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D.12.3 crypto_lib

Procedures for teaching cryptography
Gerhard Pfister, pfister@mathematik.uni-kl.de

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.


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