blog.V1ru8.net » crypto http://blog.v1ru8.net Mon, 28 Sep 2009 15:55:13 +0000 en hourly 1 http://wordpress.org/?v=3.2.1 Helpfully functions in mathematica for cryptographic http://blog.v1ru8.net/2008/01/04/helpfully-functions-in-mathematica-for-cryptographic/ http://blog.v1ru8.net/2008/01/04/helpfully-functions-in-mathematica-for-cryptographic/#comments Fri, 04 Jan 2008 19:00:22 +0000 Thomas Post http://www.v1ru8.net/2008/01/04/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
  • 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 x < p < yRandomPrime
  • Prime Factors \text{FactorInteger}[n] FactorInteger
  • Euler Phi \varphi(n) \Rightarrow \text{EulerPhi}[n] EulerPhi
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