在基于等基因的承诺中避免可信设置

IF 1.4 2区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Gustave Tchoffo Saah, Tako Boris Fouotsa, Emmanuel Fouotsa, Célestin Nkuimi-Jugnia
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引用次数: 0

摘要

2021年,Sterner提出了一种基于超奇异同基因的承诺方案。为了使该方案具有约束力,需要依赖一个可信方生成未知自同态环的起始超奇异椭圆曲线。事实上,自同态环的知识允许我们计算一个给定小素数的幂次自同态。这样的自同态可以被分成两个,以获得具有相同承诺的两个不同的消息。这就是为什么需要未知自同态环曲线的原因,而生成这种超奇异曲线的唯一方法是依赖于可信方或一些昂贵的多方计算。我们观察到,如果自同态的程度选择得很好,那么自同态环的知识不足以有效地计算这样的自同态,在某些特殊情况下,甚至可以证明一定程度的自同态不存在。利用这些观察结果,我们调整了Sterner的承诺方案,使起始曲线的自同态环可以被已知和公开。这允许我们获得基于等基因的承诺方案,它可以在没有可信设置要求的情况下实例化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Avoiding trusted setup in isogeny-based commitments

In 2021, Sterner proposed a commitment scheme based on supersingular isogenies. For this scheme to be binding, one relies on a trusted party to generate a starting supersingular elliptic curve of unknown endomorphism ring. In fact, the knowledge of the endomorphism ring allows one to compute an endomorphism of degree a power of a given small prime. Such an endomorphism can then be split into two to obtain two different messages with the same commitment. This is the reason why one needs a curve of unknown endomorphism ring, and the only known way to generate such supersingular curves is to rely on a trusted party or on some expensive multiparty computation. We observe that if the degree of the endomorphism in play is well chosen, then the knowledge of the endomorphism ring is not sufficient to efficiently compute such an endomorphism and in some particular cases, one can even prove that endomorphism of a certain degree do not exist. Leveraging these observations, we adapt Sterner’s commitment scheme in such a way that the endomorphism ring of the starting curve can be known and public. This allows us to obtain isogeny-based commitment schemes which can be instantiated without trusted setup requirements.

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来源期刊
Designs, Codes and Cryptography
Designs, Codes and Cryptography 工程技术-计算机:理论方法
CiteScore
2.80
自引率
12.50%
发文量
157
审稿时长
16.5 months
期刊介绍: Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
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