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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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DOI

10.1007/978-3-0348-8340-5

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1573-7586

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The Diffie–Hellman problem and generalization of V

Authors: Dustin Moody
Publish Date: 2009/04/17
Volume: 52, Issue: 3, Pages: 381-390
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Abstract

Bilinear pairings on elliptic curves have been of much interest in cryptography recently Most of the protocols involving pairings rely on the hardness of the bilinear Diffie–Hellman problem In contrast to the discrete log or Diffie–Hellman problem in a finite field the difficulty of this problem has not yet been much studied In 2001 Verheul Advances in Cryptology—EUROCRYPT 2001 LNCS 2045 pp 195–210 2001 proved that on a certain class of curves the discrete log and Diffie–Hellman problems are unlikely to be provably equivalent to the same problems in a corresponding finite field unless both Diffie–Hellman problems are easy In this paper we generalize Verheul’s theorem and discuss the implications on the security of pairing based systems

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Other Papers In This Journal:
  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  3. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. Point compression for the trace zero subgroup over a small degree extension field
  15. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  16. Improved lower bounds on sizes of single-error correcting codes
  17. A combinatorial problem related to sparse systems of equations
  18. Some results concerning cryptographically significant mappings over GF(2 n )
  19. A note on the reducibility of binary affine polynomials
  20. Primitive normal bases for quartic and cubic extensions: a geometric approach
  21. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  22. Some cyclic codes of length 2 p n
  23. On the correlation distribution of Delsarte–Goethals sequences
  24. Algebraic decoding of folded Gabidulin codes
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications
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