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Volumn , Issue , 2007, Pages 197-206

Integer factorization based on elliptic curve method: Towards better exploitation of reconfigurable hardware

Author keywords

Elliptic curve; Factorization; FPGA; Parallel modular multiplier

Indexed keywords

COMPUTATION THEORY; COMPUTER HARDWARE; COST EFFECTIVENESS; FACTORIZATION; FIELD PROGRAMMABLE GATE ARRAYS (FPGA); GEOMETRY; PUBLIC KEY CRYPTOGRAPHY;

EID: 47349131737     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FCCM.2007.12     Document Type: Conference Paper
Times cited : (17)

References (20)
  • 2
    • 84956985315 scopus 로고
    • Recent Progress and Prospects for Integer Factorisation Algorithms
    • COCOON'00, Springer-Verlag, pp
    • R. Brent, Recent Progress and Prospects for Integer Factorisation Algorithms, COCOON'00, LNCS 1858, Springer-Verlag, pp. 3-22, 2000.
    • (1858) LNCS , pp. 3-22
    • Brent, R.1
  • 3
    • 27244451341 scopus 로고    scopus 로고
    • A Realizable Special Hardware Sieving Device for Factoring 1024-bit Integers
    • SHARK:, CHES'05, Springer, pp
    • J. Franke, T. Kleinjung, C. Paar, J. Pelzl, C. Priplata, C. Stahlke, SHARK: A Realizable Special Hardware Sieving Device for Factoring 1024-bit Integers, CHES'05, LNCS 3659, Springer, pp. 119-130, 2005.
    • (2005) LNCS , vol.3659 , pp. 119-130
    • Franke, J.1    Kleinjung, T.2    Paar, C.3    Pelzl, J.4    Priplata, C.5    Stahlke, C.6
  • 4
    • 33750699935 scopus 로고    scopus 로고
    • Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware
    • CHES'06, Springer, pp
    • K. Gaj, S. Kwon, P. Baier, P. Kohlbrenner, H. Le, M. Khaleeluddin, R. Bachimanchi, Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware, CHES'06, LNCS 4249, Springer, pp. 119-133, 2006.
    • (2006) LNCS , vol.4249 , pp. 119-133
    • Gaj, K.1    Kwon, S.2    Baier, P.3    Kohlbrenner, P.4    Le, H.5    Khaleeluddin, M.6    Bachimanchi, R.7
  • 6
    • 27244438449 scopus 로고    scopus 로고
    • Scalable Hardware for Sparse Systems of Linear Equations, with Applications to Integer Factorization
    • CHES'05, Springer, pp
    • W. Geiselmann, A. Shamir, R. Steinwandt, E. Tromer, Scalable Hardware for Sparse Systems of Linear Equations, with Applications to Integer Factorization, CHES'05, LNCS 3659, Springer, pp. 131-146, 2005.
    • (2005) LNCS , vol.3659 , pp. 131-146
    • Geiselmann, W.1    Shamir, A.2    Steinwandt, R.3    Tromer, E.4
  • 7
    • 33645682275 scopus 로고    scopus 로고
    • Long Modular Multiplication for Cryptographic Applications, CHES'04
    • L. Hars, Long Modular Multiplication for Cryptographic Applications, CHES'04, LNCS 3156, pp. 44-61, 2004.
    • (2004) LNCS , vol.3156 , pp. 44-61
    • Hars, L.1
  • 8
    • 38149059344 scopus 로고    scopus 로고
    • Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024 bit integers
    • T. Kleinjung, Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024 bit integers, SHARCS'06, pp. 159-168, 2006.
    • (2006) SHARCS'06 , pp. 159-168
    • Kleinjung, T.1
  • 9
    • 0001258323 scopus 로고
    • Factoring integers with elliptic curves
    • H. Lenstra, Factoring integers with elliptic curves, Annals of Mathematics, Vol. 126, pp. 649- 673, 1987.
    • (1987) Annals of Mathematics , vol.126 , pp. 649-673
    • Lenstra, H.1
  • 10
    • 0003291192 scopus 로고
    • The Development of the Number Field Sieve
    • Springer-Verlag
    • A.K. Lenstra, H.W. Lenstra, The Development of the Number Field Sieve, Lecture Note in Math., Vol. 1554, Springer-Verlag, 1993.
    • (1993) Lecture Note in Math , vol.1554
    • Lenstra, A.K.1    Lenstra, H.W.2
  • 11
    • 84966243285 scopus 로고
    • Modular Multiplication without Trial Division
    • P. Montgomery, Modular Multiplication without Trial Division, Mathematics of Computation, No. 44(170), pp. 519-521, 1985.
    • (1985) Mathematics of Computation , Issue.44 170 , pp. 519-521
    • Montgomery, P.1
  • 12
    • 84968484435 scopus 로고
    • Speeding the Pollard and elliptic curve methods of factorization
    • P. Montgomery, Speeding the Pollard and elliptic curve methods of factorization, Mathematics of Computation, 48(177), pp. 243-264, 1987.
    • (1987) Mathematics of Computation , vol.48 , Issue.177 , pp. 243-264
    • Montgomery, P.1
  • 13
    • 0029226591 scopus 로고
    • Simplifying Quotient Determination in High-Radix Modular Multiplication
    • H. Orup, Simplifying Quotient Determination in High-Radix Modular Multiplication, ARITH-12, IEEE, pp. 193-199, 1995.
    • (1995) ARITH-12, IEEE , pp. 193-199
    • Orup, H.1
  • 15
    • 0000091764 scopus 로고    scopus 로고
    • A tale of Two Sieves
    • C. Pomerance, A tale of Two Sieves, Notices of the AMS, pp. 1473-1485, 1996.
    • (1996) Notices of the AMS , pp. 1473-1485
    • Pomerance, C.1
  • 16
    • 0017930809 scopus 로고
    • for Obtaining Digital Signatures and Public-Key Cryptosystems
    • R.L. Rivest, A. Shamir, L.M. Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, Communications of the ACM, Vol. 21, No. 2, pp. 120-126, 1978.
    • (1978) Communications of the ACM , vol.21 , Issue.2 , pp. 120-126
    • Rivest, R.L.1    Shamir, A.2    Adleman, L.M.3    Method, A.4
  • 17
    • 47349091274 scopus 로고    scopus 로고
    • SHARCS'05, Workshop on Special Purpose Hardware for Attacking Cryptographic Systems, Paris, 2005.
    • SHARCS'05, Workshop on Special Purpose Hardware for Attacking Cryptographic Systems, Paris, 2005.
  • 18
    • 34648844291 scopus 로고    scopus 로고
    • Modular exponentiation using parallel multipliers
    • IEEE, pp
    • S.H. Tang, K.S. Tsui, P.H.W. Leong, Modular exponentiation using parallel multipliers, FPT'03, IEEE, pp. 52-59, 2004.
    • (2004) FPT'03 , pp. 52-59
    • Tang, S.H.1    Tsui, K.S.2    Leong, P.H.W.3
  • 19
    • 84944900219 scopus 로고    scopus 로고
    • Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli
    • CTRSA' 02, Springer
    • C.D. Walter, Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli, CTRSA' 02, LNCS 2271, pp. 30-39, Springer, 2002.
    • (2002) LNCS , vol.2271 , pp. 30-39
    • Walter, C.D.1
  • 20
    • 33746698935 scopus 로고    scopus 로고
    • 20 years of ECM
    • ANTS VII, Springer, pp
    • P. Zimmermann, B. Dodson, 20 years of ECM, ANTS VII, LNCS 4076, Springer, pp. 525-542, 2006.
    • (2006) LNCS , vol.4076 , pp. 525-542
    • Zimmermann, P.1    Dodson, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.