Abstract
XTR cryptosystem makes use of an irreducible polynomial F(c, x) = x 3 - cx 2 + c p x - 1 over a finite field \( \mathbb{F}_{\mathcal{P}^2 } \). In this paper, we develop a new method to generate such an irreducible polynomial. Our method requires only computations of Jacobi symbols and thus improves those given [1], [2] and [3].
This paper was supported by the Basic Research Institute Program, Korea Research Foundation, 2000-015-DP0006.
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References
A. K. Lenstra, E. R. Verheul: The XTR public key system. Proceedings of Crypto 2000, LNCS 1880, Springer-Verlag (2000) 1–19
A. K. Lenstra, E. R. Verheul: Key improvements to XTR, Proceedings of Asiacrypt 2000, LNCS 1976, Springer-Verlag (2000) 220–233
A. K. Lenstra, E. R. Verheul: Fast irreducibility and subgroup membership testing in XTR, Proceedings of PKC 2001, LNCS 1992,l Springer-Verlag (2001) 73–86
A. K. Lenstra, E. R. Verheul: An overview of the XTR public key system, Proceedings of the Eurocrypto 2001, LNCS, Springer-Verlag ( to appear)
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Kim, J.M., Yie, I., Oh, S.I., Kim, H.D., Ryu, J. (2001). Fast Generation of Cubic Irreducible Polynomials for XTR. In: Rangan, C.P., Ding, C. (eds) Progress in Cryptology — INDOCRYPT 2001. INDOCRYPT 2001. Lecture Notes in Computer Science, vol 2247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45311-3_7
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DOI: https://doi.org/10.1007/3-540-45311-3_7
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