FPGA based Hardware Accleration for Elliptic Curve Cryptography ...

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BIBLIOGRAPHY 33 [15] J. Lopez and R. Dahab, “Improved algorithms for elliptic curve arithmetic in „ n% ,” Selected Areas in Cryptography (SAC’98), LNCS 1556, Springer-Verlag, pp. 201–212, 1998. [16] S. Okada, N. Torii, K. Itoh and M. Takenaka, “Implementation of Elliptic Curve Cryptographic Coprocessor over on an FPGA ,” Workshop on Cryptographic Hardware and Embedded Systems (CHES 2000), LNCS 1965, C.K. Koc and C. Paar Eds., Springer-Verlag, pp.25–40, 2000. [17] A. Karatsuba and Y. Ofman, “Multiplication of multidigit numbers on automata,” Sov. Phys.-Dokl (Engl. transl.), vol. 7, no. 7, pp. 595-596, 1963. [18] D. V. Bailey and C. Paar, “Efficient Arithmetic in Finie Field Extensions with Application in Elliptic Curve Cryptography,” Journal of Cryptology, vol. 14, no. 3, pp. 153–176, 2001. [19] J. L. Bentley, D. Haken and J. B. Saxe, “A general method for solving divide-and-conquer recurrences,” SIGACT News, vol. 12(3), pp. 36–44, 1980. [20] M. Rosing, “Implementing Elliptic Curve Cryptogarphy,” Manning Publications Co., ISBN 1- 884777-69-4, Greenwich, 1999. [21] Silicon Software, “microEnable Users Guide,” 1999. [22] Alpha Data Parallel Systems Ltd., “ADC-PMC-64 User Manual”, Ver. 1.1, 2002. [23] J. Lopez and R. Dahab, “Fast multiplication on elliptic curves over „ n*ô without precomputation,” Workshop on Cryptographic Hardware and Embedded Systems (CHES 99), LNCS 1717, C.K. Koc and C. Paar Eds., Springer-Verlag, pp. 316–327, 1999. [24] M. Ernst, M. Jung, F. Madlener, S. Huss and R. Bluemel, “A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over- ,” Workshop on Cryptographic Hardware and Embedded Systems (CHES 2002), Springer-Verlag, 2002.
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Page 1 and 2: Fachbereich Informatik Integrierte
Page 3 and 4: Contents List of Figures iv 1 Intro
Page 5 and 6: List of Figures c)! #"%$ d)& #"'$ 2
Page 7 and 8: 1.2. PREVIOUS WORK 2 of dividing a
Page 9 and 10: Chapter 2 Mathematical Background T
Page 11 and 12: Ymonpn _ #qkr9;=stPuiY[ v l _ wr9xK
Page 13 and 14: 2.2. FINITE FIELD ARITHMETIC 8 k P
Page 15 and 16: 2.2.4 Addition in-·‰¸º¹ » 2
Page 17 and 18: Ì Ì Ì Ì Ì Ì Ì Ì Ì Ì Ì Ì
Page 19 and 20: 2.3. SEQUENTIAL MULTIPLICATION SCHE
Page 21 and 22: 6 v |!6 v 3 5 3 î 8 ¾ v Yg5 î 8
Page 23 and 24: 2.3. SEQUENTIAL MULTIPLICATION SCHE
Page 25 and 26: 3.2. REGISTER FILE 20 3.2 Register
Page 27 and 28: 3.4. FINITE FIELD ARITHMETIC 22 3.4
Page 29 and 30: Ì Ì Ì Ì Ì 3.4. FINITE FIELD AR
Page 31 and 32: 3.6. EVALUATION SOFTWARE 26 used fo
Page 33 and 34: 4.2. XILINX XCV405E 28 implementati
Page 35 and 36: Chapter 5 Conclusions and Outlook 5
Page 37: Bibliography [1] National Institute
Page 41: 3 m°e'Ỹ %jijY l Y Ym°5 l l $ƒm

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