Analysis of the errors in the recent attacks on DSA and ECDSA using lattice theory
Abstract - Recently, in the attacks on DSA and ECDSA which based on the lattice have some new results that are published by Poulakis in [1, 2] and Draziotis in [3]. However, these papers still have some of the errors in the numerical computation examples, the definitions, and the feasibility of the attack. Namely, Poulakis [1] has an error in the numerical computation example. Draziotis [3] incorrectly defines polynomials that construct rows of matrices in the attack. Attack of Poulakis in 2016 [2] is less feasible and the numerical computation example on this paper is incorrect. We discussed with Poulakis and Draziotis about the above errors. They recognized these errors. The computationally verifiable results have made on the MAGMA Algebra Toolkit [4].
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Tài liệu tham khảo [1] D. Poulakis, "Some lattice attacks on DSA and ECDSA," Applicable Algebra in Engineering, Communication, and Computing, vol. 22, no. 5, pp. 347-358, 2011. [2] D. Poulakis, "New lattice attacks on DSA schemes," Journal of Mathematical Cryptology, vol. 10, no. 2, pp. 135-144, 2016. [3] K. A. Draziotis, "DSA lattice attacks based on Coppersmith's method," Information Processing Letters, vol. 116, no. 8, pp. 541-545, 2016. [4] J. Cannon, W. Bosma, C. Fieker, and A. Steel, "Handbook of MAGMA functions," Edition, vol. 2, 2006. [5] A. K. Lenstra, H. W. Lenstra, and L. Lovász, "Factoring polynomials with rational coefficients," Mathematische Annalen, vol. 261, no. 4, pp. 515-534, 1982. [6] A. May, "Using LLL-reduction for solving RSA and factorization problems," in The LLL algorithm: Springer, pp. 315-348, 2009. [7] D. Boneh and G. Durfee, "Cryptanalysis of RSA with private key d less than N/sup 0.292," IEEE transactions on Information Theory, vol. 46, no. 4, pp. 1339-1349, 2000. [8] I. F. Blake and T. Garefalakis, "On the security of the digital signature algorithm," Designs, Codes and Cryptography, vol. 26, no. 1, pp. 87-96, 2002. [9] P. Gallagher, "Digital signature standard (DSS)," Federal Information Processing Standards Publications, volume FIPS, pp. 186-3, 2013. [10] I. F. Blake, G. Seroussi, and N. Smart, Elliptic curves in cryptography. Cambridge university press, 1999. [11] K. Draziotis. (2017). DSA lattice attacks based on Coppersmith's method. Available: http://users.auth.gr/drazioti/extension_of_poulakis_11_elsevier.pdf |
Khúc Xuân Thành, Nguyễn Duy Anh, Nguyễn Bùi Cương
