Karatsuba-like formulae and their associated techniques

CENK M.

JOURNAL OF CRYPTOGRAPHIC ENGINEERING, cilt.8, sa.3, ss.259-269, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s13389-017-0155-8
  • Dergi Adı: JOURNAL OF CRYPTOGRAPHIC ENGINEERING
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.259-269
  • Anahtar Kelimeler: Polynomial multiplication, Karatsuba algorithm, Cryptographic computation, Chinese remainder theorem, EFFICIENT MULTIPLICATION, 5-TERM, 6-TERM
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Efficient polynomial multiplication formulae are required for cryptographic computation. From elliptic curve cryptography to homomorphic encryption, many cryptographic systems need efficient multiplication formulae. The most widely used multiplication formulae for cryptographic systems are the Karatsuba-like polynomial multiplication formulae. In this paper, these formulae and Montgomery's work yielding more efficient such formulae are introduced. Moreover, recent efforts to improve these results are discussed by presenting associated techniques. The state of art for this area is also discussed.