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Title of Journal: J Cryptol

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Abbravation: Journal of Cryptology

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Springer US

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DOI

10.1016/0165-5876(91)90014-3

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1432-1378

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Jacobian Coordinates on Genus 2 Curves

Authors: Huseyin Hisil Craig Costello
Publish Date: 2016/03/15
Volume: 30, Issue: 2, Pages: 572-600
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Abstract

This paper presents a new projective coordinate system and new explicit algorithms which together boost the speed of arithmetic in the divisor class group of genus 2 curves The proposed formulas generalize the use of Jacobian coordinates on elliptic curves and their application improves the speed of performing cryptographic scalar multiplications in Jacobians of genus 2 curves over prime fields by an approximate factor of 125x For example on a single core of an Intel Core i73770 Ivy Bridge we show that replacing the previous best formulas with our new set improves the cost of generic scalar multiplications from 239000 to 192000 cycles and drops the cost of specialized GLVstyle scalar multiplications from 155000 to 123000 cyclesWe thank Joppe Bos Michael Naehrig Benjamin Smith and Osmanbey Uzunkol for their useful comments on an early draft of this work We also thank the anonymous Asiacrypt 2014 referees for their valuable comments and Patrick Longa for independently benchmarking our code on different processors

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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. On the Amortized Complexity of Zero-Knowledge Protocols
  6. On the Efficient Generation of Prime-Order Elliptic Curves
  7. Sequential Aggregate Signatures, Multisignatures, and Verifiably Encrypted Signatures Without Random Oracles
  8. Accelerating Pollard’s Rho Algorithm on Finite Fields
  9. The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes—Okamoto—Vanstone Algorithm
  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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