52 Things: Number 25: Methods for modular reduction using "special" primes that define GF(p) and GF(2^n)
52 Things: Number 25: Methods for modular reduction using "special" primes that define GF(p) and GF(2^n)
52 Things: Number 25: Methods for modular reduction using "special" primes that define GF(p) and GF(2n)
52件事：第25件：使用定義 GF(p) 和#1的“特殊”素?cái)?shù)進(jìn)行模歸約的方法#
This is the latest in a series of blog posts to address the list of '52 Things Every PhD Student Should Know' to do Cryptography: a set of questions compiled to give PhD candidates a sense of what they should know by the end of their first year. Continuing the section on implementation details, we discuss one method of implementing efficient modular reduction: using "special" primes modulo.
這是一系列博客文章中的最新一篇，旨在解決“每個(gè)博士生都應(yīng)該知道的52件事”做密碼學(xué)：這是一組問(wèn)題，旨在讓博士生在第一年結(jié)束時(shí)了解他們應(yīng)該知道什么。繼續(xù)關(guān)于實(shí)現(xiàn)細(xì)節(jié)的部分，我們討論一種實(shí)現(xiàn)有效模歸約的方法：使用“特殊”素?cái)?shù)模。
As we have seen in the previous blogs, when implementing cryptographic schemes, one of the mostly frequently invoked operation is the modulo operation. Unfortunately, despite its massive usage modulo cannot be performed easily like some other arithmetic operations such as additions and multiplications. Montgomery representation provides one solution to this problem, and we will discuss another solution, Psudo-Mersenne Prime reduction.
正如我們?cè)谝郧暗牟┛椭兴吹降模趯?shí)現(xiàn)加密方案時(shí)，最頻繁調(diào)用的操作之一是模運(yùn)算。不幸的是，盡管模的使用量很大，但它不能像加法和乘法等其他算術(shù)運(yùn)算一樣容易地執(zhí)行。Montgomery表示為這個(gè)問(wèn)題提供了一種解決方案，我們將討論另一種解決方法，Psudo-Mersenne素?cái)?shù)約簡(jiǎn)。
Definition: A prime number p is called a Psudo-Mersenne Prime if p can be written in the form:
定義：素?cái)?shù) p 稱(chēng)為偽梅森素?cái)?shù)，如果 p 可以寫(xiě)成以下形式：
where
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這是一系列博客文章中的最新一篇，旨在解決“每個(gè)博士生都應(yīng)該知道的52件事”做密碼學(xué)：這是一組問(wèn)題，旨在讓博士生在第一年結(jié)束時(shí)了解他們應(yīng)該知道什么。繼續(xù)關(guān)于實(shí)現(xiàn)細(xì)節(jié)的部分，我們討論一種實(shí)現(xiàn)有效模歸約的方法：使用“特殊”素?cái)?shù)模。
As we have seen in the previous blogs, when implementing cryptographic schemes, one of the mostly frequently invoked operation is the modulo operation. Unfortunately, despite its massive usage modulo cannot be performed easily like some other arithmetic operations such as additions and multiplications. Montgomery representation provides one solution to this problem, and we will discuss another solution, Psudo-Mersenne Prime reduction.
正如我們?cè)谝郧暗牟┛椭兴吹降模趯?shí)現(xiàn)加密方案時(shí)，最頻繁調(diào)用的操作之一是模運(yùn)算。不幸的是，盡管模的使用量很大，但它不能像加法和乘法等其他算術(shù)運(yùn)算一樣容易地執(zhí)行。Montgomery表示為這個(gè)問(wèn)題提供了一種解決方案，我們將討論另一種解決方法，Psudo-Mersenne素?cái)?shù)約簡(jiǎn)。
Definition: A prime number p is called a Psudo-Mersenne Prime if p can be written in the form:
定義：素?cái)?shù) p 稱(chēng)為偽梅森素?cái)?shù)，如果 p 可以寫(xiě)成以下形式：
p=bn?c
where
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