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Publication Date

Fall 2019

Degree Type

Thesis - Campus Access Only

Degree Name

Master of Science (MS)

Department

Computer Engineering

Advisor

Gokay . Saldamli

Keywords

cryptography, galois field airthmetic, modular arithmetic, Mongtomery, Post-Quantum Cryptography, reduction-free

Subject Areas

Computer engineering

Abstract

Cryptography requires working with finite fields and related structures in which the fundamental arithmetic operations are carried out without error. With respect to multiplication, the complexity varies significantly based on the mathematical structure and defining polynomial. When considering fields and rings, multiplication entails a multiplication step and a reduction step. In this work we present a fully interleaved reduction-free modular multiplier over GF(2n) that interleaves Karatsuba-Ofman polynomial multiplication with bipartite reduction. The multiplier works with elements in polynomial rings and finite fields and is applicable to cryptographic schemes in the modern and post-quantum regimes, especially elliptic curve cryptography (ECC). Moreover, it is more efficient in software than its counterparts and allows for a high level of parallelism in hardware.

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