ANALYSIS AND IMPLEMENTATION OF BINARY POLYNOMIAL MULTIPLICATION

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ANALYSIS_AND_IMPLEMENTATION_OF_BINARY_POLYNOMIAL_MULTIPLICATION-2.pdf

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2021-9-09

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OLUDO, Mary Achieng

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N. Koblitz and V. Miller originally proposed the concept of elliptic curve cryptography in 1985. It is fast gaining popularity in public key cryptosystems as it boasts of an advantage over current public key cryptosystems, that is, the requirement of the key size be smaller and still maintain the same level of security. It takes advantage of elliptic curves’ mathematical properties in finite fields. Elliptic curve cryptographic systems perform operations on points on elliptic curves. Elliptic curves can be represented over prime fields and can also be represented over binary fields. In the binary field representation, the elements of these finite fields are binary polynomials. Polynomial multiplication is a key operation in binary field elliptic curve cryptographic implementation and hence an area of interest in cryptography. In this thesis,we analyse some polynomial multiplication algorithms over binary fields. For 2-way algorithms we investigate schoolbook, Karatsuba and refined Karatsuba and for 3-way algorithms we investigate schoolbook, Karatsuba and CNH 3-way split algorithms. We define a 64-bit by 64-bit multiplication as the smallest unit of computation for a polynomial multiplication which can also be improved by the sliding window method. We have observed that an optimal size of eight for the window size is attained with a time memory trade off.

Subject Keywords

Elliptic Curves, Karatsuba, CNH 3-Way Split

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https://hdl.handle.net/11511/93109

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

M. A. OLUDO, “ANALYSIS AND IMPLEMENTATION OF BINARY POLYNOMIAL MULTIPLICATION,” M.S. - Master of Science, Middle East Technical University, 2021.