TY - JOUR

T1 - A multivariate quadratic challenge toward post-quantum generation cryptography

AU - Yasuda, Takanori

AU - Dahan, Xavier

AU - Huang, Yun Ju

AU - Takagi, Tsuyoshi

AU - Sakurai, Kouichi

PY - 2015/9/1

Y1 - 2015/9/1

N2 - Multivariate polynomials over finite fields have found applications in Public Key Cryptography (PKC) where the hardness to find solutions provides the "one-way function" indispensable to such cryptosystems. Several schemes for both encryption and signature have been proposed, many of which are using quadratic (degree 2) polynomials. Finding a solution to such systems in general is called MQ problem, which easiest "generic" instances are NP-hard. An important feature of this Multivariate Pubic Key Cryptography (MPKC) is the resistance to quantum computers: no faster quantum algorithm than classical ones to solve MQ problem is known. Besides being thereby a candidate for Post-Quantum Cryptography, signatures are much shorter than to other candidates. We have established an open public "MQ Challenge" (https://www.mqchallenge.org) to stimulate progress in the design of efficient algorithms to solve MQ problem, and thus test limit parameters guaranteeing security of MPKC.

AB - Multivariate polynomials over finite fields have found applications in Public Key Cryptography (PKC) where the hardness to find solutions provides the "one-way function" indispensable to such cryptosystems. Several schemes for both encryption and signature have been proposed, many of which are using quadratic (degree 2) polynomials. Finding a solution to such systems in general is called MQ problem, which easiest "generic" instances are NP-hard. An important feature of this Multivariate Pubic Key Cryptography (MPKC) is the resistance to quantum computers: no faster quantum algorithm than classical ones to solve MQ problem is known. Besides being thereby a candidate for Post-Quantum Cryptography, signatures are much shorter than to other candidates. We have established an open public "MQ Challenge" (https://www.mqchallenge.org) to stimulate progress in the design of efficient algorithms to solve MQ problem, and thus test limit parameters guaranteeing security of MPKC.

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U2 - 10.1145/2850449.2850462

DO - 10.1145/2850449.2850462

M3 - Article

AN - SCOPUS:84948733886

VL - 49

SP - 105

EP - 107

JO - ACM Communications in Computer Algebra

JF - ACM Communications in Computer Algebra

SN - 1932-2232

IS - 3

ER -