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By Kenji Koyama, Yukio Tsuruoka, Noboru Kunihiro (auth.), Kwok-Yan Lam, Eiji Okamoto, Chaoping Xing (eds.)

Asiacrypt’99 used to be held in Singapore on 14-18 November 1999. Asiacrypt is likely one of the significant occasions within the cryptology learn neighborhood. Asiacrypt’99, the ?fth annual Asiacrypt convention, was once backed by means of the Asiacrypt steerage Comm- tee and the Centre for platforms safety of the nationwide collage of Singapore, and in cooperation with the foreign organization for Cryptology learn. because the software Co-Chairs of Asiacrypt’99, we're super commemorated to or- nize this occasion, which showcases the state of the art improvement of cryptology learn on the end of this millennium. This 12 months, a complete of ninety six study papers have been submitted to Asiacrypt’99. The portfolio of kingdom of beginning of submissions serves as an exceptional indicator of the - ternational attractiveness of the convention. nations from which submissions or- inated contain: Australia, Belgium, China, Estonia, France, Germany, Greece, India, Iran, Japan, Korea, Norway, Russia, Saudi Arabia, Switzerland, Sin- pore, Spain, Taiwan, Thailand, The Netherlands, Turkey, Ukraine, united kingdom, united states and Yugoslavia. via a stringent refereeing strategy by way of this system C- mittee, 31 papers of remarkable caliber have been authorized and are integrated within the convention complaints. authorised papers have been authored via researchers from the subsequent nations: Australia, Belgium, France, Germany, India, Japan, China, Singapore, Switzerland, Taiwan, The Netherlands, united kingdom, and USA.

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Now we can generate three sets of 2248 weak keys with 2 There is no reason why these two events should be independent. Computer simulations show however that this assumption results in a reasonable approximation. 38 Carl D’Halluin et al. a different number of equivalent keys. The intersections between these three sets are non-empty and contain weak keys with a significant number of equivalent keys. – For the case i = 1 we have KX[84] = e8e10c4d d1eb6c1dx with Hamming weight 32 and the most significant bit is set to 1.

29. This means that the KX-table effectively contains 256 · 64 = 16 384 bits. The KX-table is calculated in four steps. Firstly the table is filled with 256 pseudo-random values. Secondly the user key is XORed into the table. The goal of the stirring function is to make all the 256 entries of the table depend on the user key. Finally the last 30 entries of the table are set equal to the first 30. We discuss these steps in more detail below. 1 Filling the KX-table with Pseudo-random Values The first entries of the KX-table are initialized using three mathematical constants (with sc denoting the sub-cipher number): KX[0] = PI19 + sc (1) KX[1] = E19 * the key length KX[2] = R220 rotated left over sc bits (2) (3) where PI19 = 3141592653589793238d, E19 = 2718281828459045235d, R220 = 14142135623730950488d, sc = 3, and the key length is 128, 192, or 256.

52 8. W. Press, B. Flannery, S. Teukolsky and W. Vetterling, Numerical Recipes in C, 2nd Edition, Cambridge University Press, Cambridge, 1988. 59 9. M. A. Vanstone, ‘New public-key cryptosystems based on factorizations of finite groups’, presented at AUSCRYPT ‘92. 52 Cryptanalysis of Two Cryptosystems Based on Group Actions 61 10. M. A. Vanstone, ‘The knapsack problem in cryptography’ in Finite fields: Theory, Applications, and Algorithms, Contemporary Mathematics Vol. 168, American Mathematical Society, 1994, pp.

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