Abstract
In this paper we will compare two signature schemes proposed by different sets of authors. One is the XTR-Nyberg-Rueppel signature proposed by A.K. Lenstra and E.R. Verheul in [3] and the other is the signature scheme proposed by C.H. Tan, X. Yi and C.K. Siew (We will call it TYS signature.) in [9]. XTR-NR signature uses the third degree trace projection Tr : GF(p 6) → GF(p 2) and has been generalized in [8] by Lim et. al. as a scheme in GF(p 6m) using Tr : GF(p 6m) → GF(p 2m). On the other hand, TYS signature is based on a third order LFSR. Tan et. al. claimed that TYS signature is as secure as Schnorr signature scheme. We will explain why these two schemes are essentially the same. In addition, we will point out that TYS signature as it is has some flaws in their arguments. We will show that in order to cure the flaws of TYS signature, one should bring in exactly the same security and efficiency consideration of XTR scheme as in [8].
Yie and Kim’s work was supported by Basic Science Research Institute Program, Korea Research Foundation 1998-015-D00017.
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References
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Chik How Tan, Xun Yi and Chee Kheong Siew, Signature Schemes Based on 3rd Order Shift Registers, ACISP’01, LNCS 2119 (2001), pp.445–459.
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Lim, S., Kim, S., Yie, I., Kim, J. (2001). Comments on a Signature Scheme Based on the Third Order LFSR Proposed at ACISP2001. 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_29
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DOI: https://doi.org/10.1007/3-540-45311-3_29
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