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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 Discrete Logarithm Problem on Elliptic Curves

Authors: N P Smart
Publish Date: 1999/10/01
Volume: 12, Issue: 3, Pages: 193-196
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Abstract

In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves whose group orders are equal to the order of the finite field

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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. The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes—Okamoto—Vanstone Algorithm
  11. Constant-Round Oblivious Transfer in the Bounded Storage Model
  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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