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Modular multiplication using the core function in the residue number system

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Modular multiplication can be performed in the residue number system (RNS) using a type of Montgomery reduction. This paper presents an alternative in which RNS modular multiplication are performed by using the core function. All of the intermediate calculations use short wordlength operations within the RNS. This work contributes to the long wordlength modular multiplication operation \(Z = A \times B \mod M\), the basis of many DSPs and public-key cryptosystems.

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Authors and Affiliations

  1. Department of Engineering, Macquarie University, North Ryde, NSW, 2109, Australia

    Yinan Kong & Shahzad Asif

  2. Department of Electrical and Computer Engineering, Effat University, Jeddah, Saudi Arabia

    Mohammad A. U. Khan

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  1. Yinan Kong
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  2. Shahzad Asif
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  3. Mohammad A. U. Khan
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Correspondence to Shahzad Asif.

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Kong, Y., Asif, S. & Khan, M.A.U. Modular multiplication using the core function in the residue number system. AAECC 27, 1–16 (2016). https://doi.org/10.1007/s00200-015-0268-1

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  • DOI: https://doi.org/10.1007/s00200-015-0268-1

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