메뉴 건너뛰기




Volumn 3, Issue 4, 2003, Pages 317-344

Shor's discrete logarithm quantum algorithm for elliptic curves

Author keywords

Discrete logarithm; Elliptic curves; Quantum computation

Indexed keywords

GEOMETRY; QUANTUM COMPUTERS; QUANTUM THEORY;

EID: 0141457783     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (186)

References (29)
  • 1
    • 85115374351 scopus 로고
    • Algorithms for Quantum Computation: Discrete Logarithms and Factoring
    • IEEE Press, Nov. quant-ph/9508027
    • P. Shor, Algorithms for Quantum Computation: Discrete Logarithms and Factoring, Proc. 35th Annual Symposium on Foundations of Computer Science. IEEE Press, pp 124-134, Nov. 1994, quant-ph/9508027
    • (1994) Proc. 35th Annual Symposium on Foundations of Computer Science , pp. 124-134
    • Shor, P.1
  • 2
    • 33645002788 scopus 로고
    • Factoring with cubic integers
    • The Development of the Number Field Sieve
    • J. Pollard, Factoring with cubic integers, in The Development of the Number Field Sieve, Vol. 1554 of Lecture Notes in Math. (1993)
    • (1993) Lecture Notes in Math. , vol.1554
    • Pollard, J.1
  • 3
    • 0001637933 scopus 로고    scopus 로고
    • J. Pollard, BIT 15 (1975), p.331, also Knuth [22], Vol. 2, p.385
    • (1975) BIT] , vol.15 , pp. 331
    • Pollard, J.1
  • 4
    • 0001637933 scopus 로고    scopus 로고
    • 22
    • J. Pollard, BIT 15 (1975), p.331, also Knuth [22], Vol. 2, p.385
    • , vol.2 , pp. 385
    • Knuth1
  • 5
    • 0141642064 scopus 로고    scopus 로고
    • Circuit for Shor's algorithm using 2n+3 qubits
    • also quant-ph/0205095
    • S. Beauregard, Circuit for Shor's algorithm using 2n+3 qubits, Quantum Information and Computation, Vol. 3, No. 2 (2003) pp. 175-185, (also quant-ph/0205095)
    • (2003) Quantum Information and Computation , vol.3 , Issue.2 , pp. 175-185
    • Beauregard, S.1
  • 9
    • 0141709048 scopus 로고    scopus 로고
    • US standard FIPS 186-2 (curves are in appendix 6)
    • US standard FIPS 186-2 (curves are in appendix 6) see e.g. http://csrc.nist.gov/publications/fips/
  • 11
    • 33746688531 scopus 로고    scopus 로고
    • Quantum Algorithms and the Fourier Transform
    • also quant-ph/9707033
    • R. Jozsa, Quantum Algorithms and the Fourier Transform, Proc. R. Soc. Lond. A (1998) 454, pp.323-337, (also quant-ph/9707033)
    • (1998) Proc. R. Soc. Lond. A , vol.454 , pp. 323-337
    • Jozsa, R.1
  • 13
    • 84919085619 scopus 로고
    • An improved algorithm for computing logarithms over GF(p) and its cryptographic significance
    • S.C. Pohlig and M.E. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance, IEEE Transactions on Information Theory, 24 (1978), 106-110.
    • (1978) IEEE Transactions on Information Theory , vol.24 , pp. 106-110
    • Pohlig, S.C.1    Hellman, M.E.2
  • 14
    • 0034505623 scopus 로고    scopus 로고
    • An Improved Quantum Fourier Transform Algorithm and Applications
    • S. Hallgren and L. Hales, An Improved Quantum Fourier Transform Algorithm and Applications, FOCS 2000, (also available at http://wvw.cs.caltech.edu/̃hallgren/)
    • (2000) FOCS
    • Hallgren, S.1    Hales, L.2
  • 19
    • 33746708722 scopus 로고    scopus 로고
    • Quantum Algorithms revisited
    • also quant-ph/9708016
    • R. Cleve et. al., Quantum Algorithms revisited, Proc. R. Soc. Lond. A (1998) 454, p.339, (also quant-ph/9708016)
    • (1998) Proc. R. Soc. Lond. A , vol.454 , pp. 339
    • Cleve, R.1
  • 20
    • 0001260174 scopus 로고    scopus 로고
    • Semiclassical Fourier Transform for Quantum Computation
    • also quant-ph/9511007
    • R.B. Griffiths and C.-S. Niu Semiclassical Fourier Transform for Quantum Computation, Phys.Rev.Lett. 76 (1996) pp.3228-3231 (also quant-ph/9511007)
    • (1996) Phys.Rev.Lett. , vol.76 , pp. 3228-3231
    • Griffiths, R.B.1    Niu, C.-S.2
  • 25
    • 0002290603 scopus 로고
    • On the average length of a class of finite continued fraction
    • Papers in Honor of Edmund Landau, Plenum, New York
    • H. Heilbronn, On the average length of a class of finite continued fraction, in Number Theory and Analysis (Papers in Honor of Edmund Landau), pp. 87-96, Plenum, New York, 1969.
    • (1969) Number Theory and Analysis , pp. 87-96
    • Heilbronn, H.1
  • 28
    • 0141597344 scopus 로고    scopus 로고
    • http://www.rsasecurity.com/rsalabs/challenges/index.html
  • 29
    • 0141485716 scopus 로고    scopus 로고
    • http://www.certicom.com/research/ecc_challenge.html


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.