Sierpiński Proth Multiple Variable Non-quadratic Totient Mod

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Multivariate Polynomial Signature with a prime p is product of odd prime number q multiplied with a power x of two and then plus one.

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更新时间 2022/11/17

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Multivariate Polynomial Public Key Digital Signature (MPPK/DS) algorithm is based on the modular arithmetic property Euler power totient that for a given element g, greater than equal to two, in a prime Galois field GF(p) and two multivariate polynomials P and Q, if P is equal to Q modulo p‑1, then g to the power of P is equal to g to the power of Q modulo p. MPPK/DS is designed to make secret the element g disfavors quantum computers’ capability to solve the discrete logarithm problem, p is a sum of a product of an odd prime number q multiplied with a power x of two and one. Given such a choice of a prime, choosing even coefficients of the publicly available polynomials makes it hard to find any private information modulo p‑1, finding private information modulo the components q and power x of two is an NP‑hard problem since it involves solving multivariate equations over the chosen finite field.

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steed huang (2024). Sierpiński Proth Multiple Variable Non-quadratic Totient Mod (https://www.mathworks.com/matlabcentral/fileexchange/120763-sierpinski-proth-multiple-variable-non-quadratic-totient-mod), MATLAB Central File Exchange. 检索来源 2024/10/2.