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Algebraic Coding and Cryptography
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ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
Next seminar
May 05
Pierre Varjabedian
Thales
Next seminar
May 05
Pierre Varjabedian
Thales
Threshold linear solving in small fields and application to UOV
Threshold linear solving in small fields and application to UOV
Abstracts. Threshold signatures allow multiple parties to sign a common message by collaborating. More specifically, in a (t, n)−threshold signature scheme, at least t out of n parties must collaborate to sign a message. In particular, solving linear systems shared among some parties is a problem that naturally arises in threshold cryptography, and this paper proposes various algorithms for a set of parties to solve a shared linear system Ax = b in finite fields of low characteristic. The first two algorithms securely compute the determinant of a shared matrix. The first uses recent theoretical results on Newton’s polynomials while the second adapts an algorithm by Samuelson and Berkowitz. From these results, two algorithms can be deduced to solve the corresponding linear system. Although pre-quantum threshold signature algorithms have been extensively studied, the state of the art in the creation of post-quantum threshold algorithms remain sparse. In particular, few papers have studied the creation of a threshold algorithm based on UOV, despite the simplicity of the scheme. The two new algorithms presented in this paper enable new threshold instantiations of UOV and UOV-based schemes.
Biography. Pierre Varjabedian was born in Dijon, France, and spent most of his youth in northern France. He studied mathematics and physics for three years in the Classe préparatoire aux Grandes Écoles in Valenciennes. Following his results in the national competitive examinations, he was admitted to the Mines de Saint-Étienne ISMIN engineering school. After one year, however, he decided to focus more deeply on mathematics and joined Aix-Marseille University, where he obtained a Bachelor’s degree in Mathematics. He then continued his studies at the University of Versailles, where he completed a Master’s degree in Applied Algebra.
During his Master’s degree, he also completed an internship at THALES DIS, where he studied the distribution of an analog random number generator. This experience, together with his academic background, allowed him to begin a PhD in cryptography funded by THALES DIS.
His PhD research focuses on multivariate cryptography, with a particular emphasis on HFE, or Hidden Field Equations, and UOV, or Unbalanced Oil and Vinegar, constructions. Both families have played, or continue to play, a role in the NIST post-quantum cryptography standardization process. While all HFE-based candidates submitted to the NIST competition were eventually broken, UOV-based schemes remain among the most important and promising multivariate approaches, although they still require improvements in security, efficiency, and key size.
His research aims to improve the security and practical performance of these schemes. For HFE, he has worked on both signature and encryption settings. In the encryption setting, he introduced a new HFE-based variant designed to strengthen the construction against known attacks while maintaining efficiency. This scheme is currently one of the few secure multivariate encryption schemes.
On the UOV side, he has worked on QR-UOV and proposed an improvement that reduces the size of the public key, addressing one of the major issues of multivariate signatures. He also developed a multiparty computation protocol, connecting his work on multivariate cryptography with broader questions in secure computation.
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