V1ru8

Helpfully functions in mathematica for cryptographic

Square and multiply algorithm: $x^y \mod n \Rightarrow $PowerMod$[x,y,n]$ PowerMod
Inverse function $x \cdot x^{-1} \equiv 1 \mod n \Rightarrow n = $PowerMod$[x,-1,n]$ PowerMod
Chinese Remainder
- $x \equiv 2 \mod 3$
- $x \equiv 3 \mod 4$
- $x \equiv 2 \mod 5$
- $\Rightarrow x = $ChineseRemainder$[\{2,3,2\},\{3,4,5\}]$
- Chinese Remainder
Square root $\sqrt{y} \equiv x \mod n \Rightarrow x = $PowerModList$[y,\frac{1}{2},n]$ PowerModList
Discrete Logarithm $y^x \equiv z \mod n \Rightarrow x = \text{MultiplicativeOrder}[y,n,\{r\}]$
Prime Numbers $\text{RandomPrime}[\{x,y\}]$ returns you a prime RandomPrime
Prime Factors $\text{FactorInteger}[n]$ FactorInteger
Euler Phi $\varphi(n) \Rightarrow \text{EulerPhi}[n]$ EulerPhi