B.10 Number-Theoretic Friend Functions
B.10 Number-Theoretic Friend Functions
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const unsigned ld (const LINT& a); | return ⌊log2(a)⌋ |
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const int iseven (const LINT& a); | test a for divisibility by 2: true if a even |
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const int isodd (const LINT& a); | test a for divisibility by 2: true if a odd |
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const LINT issqr (const LINT& a); | test a for being a square |
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const int isprime (const LINT& a); | test a for primality |
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const LINT gcd (const LINT& a, const LINT& b); | return gcd of a and b |
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const LINT xgcd (const LINT& a, const LINT& b, LINT& u, int& sign_u, LINT& v, int& sign_v); | extended Euclidean algorithm with return of gcd of a and b, u and v contain the absolute values of the factors of the linear combination g = sign_u*u*a + sign_v*v*b |
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const LINT inv (const LINT& a, const LINT& b); | return the multiplicative inverse of a mod b |
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const LINT lcm (const LINT& a, const LINT& b); | return the least common multiple of a and b |
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const int jacobi (const LINT& a, const LINT& b); | return the Jacobi symbol ( |
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const LINT root (const LINT& a); | return the integer part of the square root of a |
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const LINT root (const LINT& a, const LINT& p); | return the square root of a modulo an odd prime p |
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const LINT root (const LINT& a, const LINT& p, const LINT& q); | return the square root of a modulo p*q for p and q odd primes |
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const LINT chinrem (const unsigned noofeq, LINT** coeff); | return a solution of a system of simultaneous linear congruences. In coeff is passed a vector of pointers to LINT objects as coefficients a1, m1, a2, m2, a3, m3, ... of the congruence system with noofeq equations x ≡ ai mod mi |
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const LINT primroot (const unsigned noofprimes, LINT** primes); | return a primitive root modulo p. In noofprimes is passed the number of distinct prime factors of the group order p − 1, in primes a vector of pointers to LINT objects, beginning with p − 1, then come the prime divisors p1,...,pk of the group order p − 1 = |
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const int twofact (const LINT& even, LINT& odd); | return the even part of a, odd contains the odd part of a |
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const LINT findprime (const USHORT l); | return a prime p of length l bits, i.e., 2l−1 ≤ p < 2l |
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const LINT findprime (const USHORT l, const LINT& f); | return a prime p of length l bits, i.e., 2l−1 ≤ p < 2l and gcd(p − 1, f) = 1, f odd |
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const LINT findprime (const LINT& pmin, const LINT& pmax, const LINT& f); | return a prime p with pmin ≤ p ≤ pmax and gcd(p − 1, f) = 1, f odd |
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const LINT nextprime (const LINT& a, const LINT& f); | return the smallest prime p above a with gcd(p − 1, f) = 1, f odd |
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const LINT extendprime (const USHORT l, const LINT& a, const LINT& q, const LINT& f); const LINT extendprime (const LINT& pmin, const LINT& pmax, const LINT& a, const LINT& q, const LINT& f); | return a prime p of length l bits, i.e., 2l−1 ≤ p < 2l, with p ≡ a mod q and gcd(p − 1, f) = 1, f odd |
| return a prime p with pmin ≤ p ≤ pmax, with p ≡ a mod q and gcd(p − 1, f) = 1, f odd | |
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const LINT strongprime (const USHORT l); | return a strong prime p of length l bits, i.e., 2l−1 ≤ p < 2l |
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const LINT strongprime (const USHORT l, const LINT& f); | return a strong prime p of length l bits, i.e., 2l−1 ≤ p < 2l, with gcd(p − 1, f) = 1, f odd |
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const LINT strongprime (const USHORT l, const USHORT lt, const USHORT lr, const USHORT ls, const LINT& f); | return a strong prime p of length l bits, i.e., 2l−1 ≤ p < 2l, with gcd(p − 1, f) = 1, f odd lt |
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const LINT strongprime (const LINT& pmin, const LINT& pmax, const LINT& f); | return a strong prime p with pmin ≤ p ≤ pmax, gcd(p − 1, f) = 1, f odd, default lengths lr, lt, ls of prime divisors r of p − 1, t of r−1, s of p+1:lt |
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const LINT strongprime (const LINT& pmin, const LINT& pmax, const USHORT lt, const USHORT lr, const USHORT ls, const LINT& f); | return a strong prime p with pmin ≤ p ≤ pmax, gcd(p − 1, f) = 1, f odd, lengths lr, lt, ls of prime divisors r of p − 1, t of r − 1, s of p + 1 |
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EAN: 2147483647
Pages: 127