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finite-field-multiplication
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Dual-basis superserial multipliers for secure applications and lightweight cryptographic architectures
, Article IEEE Transactions on Circuits and Systems II: Express Briefs ; Vol. 61, Issue. 2 , February , 2014 , pp. 125-129 ; ISSN: 15497747 ; Mozaffari Kermani, M ; Azarderakhsh, R ; Lee, C. Y ; Sharif University of Technology
Abstract
Cryptographic algorithms utilize finite-field arithmetic operations in their computations. Due to the constraints of the nodes which benefit from the security and privacy advantages of these algorithms in sensitive applications, these algorithms need to be lightweight. One of the well-known bases used in sensitive computations is dual basis (DB). In this brief, we present low-complexity superserial architectures for the DB multiplication over GF (2m). To the best of our knowledge, this is the first time that such a multiplier is proposed in the open literature. We have performed complexity analysis for the proposed lightweight architectures, and the results show that the hardware complexity...
High Speed Implementation of Finite Field Multiplier Suitable for Isogeny-Based Protocols
, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
Classic public key cryptographic systems are based on difficult mathematical problems that will lose their security with the advent of high-speed quantum computers. Isogeny-based cryptography is one of the five main methods in post-quantum cryptography, the hard problem of which is finding large-degree isogenies between elliptic curves. The most important advantage of isogeny-based protocols is the shorter public key length and the main problem is their low speed and low performance compared to other cryptographic systems. Due to the fact that these protocols are implemented on a finite field using basic operations, such as multiplication, squaring, addition, and subtraction, improving the...