D.12.3.1 decimal | | number corresponding to the hexadecimal number s |
D.12.3.2 exgcdN | | compute s,t,d such that d=gcd(a,n)=s*a+t*n |
D.12.3.3 eexgcdN | | T with sum_i L[i]*T[i]=T[n+1]=gcd(L[1],...,L[n]) |
D.12.3.4 gcdN | | compute gcd(a,b) |
D.12.3.5 lcmN | | compute lcm(a,b) |
D.12.3.6 powerN | | compute m^d mod n |
D.12.3.7 chineseRem | | compute x such that x = T[i] mod L[i] |
D.12.3.8 Jacobi | | the generalized Legendre symbol of a and n |
D.12.3.9 primList | | the list of all primes <=n |
D.12.3.10 primL | | first primes p_1,...,p_r such that q<p_1*...*p_r |
D.12.3.11 intPart | | the integral part of a rational number |
D.12.3.12 intRoot | | the integral part of the square root of m |
D.12.3.13 squareRoot | | the square root of a in Z/p, p prime |
D.12.3.14 solutionsMod2 | | basis solutions of Mx=0 over Z/2 |
D.12.3.15 powerX | | q-th power of the i-th variable modulo I |
D.12.3.16 babyGiant | | discrete logarithm x: b^x=y mod p |
D.12.3.17 rho | | discrete logarithm x: b^x=y mod p |
D.12.3.18 MillerRabin | | probabilistic primaly-test of Miller-Rabin |
D.12.3.19 SolowayStrassen | | probabilistic primaly-test of Soloway-Strassen |
D.12.3.20 PocklingtonLehmer | | primaly-test of Pocklington-Lehmer |
D.12.3.21 PollardRho | | Pollard's rho factorization |
D.12.3.22 pFactor | | Pollard's p-factorization |
D.12.3.23 quadraticSieve | | quadratic sieve factorization |
D.12.3.24 isOnCurve | | P is on the curve y^2z=x^3+a*xz^2+b*z^3 over Z/N |
D.12.3.25 ellipticAdd | | P+Q, addition on elliptic curves |
D.12.3.26 ellipticMult | | k*P on elliptic curves |
D.12.3.27 ellipticRandomCurve | | generates y^2z=x^3+a*xz^2+b*z^3 over Z/N randomly |
D.12.3.28 ellipticRandomPoint | | random point on y^2z=x^3+a*xz^2+b*z^3 over Z/N |
D.12.3.29 countPoints | | number of points of y^2=x^3+a*x+b over Z/N |
D.12.3.30 ellipticAllPoints | | points of y^2=x^3+a*x+b over Z/N |
D.12.3.31 ShanksMestre | | number of points of y^2=x^3+a*x+b over Z/N |
D.12.3.32 Schoof | | number of points of y^2=x^3+a*x+b over Z/N |
D.12.3.33 generateG | | m-th division polynomial of y^2=x^3+a*x+b over Z/N |
D.12.3.34 factorLenstraECM | | Lenstra's factorization |
D.12.3.35 ECPP | | primaly-test of Goldwasser-Kilian |