Helpfully functions in mathematica for cryptographic

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

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Thomas Post on January 4th 2008 in Math with tags:, ,

One Response to “Helpfully functions in mathematica for cryptographic”

  1. V1ru8 » latex for wordpress responded on 04 Jan 2008 at 20:55 #

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