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Volumn 9, Issue 7-8, 2009, Pages 0610-0621

An O(m2)-depth quantum algorithm for the elliptic curve discrete logarithm problem over GF(2m)

Author keywords

Cryptography; Elliptic Curve Discrete Logarithm Problem; Quantum Algorithms; Quantum Circuits

Indexed keywords

CRYPTOGRAPHY; MULTIPLYING CIRCUITS; POLYNOMIAL APPROXIMATION; QUANTUM THEORY;

EID: 67651151227     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (29)

References (23)
  • 1
    • 0027614379 scopus 로고    scopus 로고
    • 155). IEEE Journal on Selected Areas in Communications, 11(5):804-813, 1993.
    • 155). IEEE Journal on Selected Areas in Communications, 11(5):804-813, 1993.
  • 2
    • 23744498598 scopus 로고    scopus 로고
    • Quantum arithmetic on Galois fields
    • arXiv:quant-ph/0301163
    • S. Beauregard, G. Brassard, and J. M. Fernandez. Quantum arithmetic on Galois fields. arXiv:quant-ph/0301163, 2003.
    • (2003)
    • Beauregard, S.1    Brassard, G.2    Fernandez, J.M.3
  • 6
    • 33746688531 scopus 로고    scopus 로고
    • Quantum algorithms and the Fourier transform
    • R. Jozsa. Quantum algorithms and the Fourier transform. Proc. R. Soc. Lond. A, 454:323-337, 1998.
    • (1998) Proc. R. Soc. Lond. A , vol.454 , pp. 323-337
    • Jozsa, R.1
  • 7
    • 23744513194 scopus 로고    scopus 로고
    • Optimized quantum implementation of elliptic curve arithmetic over binary fields
    • P. Kaye. Optimized quantum implementation of elliptic curve arithmetic over binary fields. Quantum Information and Computation, 5(6):474-491, 2005.
    • (2005) Quantum Information and Computation , vol.5 , Issue.6 , pp. 474-491
    • Kaye, P.1
  • 8
    • 52649132608 scopus 로고    scopus 로고
    • Shor's algorithm, on a nearest-neighbor machine
    • September, arXiv:quant-ph/0609001
    • S. A. Kutin, Shor's algorithm, on a nearest-neighbor machine. Asian conference on Quantum Information Science, pp. 12-13, September 2007, arXiv:quant-ph/0609001.
    • (2007) Asian conference on Quantum Information Science , pp. 12-13
    • Kutin, S.A.1
  • 10
    • 85111345881 scopus 로고    scopus 로고
    • m). Proceedings of the Sixth Symposium on Applied Algebra, Algebraic Algorithms, and Error Correcting Codes, 6:297-309, 1988.
    • m). Proceedings of the Sixth Symposium on Applied Algebra, Algebraic Algorithms, and Error Correcting Codes, 6:297-309, 1988.
  • 13
    • 26944450951 scopus 로고    scopus 로고
    • Fast quantum modular exponentiation
    • R. Van Meter and K. M. Itoh. Fast quantum modular exponentiation. Physical Review A, 71:052320, 2005.
    • (2005) Physical Review A , vol.71 , pp. 052320
    • Van Meter, R.1    Itoh, K.M.2
  • 15
    • 67651188032 scopus 로고    scopus 로고
    • NSA Suite B Factsheet. http://www.nsa.gov/ia/industry/crypto-suite-b.cfm.
    • NSA Suite B Factsheet
  • 16
    • 0017949441 scopus 로고
    • A theory of Galois switching functions
    • D. K. Pradhan. A theory of Galois switching functions. IEEE Transactions on Computers, 27:239-248, 1978.
    • (1978) IEEE Transactions on Computers , vol.27 , pp. 239-248
    • Pradhan, D.K.1
  • 17
    • 0141457783 scopus 로고    scopus 로고
    • Shor's discrete logarithm quantum algorithm for elliptic curves
    • J. Proos and C. Zalka. Shor's discrete logarithm quantum algorithm for elliptic curves. Quantum Information and Computation, 3:317-344, 2003.
    • (2003) Quantum Information and Computation , vol.3 , pp. 317-344
    • Proos, J.1    Zalka, C.2
  • 18
    • 3242725230 scopus 로고    scopus 로고
    • m). IEEE Transactions on Computers, 53:945-959, 2004.
    • m). IEEE Transactions on Computers, 53:945-959, 2004.
  • 19
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal of Computing, 26:1484-1509, 1997.
    • (1997) SIAM Journal of Computing , vol.26 , pp. 1484-1509
    • Shor, P.W.1
  • 21
    • 67651182584 scopus 로고    scopus 로고
    • Elliptic Curve Cryptography: The next generation of wireless security
    • April 23
    • S. A. Vanstone. Elliptic Curve Cryptography: The next generation of wireless security. Markt and Technik, 17:20-23, April 23, 2004.
    • (2004) Markt and Technik , vol.17 , pp. 20-23
    • Vanstone, S.A.1
  • 22
    • 67651185561 scopus 로고    scopus 로고
    • J. Von Zur Gathen and J. Gerhard, Modern Computer Algebra. Cambridge University Press, 1999.
    • J. Von Zur Gathen and J. Gerhard, Modern Computer Algebra. Cambridge University Press, 1999.
  • 23
    • 85111345079 scopus 로고    scopus 로고
    • 2 - 1.
    • 2 - 1.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.