A multivariate quadratic challenge toward post-quantum generation cryptography

Takanori Yasuda, Xavier Dahan, Yun Ju Huang, Tsuyoshi Takagi, Kouichi Sakurai

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)105-107
Number of pages3
JournalACM Communications in Computer Algebra
Issue number3
Publication statusPublished - Sept 2015

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Computational Mathematics


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