Multifunction residue architectures for cryptography

Dimitrios Schinianakis, Thanos Stouraitis

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A design methodology for incorporating Residue Number System (RNS) and Polynomial Residue Number System (PRNS) in Montgomery modular multiplication in GF(p) or GF(2n) respectively, as well as a VLSI architecture of a dual-field residue arithmetic Montgomery multiplier are presented in this paper. An analysis of input/output conversions to/from residue representation, along with the proposed residue Montgomery multiplication algorithm, reveals common multiply-accumulate data paths both between the converters and between the two residue representations. A versatile architecture is derived that supports all operations of Montgomery multiplication in GF(p) and GF(2n), input/output conversions, Mixed Radix Conversion (MRC) for integers and polynomials, dual-field modular exponentiation and inversion in the same hardware. Detailed comparisons with state-of-the-art implementations prove the potential of residue arithmetic exploitation in dual-field modular multiplication.

Original languageBritish English
Article number6693749
Pages (from-to)1156-1169
Number of pages14
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number4
StatePublished - Apr 2014


  • Computations in finite fields
  • computer arithmetic
  • Montgomery multiplication
  • parallel arithmetic and logic structures


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