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本文为法国巴黎高等师范学院(作者:DIANA ¸STEFANIA MAIMU ¸T)的博士论文,共197页。
本文讨论了密码学中的各种问题,即协议设计、算法改进和攻击。此外,我们还从密码学的角度出发,提出了两种新的密码技术在纠错码中的应用。我们的主要结果包括一个可证明安全的共同签名协议和一个可证明安全的认证加密方案。我们的共同签名协议实现了法律上的公平,这是一种不依赖第三方的新型公平变体。使用Schnorr签名实现法律公平。本文还提出了一种分布式Fiat-Shami认证协议。论文的第二部分致力于计算量改进,我们讨论了一种利用特定的复合模使Barrett算法速度加倍的方法,并利用Barrett算法的多项式扩展设计了新的BCH加速策略,描述了一种适用于轻量级微处理器的基于回溯的乘法算法,并给出了一种新的数论纠错码。进一步综述了缺陷注入攻击,提出了一种新的针对ECC实现的缺陷攻击方法。
This thesis addresses various topics incryptology, namely protocol design, algorithmic improvements and attacks. Inaddition, we venture out of cryptography and propose two new applications ofcryptographic techniques to error correcting codes. Our main results comprise aprovably secure co-signature protocol and a provably secure authenticatedencryption scheme. Our co-signature protocol achieves legal fairness, a novelfairness variant that does not rely on third parties. Legal fairness isimplemented using Schnorr signatures. We also present a distributed Fiat-Shamirauthentication protocol. The second part of the thesis is devoted tocomputational improvements, we discuss a method for doubling the speed ofBarrett’s algorithm by using specific composite moduli, devise new BCH speed-upstrategies using polynomial extensions of Barrett’s algorithm, describe a newbacktracking-based multiplication algorithm suited for lightweightmicroprocessors and present a new number theoretic error-correcting code. Faultinjection attacks are further overviewed and a new fault attack on ECCimplementations is proposed.
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