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Sieve Method for Polynomial Linear Equivalence

Author

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  • Baocang Wang
  • Yupu Hu

Abstract

We consider the polynomial linear equivalence (PLE) problem arising from the multivariate public key cryptography, which is defined as to find an invertible linear transformation โ„’ satisfying ๐’ซ = ๐’ฎโˆ˜โ„’ for given nonlinear polynomial maps ๐’ซ and ๐’ฎ over a finite field ๐”ฝq. Some cryptographic and algebraic properties of PLE are discussed, and from the properties we derive three sieves called multiplicative, differential, and additive sieves. By combining the three sieves, we propose a sieve method for the PLE problem. As an application of our sieve method, we show that it is infeasible to construct public key encryption schemes from the PLE problem.

Suggested Citation

  • Baocang Wang & Yupu Hu, 2013. "Sieve Method for Polynomial Linear Equivalence," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:872962
    DOI: 10.1155/2013/872962
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    References listed on IDEAS

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    1. Ping Wang & Fangguo Zhang, 2012. "An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollardโ€ฒs Rho," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Ping Wang & Fangguo Zhang, 2012. "An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollard's Rho," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, January.
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