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Volumn 5, Issue 4, 1996, Pages 257-273

Factoring integers with large-prime variations of the quadratic sieve

Author keywords

Cluster of workstations; Factorization; Multiple polynomial quadratic sieve; Vector supercomputer

Indexed keywords


EID: 85023960883     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.1996.10504592     Document Type: Article
Times cited : (7)

References (27)
  • 1
    • 34648812524 scopus 로고
    • Implementing the self-initializing quadratic sieve on a distributed network
    • (NTAMCS '93: Moscow, 1993), edited by A. J. van der Poorten et al., World Scientific, River Edge, NJ
    • W. R. Alford and C. Pomerance, "Implementing the self-initializing quadratic sieve on a distributed network", pp. 163-174 in Number-theoretic and algebraic methods in computer science (NTAMCS '93: Moscow, 1993), edited by A. J. van der Poorten et al., World Scientific, River Edge, NJ, 1995.
    • (1995) Number-Theoretic and Algebraic Methods in Computer Science , pp. 163-174
    • Alford, W.R.1    Pomerance, C.2
  • 2
    • 84955575947 scopus 로고
    • The magic words are squeamish ossifrage
    • edited by J. Pieprzyk and R. Safavi-Naini, Lecture Notes in Comp. Sci. 917, Springer, Berlin
    • D. Atkins, M. Graff, A. K. Lenstra, and P. C. Leyland, "The magic words are squeamish ossifrage", pp. 263-277 in Advances in cryptology (ASIACRYPT '94: Wollongong, 1994), edited by J. Pieprzyk and R. Safavi-Naini, Lecture Notes in Comp. Sci. 917, Springer, Berlin, 1995.
    • (1995) Advances in Cryptology (ASIACRYPT '94: Wollongong, 1994) , pp. 263-277
    • Atkins, D.1    Graff, M.2    Lenstra, A.K.3    Leyland, P.C.4
  • 3
    • 0004219960 scopus 로고
    • Academic Press, London and Orlando, FL
    • B. Bollobás, Random graphs, Academic Press, London and Orlando, FL, 1985.
    • (1985) Random Graphs
    • Bollobás, B.1
  • 4
    • 0039851334 scopus 로고    scopus 로고
    • Technical Report NM-R9212, Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands, June 1992. Updates to this report have appeared as CWI Report NMR9419, September 1994 and CWI Report NMR9609, March 1996, with P. L. Montgomery as a coauthor. The complete tables, incorporating these updates, are available
    • n ± 1, 13 ≤ a < 100", Technical Report NM-R9212, Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands, June 1992. Updates to this report have appeared as CWI Report NMR9419, September 1994 and CWI Report NMR9609, March 1996, with P. L. Montgomery as a coauthor. The complete tables, incorporating these updates, are available at ftp://nimbus.anu.edu.au/pub/Brent/factorsorftp://ftp.cwi.nl/pub/herman/factors.
    • n ± 1, 13 ≤ a < 100
    • Brent, R.P.1    Te Riele, H.J.J.2
  • 14
    • 0003638131 scopus 로고
    • The development of the number field sieve
    • Springer, Berlin
    • A. K. Lenstra and H. W. Lenstra Jr. (editors), The development of the number field sieve, Lecture Notes in Math. 1554, Springer, Berlin, 1993.
    • (1993) Lecture Notes in Math , vol.1554
    • Lenstra, A.K.1    Lenstra, H.W.2
  • 15
    • 84968499118 scopus 로고
    • Factoring with two large primes
    • A. K. Lenstra and M. S. Manasse, "Factoring with two large primes", Math. Comp. 63 (1994), 785-798.
    • (1994) Math. Comp , vol.63 , pp. 785-798
    • Lenstra, A.K.1    Manasse, M.S.2
  • 16
    • 84966219731 scopus 로고
    • A method of factoring and the factorization of F7"
    • M. A. Morrison and J. Brillhart, "A method of factoring and the factorization of F7", Math. Comp. 29 (1975), 183-205.
    • (1975) Math. Comp , vol.29 , pp. 183-205
    • Morrison, M.A.1    Brillhart, J.2
  • 17
    • 0021470978 scopus 로고
    • A compact algorithm for Gaussian elimination over GF(2) implemented on highly parallel computers
    • D. Parkinson and W. Wunderlich, "A compact algorithm for Gaussian elimination over GF(2) implemented on highly parallel computers", Parallel Comput. 1 (1984), 65-73.
    • (1984) Parallel Comput , vol.1 , pp. 65-73
    • Parkinson, D.1    Wunderlich, W.2
  • 18
    • 0014567146 scopus 로고
    • An algorithm for finding a fundamental set of cycles of a graph
    • K. Paton, "An algorithm for finding a fundamental set of cycles of a graph", Comm. ACM 12 (1969), 514-518.
    • (1969) Comm. ACM , vol.12 , pp. 514-518
    • Paton, K.1
  • 20
    • 0005599967 scopus 로고
    • Analysis and comparison of some integer factoring algorithms
    • H. W. Lenstra, Jr. and R. Tijdeman, Mathematisch Centrum, Amsterdam
    • C. Pomerance, "Analysis and comparison of some integer factoring algorithms", pp. 89-139 in Computational methods in number theory, I, edited by H. W. Lenstra, Jr. and R. Tijdeman, Mathematisch Centrum, Amsterdam, 1982.
    • (1982) Computational Methods in Number Theory , vol.1 , pp. 89-139
    • Pomerance, C.1
  • 21
    • 85027100501 scopus 로고
    • "The quadratic sieve factoring algorithm
    • edited by T. Beth et al., Lecture Notes in Comp. Sci. 209, Springer-Verlag, New York
    • C. Pomerance, "The quadratic sieve factoring algorithm", pp. 169-182 in Advances in cryptology (EUROCRYPT '84: Paris, 1984), edited by T. Beth et al., Lecture Notes in Comp. Sci. 209, Springer-Verlag, New York, 1985.
    • (1985) Advances in Cryptology (EUROCRYPT '84: Paris, 1984) , pp. 169-182
    • Pomerance, C.1
  • 22
    • 0023984995 scopus 로고
    • A pipeline architecture for factoring large integers with the quadratic sieve algorithm
    • C. Pomerance, J. W. Smith, and R. Tuler, "A pipeline architecture for factoring large integers with the quadratic sieve algorithm", SIAM J. Comput. 17 (1988), 387-403.
    • (1988) SIAM J. Comput , vol.17 , pp. 387-403
    • Pomerance, C.1    Smith, J.W.2    Tuler, R.3
  • 23
    • 0024731663 scopus 로고
    • Factoring with the quadratic sieve on large vector computers
    • H. J. J. te Riele, W. M. Lioen, and D. T. Winter, "Factoring with the quadratic sieve on large vector computers", J. Comp. Appl. Math. 27 (1989), 267-278.
    • (1989) J. Comp. Appl. Math , vol.27 , pp. 267-278
    • Te Riele, H.J.J.1    Lioen, W.M.2    Winter, D.T.3
  • 24
    • 0040444227 scopus 로고    scopus 로고
    • Factorization beyond the googol with MPQS on a single computer
    • (March 1991)
    • H. te Riele, W. Lioen, and D. Winter, "Factorization beyond the googol with MPQS on a single computer", CWI Quarterly 4 (March 1991), 69-72.
    • CWI Quarterly , vol.4 , pp. 69-72
    • Te Riele, H.1    Lioen, W.2    Winter, D.3
  • 25
    • 0003226380 scopus 로고
    • Prime numbers and computer methods for factorization
    • Birkhsuser, Boston
    • H. Riesel, Prime numbers and computer methods for factorization, Progress in Math. 126, Birkhsuser, Boston, 1985.
    • (1985) Progress in Math , vol.126
    • Riesel, H.1
  • 26
    • 84968510096 scopus 로고
    • The multiple polynomial quadratic sieve
    • R. D. Silverman, "The multiple polynomial quadratic sieve", Math. Oomp. 48 (1987), 329-339.
    • (1987) Math. Oomp , vol.48 , pp. 329-339
    • Silverman, R.D.1
  • 27
    • 85023906373 scopus 로고
    • December 13, Regular letter to subscribers describing the state of the Cunningham factorization project
    • S. S. Wagstaff Jr., December 13, 1993. Regular letter to subscribers describing the state of the Cunningham factorization project.
    • (1993)
    • Wagstaff, S.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.