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Karatsuba-like formulae and their associated techniques

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Abstract

Efficient polynomial multiplication formulae are required for cryptographic computation. From elliptic curve cryptography to homomorphic encryption, many cryptographic systems need efficient multiplication formulae. The most widely used multiplication formulae for cryptographic systems are the Karatsuba-like polynomial multiplication formulae. In this paper, these formulae and Montgomery’s work yielding more efficient such formulae are introduced. Moreover, recent efforts to improve these results are discussed by presenting associated techniques. The state of art for this area is also discussed.

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Acknowledgements

The author thanks two anonymous reviewers for provided helpful comments. This work was supported in part by TUBITAK under Grant No 115R289.

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  1. Institute of Applied Mathematics, Middle East Technical University, Cankaya, Ankara, Turkey

    Murat Cenk

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  1. Murat Cenk
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Cenk, M. Karatsuba-like formulae and their associated techniques. J Cryptogr Eng 8, 259–269 (2018). https://doi.org/10.1007/s13389-017-0155-8

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  • DOI: https://doi.org/10.1007/s13389-017-0155-8

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