IKBFU's Vestnik

2015 Issue №04

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An analysis of the resistance of McEliece CS based on an AG-code to quantum Fourier sampling attack

Pages
120-124

Abstract

This article tests the quantum resistance of McEliece CS based on an AG-code over any elliptic curve. Using the criteria suggested by Dinh, Moore, and Russell [3], the author proves the resistance of this CS to quantum Fourier sampling attack. Thus, Shor’s algorithm cannot identify the group structure of the code and break the CS.

Reference

1. Shor P. W. Algorithms for quantum computation: discrete logarithms and factoring // Found. of Computer Science : Conference Publications. 1994. P. 124—134.
2. McEliece R. J. A public-key cryptosystem based on algebraic coding theory // DSN Progress Report. 1978. № 42—44. P. 114—116.
3. Dinh H., Moore C., Russell A. The McEliece cryptosystem resists quantum Fourier sampling attacks. 2010. URL: http://arxiv.org/abs/1008.2390 (дата обращения: 12.02.2015).
4. Stichtenoth H. On automorphisms of geometric Goppa codes // Journal of Al-gebra. 1990. № 130(1). P. 113—121.
5. Stichtenoth H. Algebraic function fields and codes. Springer, 2008.
6. Silverman J. Arithmetic of elliptic curves. Springer, 2009.