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Title of Journal: J Cryptology

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Abbravation: Journal of Cryptology

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Springer-Verlag

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1432-1378

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The Improbability That an Elliptic Curve Has Subex

Authors: R Balasubramanian Neal Koblitz
Publish Date: 1998/03/01
Volume: 11, Issue: 2, Pages: 141-145
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Abstract

The security of elliptic curve cryptosystems is based on the presumed intractability of the discrete logarithm problem on the curve Other than algorithms that work in an arbitrary group and are exponential in the general case the only generalpurpose algorithm that has ever been proposed for the elliptic curve discrete logarithm is that of Menezes—Okamoto—Vanstone MOV The MOV algorithm which embeds an elliptic curve group of prime order l in the multiplicative group of a field F qk is subexponential only under special circumstances however In this paper we first prove that under a mild condition that always holds in practical applications the condition that lq k 1 which is obviously necessary for realizing the MOV algorithm is also sufficient We next give an improved upper bound for the frequency of occurrence of pairs of primes l p such that lp k 1 for k small where l is in the Hasse interval p+12sqrtpp+1+2sqrtp

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Other Papers In This Journal:
  1. Handling Expected Polynomial-Time Strategies in Simulation-Based Security Proofs
  2. Resource Requirements of Private Quantum Channels and Consequences for Oblivious Remote State Preparation
  3. Formal Proofs for the Security of Signcryption
  4. Concurrent Knowledge Extraction in Public-Key Models
  5. Jacobian Coordinates on Genus 2 Curves
  6. On the Amortized Complexity of Zero-Knowledge Protocols
  7. On the Efficient Generation of Prime-Order Elliptic Curves
  8. Sequential Aggregate Signatures, Multisignatures, and Verifiably Encrypted Signatures Without Random Oracles
  9. Accelerating Pollard’s Rho Algorithm on Finite Fields
  10. Constant-Round Oblivious Transfer in the Bounded Storage Model
  11. The Discrete Logarithm Problem on Elliptic Curves of Trace One
  12. Short Signatures from Diffie–Hellman: Realizing Almost Compact Public Key
  13. Integral Cryptanalysis on Full MISTY1
  14. Integral Cryptanalysis on Full MISTY1
  15. Universally Composable Symbolic Security Analysis
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