标签：10 What RSA 52 nbsp problem minus mod

52 Things: Number 10: What is the difference between the RSA and strong-RSA problem?

52 件事：数字 10：RSA 和强 RSA 问题有什么区别？ 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. This blog post introduces the RSA and Strong-RSA problems and highlights the differences between the two.
这是一系列博客文章中的最新一篇，旨在解决“每个博士生都应该知道的 52 件事来做密码学”列表：一组问题，旨在让博士生在第一年结束时了解他们应该知道什么。这篇博文介绍了 RSA 和 Strong-RSA 问题，并重点介绍了两者之间的区别。

Cryptography relies heavily on the assumption that certain mathematical problems are hard to solve in a realistic amount of time. When looking at Public-Key (Asymmetric) Cryptography, which is what we'll be focusing on in this blog post we use the assumed existence of One-Way functions, i.e. functions that are easy to compute one way but are difficult to invert. We use problems from algorithmic number theory to produce these functions.
密码学在很大程度上依赖于这样的假设，即某些数学问题很难在现实的时间内解决。在查看公钥（非对称）密码学时，我们将在本博客文章中重点介绍的内容，我们使用单向函数的假设存在，即易于单向计算但难以反转的函数。我们使用算法数论中的问题来产生这些函数。 Factoring 保理 The first difficult problem from number theory to talk about is factoring. Given a composite integer N the factoring problem is to find positive integers p,q such that N=pq. Although on the face of it this seems like a very simple problem, this is in fact a very tough, well studied problem. This can be solved in exponential time by checking all the numbers p=2,…,N−−√. However, solving a problem in exponential time is not fast enough. No polynomial time algorithm has been developed to solve the factoring problem, despite many years of research. Clearly there are examples of N for which this is very easy to solve, for example whenever N is even. Therefore, when starting to think about using this in a Cryptographic construction we consider N as very large and being constructed by 2 large primes p,q.
数论中要讨论的第一个难题是因式分解。给定一个复合整数 N ，分解问题是找到 p,q 正整数，使得 N=pq .虽然从表面上看，这似乎是一个非常简单的问题，但实际上这是一个非常棘手、经过充分研究的问题。这可以通过检查所有数字 p=2,…,N−−√ 在指数时间内解决。然而，在指数时间内解决问题还不够快。尽管进行了多年的研究，但尚未开发出多项式时间算法来解决因式分解问题。显然，有一些例子 N 很容易解决，例如，只要 N 是偶数。因此，当开始考虑在加密结构中使用它时，我们认为 N 它非常大，并且由 2 个大素数构造 p,q 。 The RSA Problem RSA 问题

In RSA public-key encryption [1] Alice encrypts a plaintext M using Bob's public key (n,e) to ciphertext C by C=Me(mod n) where n is the product of two large primes and e≥3 is an odd integer that is coprime to the order of Z&lowast;n, the group of invertible elements of Zn. Bob knows the private key (n,d) where de=1( mod (p−1)(q−1)) meaning he can compute M=Cd(mod n). An adversary can eavesdrop C and can know the public key (n,e) however to calculate M the adversary must find the factors of n. Therefore, this means the RSA problem is no harder than integer factorisation but is still a very hard problem to solve provided a suitable n is chosen.
在 RSA 公钥加密 [1] 中，Alice 使用 Bob 的公钥 (n,e) 对明 C 文 M 进行加密， C=Me(mod n) 其中 n 是两个大素数的乘积， e≥3 是一个奇数整数，与的 Z&lowast;n 顺序是的互质数，是的 Zn 可逆元素组。Bob 知道私钥 (n,d) ， de=1( mod (p−1)(q−1)) 这意味着他可以计算 M=Cd(mod n) 。攻击者可以窃听 C 并可以知道公钥 (n,e) ，但是要计算 M 攻击者必须找到 n 的因子。因此，这意味着 RSA 问题并不比整数分解更难，但只要选择合适的 n 问题，它仍然是一个非常难以解决的问题。
The Strong RSA Assumption
强大的 RSA 假设

The strong RSA assumption differs from the RSA assumption in that the adversary can choose the (odd) public exponent e≥3. The adversary's task is to compute the plaintext M from the ciphertext given that C=Me(mod n). This is at least as easy as the RSA problem meaning that the strong RSA assumption is, unsurprisingly, a stronger assumption. The RSA problem is now over a quarter of a century old. Public key encryption schemes have been developed that derive their strength fully from the RSA problem.
强 RSA 假设与 RSA 假设的不同之处在于，攻击者可以选择（奇数）公共指数 e≥3 。攻击者的任务是从密文中计算明文 M ，因为 C=Me(mod n) .这至少和 RSA 问题一样简单，这意味着不出所料，强 RSA 假设是一个更强的假设。RSA问题现在已经有四分之一个世纪的历史了。已经开发了公钥加密方案，这些方案完全从RSA问题中获得了优势。

标签：10,What,RSA,52,nbsp,problem,minus,mod
From： https://www.cnblogs.com/3cH0-Nu1L/p/18104691

52 Things: Number 10: What is the difference between the RSA and strong-RSA problem?

52 Things: Number 10: What is the difference between the RSA and strong-RSA problem?

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