Tag: Math

2018
0
HackingCrypto

Discrete Logarithm

1. ElGamal SystemsKey Generation$({\mathbb {Z}}_{p}^{*}, \cdot)$ : Cyclic group1) $p$ : prime.2) $e_1$ : primitive root of $({\mathbb {Z}}_{p}^{*}, \cdot)$ choose $d \in {\mathbb {Z}}_{p}^{*}$

0
HackingCrypto

RSA Systems

1. RSA Cryptosystem Key Generation1) Choose two distinct prime numbers $p$ and $q$, $\quad N = p \cdot q$2) Choose $e$ s.t $gcd(e, \varphi(N)) = 1$3) $d$ : private key. s.t $ed \equiv 1 \mod \varp

0
HackingCrypto

Integer Arithmetic

1. Division Algorithm (Def)Let $a, b\in Z$ and $b \ne 0$.$b \mid a$ if $\exists \in Z$ s.t. $a = bc$ and$b \nmid a$ otherwise. (Division Algorithm)For $a, n \in Z$ and $n > 0$, $\exists!q,