Efficient interleaved Montgomery modular multiplication for lattice-based cryptography

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AKLEYLEK S., Tok Z. Y.

IEICE ELECTRONICS EXPRESS, cilt.11, sa.22, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 22
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1587/elex.11.20140960
  • Dergi Adı: IEICE ELECTRONICS EXPRESS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: interleaved Montgomery modular multiplication, lattice-based cryptography, NTRUEncrypt, GPU implementation, NTRU
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we give modified version of interleaved Montgomery modular multiplication method for lattice-based cryptography. With the proposed algorithms, we improve the multiplication complexity and embed the conversion operation into the algorithm with almost free cost. We implement the proposed methods for the quotient ring (Z/qZ)[x]/(x(n) - 1) and (Z/pZ)[x]/(x(n) + 1) on the GPU (NVIDIA Quadro 600) using the CUDA platform. NTRUEncrypt is accelerated approximately 35% on the GPU by using the proposed method. We receive at least 19% improvement with the proposed method for the polynomial multiplication in (Z/pZ)[x]/(x(n) + 1), where n is an element of{1024, 2048, 4096}.