B.4 Basic Operations: Friend Functions

const LINT operator + (const LINT& a, const LINT& b);

addition c = a + b;

const LINT operator - (const LINT& a, const LINT& b);

subtraction c = a − b;

const LINT operator * (const LINT& a, const LINT& b);

multiplication c = a * b;

const LINT operator / (const LINT& a, const LINT& b);

division c = a / b;

const LINT operator % (const LINT& a, const LINT& b);

remainder c = a % b;

const LINT add (const LINT& a, const LINT& b);

addition c = add (a, b);

const LINT sub (const LINT& a, const LINT& b);

subtraction c = sub (a, b);

const LINT mul (const LINT& a, const LINT& b);

multiplication c = mul (a, b);

const LINT sqr (const LINT& a);

squaring b = sqr (a);

const LINT divr (const LINT& a, const LINT& b, LINT& r);

division with remainder quotient = div (dividend, divisor, remainder);

const LINT& mod (const LINT& m);

remainder b = a.mod (m);

const LINT& mod2 (const USHORT u);

remainder modulo power of two 2 ^u , b = a.mod (u);

const int mequ (const LINT& b, const LINT& m) const;

comparison of a and b modulo m if (a.mequ (b, m)) ...

const LINT& madd (const LINT& b, const LINT& m);

modular addition, c = a.madd (b, m);

const LINT& msub (const LINT& b, const LINT& m);

modular subtraction, c = a.msub(b, m);

const LINT& mmul (const LINT& b, const LINT& m);

modular multiplication, c = a.mmul (b, m);

const LINT& msqr (const LINT& m);

modular squaring, c = a.msqr (m);

const LINT& mexp (const LINT& e, const LINT& m);

modular exponentiation with Montgomery reduction for odd modulus m,c = a.mexp (e, m);

const LINT& mexp (const USHORT u, const LINT& m);

modular exponentiation with USHORT exponent, Montgomery reduction for odd modulus m, c = a.mexp (u, m);

const LINT& mexp5m (const LINT& e, const LINT& m);

modular exponentiation with Montgomery reduction for odd modulus m,c = a.mexp5m (e, m);

const LINT& mexpkm (const LINT& e, const LINT& m);

modular exponentiation with Montgomery reduction for odd modulus m, c = a.mexpkm (e, m);

const LINT& mexp2 (const USHORT u, const LINT& m);

modular exponentiation with power of two exponent 2 ^u , c = a.mexp2 (u, m);

const LINT mod (const LINT& a, const LINT& m);

remainder b = mod (a, m);

const LINT mod2 (const LINT& a, const USHORT u);

remainder modulo power of two 2 ^u , b = mod (a, u);

const int mequ (const LINT& a, const LINT& b, const LINT& m);

comparison of a and b modulo m if (mequ (a, b, m)) ...

const LINT madd (const LINT& a, const LINT& b, const LINT& m);

modular addition, c = madd (a, b, m);

const LINT msub (const LINT& a, const LINT& b, const LINT& m);

modular subtraction, c = msub(a, b, m);

const LINT mmul (const LINT& a, const LINT& b, const LINT& m);

modular multiplication, c = mmul (a, b, m);

const LINT msqr (const LINT& a, const LINT& m);

modular squaring, c = msqr (a, m);

const LINT mexp (const LINT& a, const LINT& e, const LINT& m);

modular exponentiation with Montgomery reduction for odd modulus m, c = mexp (a, e, m);

const LINT mexp (const USHORT u, const LINT& e, const LINT& m);

modular exponentiation with USHORT base, Montgomery reduction for odd modulus m, c = mexp (u, e, m);

const LINT mexp (const LINT& a, const USHORT u, const LINT& m);

modular exponentiation with USHORT exponent, Montgomery reduction for odd modulus m, c = mexp (a, u, m);

const LINT mexp5m (const LINT& a, const LINT& e, const LINT& m);

modular exponentiation with Montgomery reduction, only for odd modulus m, c = mexp5m (a, e, m);

const LINT mexpkm (const LINT& a, const LINT& b, const LINT& m);

modular exponentiation with Montgomery reduction, only for odd modulus m, c = mexpkm (a, e, m);

const LINT mexp2 (const LINT& a, const USHORT u, const LINT& m);

modular exponentiation with power of two exponent 2 ^u , c = mexp2 (a, u, m);