Cryptanalysis of two sparse polynomial basedpublic key cryptosystems

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Abstract

The application of sparse polynomials in cryptography has been studied recently. A public key encryption scheme EnRoot [4] and an identification scheme SPIFI [1] based on sparse polynomials were proposed. In this paper, we show that both of them are insecure. The designers of SPIFI proposed the modified SPIFI [2] after Schnorr pointed out some weakness in its initial version. Unfortunately, the modified SPIFI is still insecure. The same holds for the generalization of EnRoot proposed in.

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Bao, F., Deng, R. H., Geiselmann, W., Schnorr, C., Steinwandt, R., & Wu, H. (2001). Cryptanalysis of two sparse polynomial basedpublic key cryptosystems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1992, pp. 153–164). Springer Verlag. https://doi.org/10.1007/3-540-44586-2_11

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