1 Montgomery Modular Multiplication in Hard- ware

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FEI KEMT [62] Fischer, V., Drutarovsk´y, M., ˇ Simka, M., and Celle, F. Simple PLL-based True Random Number Generator for Embedded Digital Systems. In Proceedings of IEEE Design and Diagnostics of Electronic Circuits and Systems Workshop – DDECS 2004 (Stará Lesná, Slovakia, Apr. 18–21, 2004), pp. 129–136. [63] Franke, J., and Kleinjung, T. E-mail announcement. http://www.crypto-world.com/announcements/rsa200.txt, May 2005. [64] Franke, J., Kleinjung, T., Paar, C., Pelzl, J., Priplata, C., and Stahlke, C. SHARK — A Realizable Special Hardware Sieving Device for Factoring 1024-bit Integers. In Workshop on Cryptographic Hardware and Embedded Systems — CHES 2005, Edinburgh (August 2005), LNCS, Springer. To appear. [65] Franke, J., Kleinjung, T., Paar, C., Pelzl, J., Priplata, C., ˇ Simka, M., and Stahlke, C. An effcient hardware architecture for factoring integers with the Elliptic Curve Method. In 1st Workshop on Special-purpose Hardware for Attacking Cryptographic Systems – SHARCS 2005 (Paris, France, Feb. 24– 25, 2005), pp. 51–62. [66] Frolek, V. Implementation of asymmetric encryption algorithms in reconfigurable circuits. Master’s thesis, Technical University of Koˇsice, Department of Electronics and Multimedia Communications, Jan.-May 2002. [67] Gaj, K., Kwon, S., Baier, P., Kohlbrenner, P., Le, H., Khaleelud- din, M., and Bachimanchi, R. Implementing the elliptic curve method of factoring in reconfigurable hardware. In Workshop on Special-purpose Hard- ware for Attacking Cryptographic Systems – SHARCS 2006 (Cologne, Ger- many, Apr. 03–04, 2006). [68] Gennaro, R. Randomness in cryptography. IEEE Security and Privacy 4, 2 (2006), 64–67. [69] Goldberg, I., and Wagner, D. Randomness and the Netscape browser. Dr. Dobb’s Journal (Jan. 1996), 66–70. [70] Golic, J. New methods for digital generation and postprocessing of random data. IEEE Transaction on Computers 55, 10 (2006), 1217–1229. 133
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Technical University of Koˇsice Fa
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Metadata Sheet Author: Martin ˇ Si
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FEI KEMT ciel’ovej platformy a vl
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Acknowledgement There are several p
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Contents Introduction 1 1 Montgomer
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FEI KEMT 6.2.3 Analysis of TRNG in
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FEI KEMT 6 - 2 Block diagram of dig
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List of Algorithms 1 - 1 Montgomery
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FEI KEMT π(p) prime counting funct
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FEI KEMT MWR2MM Multiple Word Radix
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FEI KEMT and Elliptic Curve Cryptog
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FEI KEMT The hardware implementatio
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FEI KEMT data inputs clock Look-up
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FEI KEMT A (X) request for B’s pr
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FEI KEMT Algorithm 1 - 1 Montgomery
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FEI KEMT In the Algorithm 1 - 1 the
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FEI KEMT by the radix b changes to
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FEI KEMT the ECC instead of the RSA
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FEI KEMT Algorithm 1 - 5 Key genera
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FEI KEMT 2 Montgomery Modular Multi
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FEI KEMT not significant. On the ot
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FEI KEMT Algorithm 2 - 2 The multip
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FEI KEMT Beside the internal struct
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FEI KEMT q x i S (j) 2 w-1 S (j) 1
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FEI KEMT x i x i-1 xi-n+1 Y (j) M (
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FEI KEMT especially if the access t
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FEI KEMT 2.2.3 Interface to Control
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FEI KEMT Clock Signal Distribution
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FEI KEMT 2.3.2 Montgomery Multiplic
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FEI KEMT 1. Fully software solution
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FEI KEMT 2.3.4 Implementation Resul
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FEI KEMT 3 Elliptic Curve Method in
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FEI KEMT improving the area-time pr
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FEI KEMT 3.3.1 Pollard’s (p − 1
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FEI KEMT If the order of P ∈ E(Fq
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FEI KEMT handicap of the Montgomery
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FEI KEMT Two major improvements hav
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FEI KEMT and case study with GNFS b
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FEI KEMT Table 4 - 1 Computational
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FEI KEMT from or writing to a singl
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FEI KEMT Algorithm 4 - 1 Modified M
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FEI KEMT Algorithm 4 - 2 Modular ad
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FEI KEMT microprocessor, e.g. Alter
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FEI KEMT timings of ECM implementat
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FEI KEMT hardware was implemented o
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FEI KEMT [68] what can be expressed
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FEI KEMT and a harvesting mechanism
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FEI KEMT control also all the syste
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FEI KEMT we can mention a generator
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FEI KEMT noise to binary signal a c
Page 101 and 102: FEI KEMT over time. For this reason
Page 103 and 104: FEI KEMT The Bucci and Luzzi Testab
Page 105 and 106: FEI KEMT CLI PLL PLL 1 2 CLJ CLK D
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Page 109 and 110: FEI KEMT extraction. In other words
Page 111 and 112: FEI KEMT and effort needed for repr
Page 113 and 114: FEI KEMT 6 True Random Number Gener
Page 115 and 116: FEI KEMT clock input F IN F FB Phas
Page 117 and 118: FEI KEMT Table 6 - 2 Parameters of
Page 119 and 120: FEI KEMT Since the size of the jitt
Page 121 and 122: FEI KEMT Table 6 - 3 Parameters set
Page 123 and 124: FEI KEMT where N1 is the number of
Page 125 and 126: FEI KEMT oscillator with frequency
Page 127 and 128: FEI KEMT Table 6 - 7 Area occupatio
Page 129 and 130: FEI KEMT 0,75 0,5 0,25 1 0 1 30 59
Page 131 and 132: FEI KEMT Stochastic Model The clock
Page 133 and 134: FEI KEMT Table 6 - 8 Mean values me
Page 135 and 136: FEI KEMT Figure 6 - 8 Sampled wavef
Page 137 and 138: FEI KEMT Table 6 - 9 Results of sta
Page 139 and 140: FEI KEMT Figure 6 - 11 Amount of sa
Page 141 and 142: FEI KEMT Figure 6 - 13 Amount of sa
Page 143 and 144: FEI KEMT 7 Research Contribution Wi
Page 145 and 146: FEI KEMT Curriculum vitae Professio
Page 147 and 148: FEI KEMT [16] Altera Corporation. S
Page 149 and 150: FEI KEMT [37] Bundesamt für Sicher
Page 151: FEI KEMT [54] Federal Information P
Page 155 and 156: FEI KEMT of Commerce, month = aug,
Page 157 and 158: FEI KEMT and C. Paar, Eds., no. 216
Page 159: FEI KEMT [128] Zimmermann, P. ECMNE
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