메뉴 건너뛰기




Volumn , Issue , 2007, Pages 230-239

Montgomery reduction algorithm for modular multiplication using low-weight polynomial form integers

Author keywords

Adapted modular number system; Low weight polynomial form integers; Montgomery reduction algorithm; More generalized Mersenne numbers; Polynomial modular number system

Indexed keywords

ALGORITHMS; INTEGER PROGRAMMING; NUMBER THEORY; POLYNOMIALS;

EID: 36049021578     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ARITH.2007.23     Document Type: Conference Paper
Times cited : (9)

References (19)
  • 1
    • 85008047428 scopus 로고    scopus 로고
    • Low-weight polynomial form integers for efficient modular multiplication
    • J. Chung and M. A. Hasan, "Low-weight polynomial form integers for efficient modular multiplication," IEEE Transactions on Computers, vol. 56, no. 1, pp. 44-57, 2007.
    • (2007) IEEE Transactions on Computers , vol.56 , Issue.1 , pp. 44-57
    • Chung, J.1    Hasan, M.A.2
  • 2
    • 34547722936 scopus 로고    scopus 로고
    • More generalized Mersenne numbers
    • Selected Areas in Cryptography, SAC 2003, Springer-Verlag
    • J. Chung and A. Hasan, "More generalized Mersenne numbers," in Selected Areas in Cryptography - SAC 2003, LNCS 3006, pp. 335-347, Springer-Verlag, 2003.
    • (2003) LNCS , vol.3006 , pp. 335-347
    • Chung, J.1    Hasan, A.2
  • 3
    • 24144452461 scopus 로고    scopus 로고
    • Modular number systems: Beyond the Mersenne family
    • Selected Areas in Cryptography 2004, Springer-Verlag
    • J.-C. Bajard, L. Imbert, and T. Plantard, "Modular number systems: Beyond the Mersenne family," in Selected Areas in Cryptography 2004, LNCS 3357, pp. 159-169, Springer-Verlag, 2004.
    • (2004) LNCS , vol.3357 , pp. 159-169
    • Bajard, J.-C.1    Imbert, L.2    Plantard, T.3
  • 6
    • 0011936983 scopus 로고
    • The complexity of a scheme of functional elements realizing the multiplication of integers
    • A. L. Toom, "The complexity of a scheme of functional elements realizing the multiplication of integers," Soviet Math, vol. 3, pp. 714-716, 1963.
    • (1963) Soviet Math , vol.3 , pp. 714-716
    • Toom, A.L.1
  • 8
    • 14844351609 scopus 로고    scopus 로고
    • Five, six, and seven-term Karatsuba-like formulae
    • P. L. Montgomery, "Five, six, and seven-term Karatsuba-like formulae," IEEE Transaction on Computers, vol. 54, no. 3, pp. 362-369, 2005.
    • (2005) IEEE Transaction on Computers , vol.54 , Issue.3 , pp. 362-369
    • Montgomery, P.L.1
  • 9
    • 84966243285 scopus 로고
    • Modular multiplication without trial division
    • P. L. Montgomery, "Modular multiplication without trial division," Mathematics of Computation, vol. 44, no. 170, pp. 519-521, 1985.
    • (1985) Mathematics of Computation , vol.44 , Issue.170 , pp. 519-521
    • Montgomery, P.L.1
  • 10
    • 84943632039 scopus 로고    scopus 로고
    • Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems
    • Advances in Cryptology, CRYPTO '96, Springer-Verlag
    • P. Kocher, "Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems," in Advances in Cryptology - CRYPTO '96, LNCS 1109, pp. 104-113, Springer-Verlag, 1996.
    • (1996) LNCS , vol.1109 , pp. 104-113
    • Kocher, P.1
  • 11
    • 68549092451 scopus 로고
    • A timing attack against RSA with the Chinese remainder theorem
    • Cryptographic Hardware and Embedded Systems CHES 2000, Springer-Verlag
    • W. Schindler, "A timing attack against RSA with the Chinese remainder theorem," in Cryptographic Hardware and Embedded Systems CHES 2000, LNCS 1965, pp. 109-124, Springer-Verlag, 2000.
    • (1965) LNCS , pp. 109-124
    • Schindler, W.1
  • 12
    • 84937560280 scopus 로고    scopus 로고
    • Distinguishing exponent digits by observing modular subtractions
    • Progress in Cryptology, CT-RSA 2001, Springer-Verlag
    • C. D. Walter and S. Thompson, "Distinguishing exponent digits by observing modular subtractions," in Progress in Cryptology - CT-RSA 2001, LNCS 2020, pp. 192-207, Springer-Verlag, 2001.
    • (2001) LNCS , vol.2020 , pp. 192-207
    • Walter, C.D.1    Thompson, S.2
  • 13
    • 0033204468 scopus 로고    scopus 로고
    • Montgomery exponentiation needs no final subtractions
    • C. D. Walter, "Montgomery exponentiation needs no final subtractions," Electronics Letters, vol. 35, no. 21, pp. 1831-1832, 1999.
    • (1999) Electronics Letters , vol.35 , Issue.21 , pp. 1831-1832
    • Walter, C.D.1
  • 14
    • 68549090587 scopus 로고
    • Montgomery exponentiation with no final subtractions: Improved results
    • Cryptographic Hardware and Embedded Systems, CHES 2000, Springer-Verlag
    • G. Hachez and J.-J. Quisquater, "Montgomery exponentiation with no final subtractions: Improved results," in Cryptographic Hardware and Embedded Systems - CHES 2000, LNCS 1965, pp. 293-301, Springer-Verlag, 2000.
    • (1965) LNCS , pp. 293-301
    • Hachez, G.1    Quisquater, J.-J.2
  • 15
    • 84944900219 scopus 로고    scopus 로고
    • Precise bounds for Montgomery modular multiplication and some potentially insecure RSA moduli
    • Topics in Cryptology, CT-RSA 2002, Springer-Verlag
    • C. D. Walter, "Precise bounds for Montgomery modular multiplication and some potentially insecure RSA moduli," in Topics in Cryptology - CT-RSA 2002, LNCS 2271, pp. 30-39, Springer-Verlag, 2002.
    • (2002) LNCS , vol.2271 , pp. 30-39
    • Walter, C.D.1
  • 18
    • 0036859286 scopus 로고    scopus 로고
    • Finite field multiplier using redundant representation
    • H. Wu, M. A. Hasan, I. F. Blake, and S. Gao, "Finite field multiplier using redundant representation," IEEE Transactions on Computers, vol. 51, no. 11, pp. 1306-1316, 2002.
    • (2002) IEEE Transactions on Computers , vol.51 , Issue.11 , pp. 1306-1316
    • Wu, H.1    Hasan, M.A.2    Blake, I.F.3    Gao, S.4
  • 19
    • 0000895310 scopus 로고    scopus 로고
    • m) yielding small complexity arithmetic circuits
    • m) yielding small complexity arithmetic circuits," IEEE Transactions on Computers, vol. 47, no. 9, 1998.
    • (1998) IEEE Transactions on Computers , vol.47 , Issue.9
    • Drolet, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.