B ⚬ C * B

@TrustlessState @ArthurB @danrobinson 现在，我们开始配对。用加法表示法描述，配对让您“乘”两个椭圆曲线点*彼此*（结果不是曲线点，而是称为“GT 元素”的不同事物）
A * B = X
(3A) * B = A * (3B) = X⚬X⚬X
(A C) * B = A * B ⚬ C * B

@TrustlessState @ArthurB @danrobinson But people "born and raised" in elliptic curve land are more likely to prefer additive notation, because it's more convenient.
Eg. in Schnorr signatures:
Sign: s = r - x * e
Verify: R = G * s + X * e
In additive notation, it's easier to see the "symmetry" between the two eqs.

@TrustlessState @ArthurB @danrobinson 但是在椭圆曲线领域“出生和长大”的人更有可能更喜欢加法符号，因为它更方便。
例如。在 Schnorr 签名中：
符号：s = r - x * e
验证：R = G * s X * e
在加法表示法中，更容易看到两个方程之间的“对称性”。

@TrustlessState @ArthurB @danrobinson "Traditional cryptographers" often tend to prefer multiplicative notation, in part because in forms of cryptography that were popular before elliptic curves, the equivalent to ⚬ literally was multiplication. RSA, for example, uses multiplication and exponentiation.

@TrustlessState @ArthurB @danrobinson “传统密码学家”通常更喜欢乘法符号，部分原因是在椭圆曲线之前流行的密码学形式中，相当于 ⚬ 字面意思是乘法。例如，RSA 使用乘法和求幂。

@TrustlessState @ArthurB @danrobinson "Additive notation" means using the "⚬ = addition, repeated ⚬ = multiplication" metaphor for elliptic curve points.
"Multiplicative notation" means using the "⚬ = multiplication, repeated ⚬ = exponentiation" metaphor.

@TrustlessState @ArthurB @danrobinson “加法表示法”意味着对椭圆曲线点使用“⚬ = 加法，重复 ⚬ = 乘法”隐喻。
“乘法符号”是指使用“⚬ = 乘法，重复 ⚬ = 取幂”的比喻。

@TrustlessState @ArthurB @danrobinson The reason why "⚬ = addition, repeated ⚬ = multiplication" and "⚬ = multiplication, repeated ⚬ = exponentiation" are both valid metaphors is because when we work with numbers, * is repeated +, and ^ is repeated *.
2 * 4 = 2 + 2 + 2 + 2
2 ^ 4 = 2 * 2 * 2 * 2

@TrustlessState @ArthurB @danrobinson “⚬ = 加法，重复 ⚬ = 乘法”和“⚬ = 乘法，重复 ⚬ = 取幂”都是有效的隐喻，因为当我们处理数字时，* 重复，^ 重复*。
2 * 4 = 2 2 2 2
2 ^ 4 = 2 * 2 * 2 * 2

@TrustlessState @ArthurB @danrobinson For example, the standard way to convert a private key `k` into the corresponding public key `K` is to agree on a standardized generator point `G`, and apply the operation to it `k` times:
K = G⚬G⚬G ... G [with `k` G's]

@TrustlessState @ArthurB @danrobinson 例如，将私钥`k`转换为对应的公钥`K`的标准方法是约定一个标准化的生成点`G`，并对其应用`k`次操作：
K = G⚬G⚬G ... G [带 `k` G's]

@TrustlessState @ArthurB @danrobinson There is an operation A⚬B -> C on elliptic curve points, and we often do it to the same point many times: A⚬A⚬A ... ⚬A -> D
There are 2 ways to talk about this:
1. ⚬ = "addition", repeating it = "multiplication"
2. ⚬ = "multiplication", repeating it = "exponentiation"

@TrustlessState @ArthurB @danrobinson 有一个操作A⚬B -

@danrobinson The chad take is to use additive notation even for the GT group.

@danrobinson 乍得采取的是即使对于 GT 组也使用加法表示法。

@Nowooski "God, brought to you by Samsung" https://t.co/6pHpLTUpm1

@Nowooski “上帝，三星带给你的” https://t.co/6pHpLTUpm1

@sama Internet opened a new low hanging fruit era and most of the low hanging fruits have now been picked?

@sama Internet开启了一个新的低挂水果时代，现在大部分低挂水果都被摘了？

@0xstark @davidgerard I've had feedback to my drafts that was significant enough that it caused me to rethink the topic and rewrite the entire post. Any of the frequently appearing "special thanks" names has done that at least once.

@0xstark @davidgerard 我收到了对草稿的反馈，这些反馈非常重要，以至于我重新思考了这个话题并重写了整篇文章。任何经常出现的“特别感谢”的名字都至少做过一次。

@RJMacReadyBTC dude ur ability to hold coins and get rich and shitpost about it on twitter depends on elliptic curve math, show some respect

@RJMacReadyBTC 伙计，你持有硬币和致富的能力以及在推特上发布关于它的狗屎取决于椭圆曲线数学，表示尊重

RT: Latest Week in Ethereum News
🐼 Ethereum now secured by Proof of Stake
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Thanks to https://speedrunethereum.com/ for making this issue possible 🙏

RT：以太坊新闻的最新一周
🐼 以太坊现在由权益证明保护
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Thread by @davidgerard, criticizing @VitalikButerin. https://twitter.com/davidgerar...

@davidgerard 的主题，批评 @VitalikButerin。 https://twitter.com/davidgerar...