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RNS arithmetic approach in lattice-based cryptography: accelerating the 'rounding-off' core procedure

Conference Paper


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Abstract


  • Residue Number Systems (RNS) are naturally considered as an interesting candidate to provide efficient arithmetic for implementations of cryptosystems such as RSA, ECC (Elliptic Curve Cryptography), pairings, etc. More recently, RNS have been used to accelerate fully homomorphic encryption as lattice-based cryptogaphy. In this paper, we present an RNS algorithm resolving the Closest Vector Problem (CVP). This algorithm is particularly efficient for a certain class of lattice basis. It provides a full RNS Babai round-off procedure without any costly conversion into alternative positional number system such as Mixed Radix System (MRS). An optimized Cox-Rower architecture adapted to the proposed algorithm is also presented. The main modifications reside in the Rower unit whose feature is to use only one multiplier. This allows to free two out of three multipliers from the Rower unit by reusing the same one with an overhead of 3 more cycles per inner reduction. An analysis of feasibility of implementation within FPGA is also given.

UOW Authors


  •   Bajard, Jean-Claude (external author)
  •   Eynard, Julien (external author)
  •   Merkiche, Nabil (external author)
  •   Plantard, Thomas

Publication Date


  • 2015

Citation


  • Bajard, J., Eynard, J., Merkiche, N. & Plantard, T. (2015). RNS arithmetic approach in lattice-based cryptography: accelerating the 'rounding-off' core procedure. In J. Muller, A. Tisserand & J. Villalba (Eds.), Proceedings of the 2015 IEEE Symposium on Computer Arithmetic (ARITH 22) (pp. 113-120). Piscataway, New Jersey, United States: IEEE.

Scopus Eid


  • 2-s2.0-84952315470

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6050&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5023

Has Global Citation Frequency


Start Page


  • 113

End Page


  • 120

Place Of Publication


  • Piscataway, New Jersey, United States

Abstract


  • Residue Number Systems (RNS) are naturally considered as an interesting candidate to provide efficient arithmetic for implementations of cryptosystems such as RSA, ECC (Elliptic Curve Cryptography), pairings, etc. More recently, RNS have been used to accelerate fully homomorphic encryption as lattice-based cryptogaphy. In this paper, we present an RNS algorithm resolving the Closest Vector Problem (CVP). This algorithm is particularly efficient for a certain class of lattice basis. It provides a full RNS Babai round-off procedure without any costly conversion into alternative positional number system such as Mixed Radix System (MRS). An optimized Cox-Rower architecture adapted to the proposed algorithm is also presented. The main modifications reside in the Rower unit whose feature is to use only one multiplier. This allows to free two out of three multipliers from the Rower unit by reusing the same one with an overhead of 3 more cycles per inner reduction. An analysis of feasibility of implementation within FPGA is also given.

UOW Authors


  •   Bajard, Jean-Claude (external author)
  •   Eynard, Julien (external author)
  •   Merkiche, Nabil (external author)
  •   Plantard, Thomas

Publication Date


  • 2015

Citation


  • Bajard, J., Eynard, J., Merkiche, N. & Plantard, T. (2015). RNS arithmetic approach in lattice-based cryptography: accelerating the 'rounding-off' core procedure. In J. Muller, A. Tisserand & J. Villalba (Eds.), Proceedings of the 2015 IEEE Symposium on Computer Arithmetic (ARITH 22) (pp. 113-120). Piscataway, New Jersey, United States: IEEE.

Scopus Eid


  • 2-s2.0-84952315470

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6050&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5023

Has Global Citation Frequency


Start Page


  • 113

End Page


  • 120

Place Of Publication


  • Piscataway, New Jersey, United States