Cryptanalysis of Two Sparse Polynomial Based Public Key Cryptosystems
The application of sparse polynomials in cryptography has been studied recently. A public key encryption scheme EnRoot  and an identification scheme SPIFI  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  after Schnorr pointed out some weakness in its initial version. Unfortunately, the modi fied SPIFI is still insecure. The same holds for the generalization of EnRoot proposed in .
- 1.W. Banks, D. Lieman and I. Shparlinski, “An Identification Scheme Based on Sparse Polynomials”, in Proceedings of PKC’2000, LNCS 1751, Springer-Verlag, pp. 68–74, 2000.Google Scholar
- 2.W. Banks, D. Lieman and I. Shparlinski, “Cryptographic Applications of Sparse Polynomials over Finite Rings”, to appear in ICISC’2000.Google Scholar
- 4.D. Grant, K. Krastev, D. Lieman and I. Shparlinski, “A Public Key Cryptosystem Based on Sparse Polynomials”, in Proceedings of an International Conference on Coding Theory, Cryptography and Related Areas, LNCS, Springer-Verlag, pp. 114–121, 2000.Google Scholar
- 5.J. Hoffstein, D. Lieman and J. H. Silverman, “Polynomial Rings and Efficient Public Key Authentication”, Proceedings of the International Workshop on Cryptographic Techniques and E-Commerce, pp. 7–19, M. Blum and C. H. Lee, eds., July 5-8, 1999, Hong Kong. At the time of writing also available at the URL http://www.ntru.com/technology/tech.technical.htm.
- 6.J. Hoffstein, J. Pipher and J. H. Silverman, “NTRU: A Ring Based Public Key System”, Proceedings of ANTS III, Porland (1998), Springer-Verlag.Google Scholar
- 7.V. Miller, “Uses of Elliptic Curves in Cryptography”, in Advances in Cryptology-Crypto’85, LNCS 218, Springer-Verlag, pp. 417–426, 1986.Google Scholar