> | ### D.12.3 crypto_lib Library: crypto.lib Purpose: Procedures for teaching cryptography Author: Gerhard Pfister, pfister@mathematik.uni-kl.de Overview: The library contains procedures to compute the discrete logarithm, primality-tests, factorization included elliptic curves. The library is intended to be used for teaching purposes but not for serious computations. Sufficiently high printlevel allows to control each step, thus illustrating the algorithms at work. Procedures:
> D.12.3.1 decimal |  | number corresponding to the hexadecimal number s
> D.12.3.2 eexgcdN |  | T with sum_i L[i]*T[i]=T[n+1]=gcd(L[1],...,L[n])
> D.12.3.3 lcmN |  | compute lcm(a,b)
> D.12.3.4 powerN |  | compute m^d mod n
> D.12.3.5 chineseRem |  | compute x such that x = T[i] mod L[i]
> D.12.3.6 Jacobi |  | the generalized Legendre symbol of a and n
> D.12.3.7 primList |  | the list of all primes <=n
> D.12.3.8 primL |  | first primes p_1,...,p_r such that q<p_1*...*p_r
> D.12.3.9 intPart |  | the integral part of a rational number
> D.12.3.10 intRoot |  | the integral part of the square root of m
> D.12.3.11 squareRoot |  | the square root of a in Z/p, p prime
> D.12.3.12 solutionsMod2 |  | basis solutions of Mx=0 over Z/2
> D.12.3.13 powerX |  | q-th power of the i-th variable modulo I
> D.12.3.14 babyGiant |  | discrete logarithm x: b^x=y mod p
> D.12.3.15 rho |  | discrete logarithm x: b^x=y mod p
> D.12.3.16 MillerRabin |  | probabilistic primaly-test of Miller-Rabin
> D.12.3.17 SolowayStrassen |  | probabilistic primaly-test of Soloway-Strassen
> D.12.3.18 PocklingtonLehmer |  | primaly-test of Pocklington-Lehmer
> D.12.3.19 PollardRho |  | Pollard's rho factorization
> D.12.3.20 pFactor |  | Pollard's p-factorization
> D.12.3.21 quadraticSieve |  | quadratic sieve factorization
> D.12.3.22 isOnCurve |  | P is on the curve y^2z=x^3+a*xz^2+b*z^3 over Z/N
> D.12.3.23 ellipticAdd |  | P+Q, addition on elliptic curves
> D.12.3.24 ellipticMult |  | k*P on elliptic curves
> D.12.3.25 ellipticRandomCurve |  | generates y^2z=x^3+a*xz^2+b*z^3 over Z/N randomly
> D.12.3.26 ellipticRandomPoint |  | random point on y^2z=x^3+a*xz^2+b*z^3 over Z/N
> D.12.3.27 countPoints |  | number of points of y^2=x^3+a*x+b over Z/N
> D.12.3.28 ellipticAllPoints |  | points of y^2=x^3+a*x+b over Z/N
> D.12.3.29 ShanksMestre |  | number of points of y^2=x^3+a*x+b over Z/N
> D.12.3.30 Schoof |  | number of points of y^2=x^3+a*x+b over Z/N
> D.12.3.31 generateG |  | m-th division polynomial of y^2=x^3+a*x+b over Z/N
> D.12.3.32 factorLenstraECM |  | Lenstra's factorization
> D.12.3.33 ECPP |  | primaly-test of Goldwasser-Kilian

User manual for Singular version 4-0-2, 2015, generated by texi2html.