Advances in Cryptology - ASIACRYPT’99: International by Kenji Koyama, Yukio Tsuruoka, Noboru Kunihiro (auth.),

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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 study neighborhood. Asiacrypt’99, the ?fth annual Asiacrypt convention, was once backed via the Asiacrypt steerage Comm- tee and the Centre for structures safeguard of the nationwide collage of Singapore, and in cooperation with the foreign organization for Cryptology learn. because the application Co-Chairs of Asiacrypt’99, we're super venerated to or- nize this occasion, which showcases the cutting-edge improvement of cryptology examine on the end of this millennium. This 12 months, a complete of ninety six examine papers have been submitted to Asiacrypt’99. The portfolio of kingdom of beginning of submissions serves as a great indicator of the - ternational acceptance of the convention. nations from which submissions or- inated comprise: 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 method via this system C- mittee, 31 papers of remarkable caliber have been accredited and are incorporated within the convention complaints. authorized papers have been authored by means of researchers from the next nations: Australia, Belgium, France, Germany, India, Japan, China, Singapore, Switzerland, Taiwan, The Netherlands, united kingdom, and USA.

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Additional info for Advances in Cryptology - ASIACRYPT’99: International Conference on the Theory and Application of Cryptology and Information Security, Singapore, November 14-18, 1999. Proceedings

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2 Background Both the Yamamura cryptosystems are based on properties of the group SL2 (Z) of 2 × 2 integer matrices of determinant 1 under multiplication. This section summarises properties of this group that we will need. Define matrices A, B ∈ SL2 (Z) by A= 1 −1 1 0 and B= 0 −1 1 0 . It is well known that these matrices generate SL2 (Z). It is easy to check that A3 = B 2 = −I, where I is the 2 × 2 identity matrix. 4] for any facts about amalgamated free products that we use. The theory of amalgamated free products shows that each element g ∈ SL2 (Z) has a unique representation as an element in ‘normal form’.

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.

Memon, ‘Algebraic properties of cryptosystem PGM’, J. Cryptology, Vol. 5 (1992), pp. 167-183. 52 7. P. Nguyen and J. S. Kaliski (Ed) Advances in Cryptology — CRYPTO ’97, Lecture Notes in Computer Science 1294, Springer, Berlin, 1997, pp. 198-212. 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.

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