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Efficient computation of full Lucas sequences

Efficient computation of full Lucas sequences

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  • Author(s): M. Joye 1  and  J.-J. Quisquater 2
    • View affiliations
    • Affiliations: 1: Department of Mathematics (AGEL), UCL Crypto Group, University of Louvain, Louvain-la-Neuve, Belgium
      2: Department of Electrical Engineering (DICE), UCL Crypto Group, University of Louvain, Louvain-la-Neuve, Belgium
  • Source: Volume 32, Issue 6, 14 March 1996, p. 537 – 538
    DOI:  10.1049/el:19960359 , Print ISSN 0013-5194, Online ISSN 1350-911X
© IEE
Published

Recently, Yen and Laih (1995) proposed an algorithm to compute LUC digital signatures quickly. This signature is based on a special type of Lucas sequence Vk. The authors generalise their method to any type of Lucas sequence, and extend it to the ‘sister’ Lucas sequence, Uk. As an application, the order of an elliptic curve over GF(2m) is computed quickly.

Inspec keywords: number theory; sequences; cryptography

Other keywords: full Lucas sequences; sequence computation; digital signatures; elliptic curve order

Subjects: Data security; Combinatorial mathematics; Codes; Information theory; Combinatorial mathematics

References

    1. 1)
      • S.M. Yen , C.S. Laih . Common-multiplicand multiplication and its applications to public keycryptography. Electron. Lett. , 17 , 1583 - 1584
    2. 2)
      • C. Batut , D. Bernardi , H. Cohen , M. Olivier . (1995) User's guide to PARI-GP.
    3. 3)
      • H. Riesel . (1985) Prime numbers and computer methods for factorization, Progress in Mathematics.
    4. 4)
      • A.J. Menezes , M. Qu , S. Vanstone . (1995) Draft of IEEE P1363.
    5. 5)
      • P. Ribenboim . (1991) The little book of big primes.
    6. 6)
      • S.-M. Yen , C.-S. Laih . Fast algorithms for LUC digital signature computation. IEE Proc., Comput. Digit. Tech. , 2 , 165 - 169
    7. 7)
      • C. Pomerance , J.L. Selfridge , S.S. Wagstaff . The pseudoprimes to 25·109. Math. Comput. , 151 , 1003 - 1026
    8. 8)
      • A.J. Menezes . (1993) Elliptic curve public key cryptosystems.
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