Cryptography

Number theory module

Module contains functions used for number theory problems in cryprography.

Algorithms:

1. Prime numbers test (Miller-Rabin)
2. greatest common divisor - gcd
3. multiplicative inverse mod n
4. Euler’s function
5. matrix inverse mod n
6. primitive root mod n

Classic chipers

1. Cesar chiper
2. Hill chiper
3. Affine chiper

DES function f

Implementation of f function from DES using S-boxes. This function is used for 16 iterations in DES algorithm. Function f takes 2 array arguments A and J , the first one is 32 bits and the second is 48 bits long.

There are 4 stages of calculating this function output.

1.The first argument A is expanded with expand function E , such that it becomes array E(A) of the 48 bits.

2.B = E(A) XOR J = B1B2…B8

3.For each Bj using S-box Sj , Cj = Sj(Bj) is computed.

4.f(A,J) = P(C1…C8) where P is final permutation.

El Gamal chiper

Example of asymetric cryptosystem based on public-key cryptography. It is based on difficulty to solve discrete-logarithm problem in multiplicaition group of remainders mod p (p is prime number).This cryptosystem can be defined over any cyclic group G. The security depends on properties of chosen group G.