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1994•International Symposium on Information Theory and its ApplicationsRequires access

Solving the Quadratic Congruence Equation Module a Prime Number p

Baoan Guo, Xiaodong Zhou, Kai-cheng Lu

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Abstract

It is very important to solve the quadratic congruence equation over a finite field GF(p) in cryptography. In this paper we discussed the graphic structure of the quadratic roots module, a prime number p . A deterministic polynomial algorithm is presented to detect the quadratic roots if a quadratic non-residue is provided no matter what kind of the prime number p is. Some examples are given in the end of the paper.

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What this paper is about

It is very important to solve the quadratic congruence equation over a finite field GF(p) in cryptography. In this paper we discussed the graphic structure of the quadratic roots module, a prime number p . A deterministic polynomial algorithm is presented to detect the quadratic roots if a quadratic non-residue is provided no matter what kind of the prime number p is. Some examples are given in the end of the paper.

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Available abstract

It is very important to solve the quadratic congruence equation over a finite field GF(p) in cryptography. In this paper we discussed the graphic structure of the quadratic roots module, a prime number p . A deterministic polynomial algorithm is presented to detect the quadratic roots if a quadratic non-residue is provided no matter what kind of the prime number p is. Some examples are given in the end of the paper.

Key concepts: Quadratic residue, Congruence (geometry), Legendre symbol, Quadratic equation, Mathematics, Prime (order theory), Quadratic field, Binary quadratic form

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