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RNS in Cryptography

In: Residue Number Systems

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  • P. V. Ananda Mohan

    (CDAC, R&D)

Abstract

In cryptographic applications such as RSA encryption, Diffie-Hellman Key exchange, Elliptic curve cryptography, etc., modulo multiplication and modulo exponentiation of large numbers, of bit lengths varying between 160 bits to 2048 bits, typically will be required. Two popular techniques are based on Barrett reduction and Montgomery multiplication. However, to perform the operation (X Y ) mod N for a single modulus, RNS using several small word lengths moduli can be employed. This topic has received recently considerable attention. We deal with both RNS-based and non-RNS based (i.e. using only one modulus) implementations in the following sections. In this chapter, we also consider applications of RNS in Elliptic Curve Cryptography processors and for implementation of Pairing protocols.

Suggested Citation

  • P. V. Ananda Mohan, 2016. "RNS in Cryptography," Springer Books, in: Residue Number Systems, chapter 0, pages 263-347, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-41385-3_10
    DOI: 10.1007/978-3-319-41385-3_10
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