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Given the binary quadratic form ax^2+2bxy+cy^2 (1) with polynomial discriminant b^2-ac, let x = pX+qY (2) y = rX+sY. (3) Then a(pX+qY)^2+2b(pX+qY)(rX+sY)+c(rX+sY)^2 ...

A public-key cryptography algorithm which uses prime factorization as the trapdoor one-way function. Define n=pq (1) for p and q primes. Also define a private key d and a ...

The primes with Legendre symbol (n/p)=1 (less than N=pi(d) for trial divisor d) which need be considered when using the quadratic sieve factorization method.

The projective general linear group PGL_n(q) is the group obtained from the general linear group GL_n(q) on factoring by the scalar matrices contained in that group.

The projective general orthogonal group PGO_n(q) is the group obtained from the general orthogonal group GO_n(q) on factoring the scalar matrices contained in that group.

The projective general unitary group PGU_n(q) is the group obtained from the general unitary group GU_n(q) on factoring the scalar matrices contained in that group.

The projective symplectic group PSp_n(q) is the group obtained from the symplectic group Sp_n(q) on factoring by the scalar matrices contained in that group. PSp_(2m)(q) is ...

A prime factorization algorithm which uses residues produced in the continued fraction of sqrt(mN) for some suitably chosen m to obtain a square number. The algorithm solves ...

Given a sum and a set of weights, find the weights which were used to generate the sum. The values of the weights are then encrypted in the sum. This system relies on the ...

The projective special linear group PSL_n(q) is the group obtained from the special linear group SL_n(q) on factoring by the scalar matrices contained in that group. It is ...