RSA计算d [英] RSA calculate d

问题描述

不知道这是否是正确的地方提出加密问题，但是这里。

Not sure if this is the correct place to ask a cryptography question, but here goes.

我正在尝试在RSA中找出d，我有制定p，q，e，n和øn;

I am trying to work out "d" in RSA, I have worked out p, q, e, n and øn;

p = 79, q = 113, e = 2621

n = pq                   øn = (p-1)(q-1)
n = 79 x 113 = 8927      øn = 78 x 112 = 8736

e = 2621
d =

我似乎找不到d，我知道d意在成为一个值ed modø（n）= 1.任何帮助将不胜感激

I cant seem to find d, I know that d is meant to be a value that.. ed mod ø(n) = 1. Any help will be appreciated

编辑：一个例子是e = 17，d = 2753，øn= 3120

edit: an example would be e = 17, d = 2753, øn = 3120

17 * 2753 mod 3120 = 1

17 * 2753 mod 3120 = 1

推荐答案

您正在寻找模块化的的 e （mod n ），可以使用扩展的欧几里得算法计算：

You are looking for the modular inverse of e (mod n), which can be computed using the extended Euclidean algorithm:

function inverse(x, m)
    a, b, u := 0, m, 1
    while x > 0
        q := b // x # integer division
        x, a, b, u := b % x, u, x, a - q * u
    if b == 1 return a % m
    error "must be coprime"

因此，在您的示例中， inverse（17，3120） = 2753和 inverse（2621，8736） = 4373.如果你不想实现算法，您可以询问 Wolfram | Alpha 的答案。

Thus, in your examples, inverse(17, 3120) = 2753 and inverse(2621, 8736) = 4373. If you don't want to implement the algorithm, you can ask Wolfram|Alpha for the answer.

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