1 Montgomery Modular Multiplication in Hard- ware

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FEI KEMT References [1] Actel Corporation. ProASICplus Evaluation Board, User’s guide, 2002. [2] Actel Corporation. Axcelerator Family PLL and Clock Management, Ap- plication Note, June 2003. [3] Actel Corporation. Using ProASICplus Clock Conditioning Circuits, Ap- plication Note, Dec. 2004. [4] Actel Corporation. ProASIC3(E) Flash Family FPGAs, Datasheet, Jan. 2005. [5] Actel Corporation. ProASICplus Flash Family FPGAs, ver. 5.3, May 2006. [6] Altera Corporation. Metastability in Altera Devices ver.4.0, May 1999. [7] Altera Corporation. ACEX 1K Programmable Logic Device Family, Data Sheet, Sept. 2001. ver. 3.3. [8] Altera Corporation. APEX 20K Programmable Logic Device Family, Data Sheet, Feb. 2002. ver. 4.3. [9] Altera Corporation. Avalon Bus Specification, Reference Manual, Jan. 2002. ver. 2.0. [10] Altera Corporation. Nios Embedded Processor Development Board ver.2.1, Apr. 2002. [11] Altera Corporation. Using PLLs in Stratix Devices, Feb. 2002. ver. 1.0. [12] Altera Corporation. Cyclone Device Handbook, Using PLLs in Cyclone Devices, Oct. 2003. ver. 1.2. [13] Altera Corporation. Cyclone Programmable Logic Device Family, Data Sheet, Mar. 2003. ver. 1.1. [14] Altera Corporation. Using the ClockLock & ClockBoost PLL Features in APEX Devices, Nov. 2003. Application Note 115, ver. 2.6. [15] Altera Corporation. Stratix Device Handbook, General-Purpose PLLs in Stratix & Stratix GX Devices, Sept. 2004. ver. 3.1. 127
FEI KEMT [16] Altera Corporation. Stratix EP1S25 DSP Development Board, Dec. 2004. ver. 1.6. [17] Altera Corporation. Cyclone II Device Handbook, PLLs in Cyclone II Devices, Feb. 2005. ver. 1.2. [18] Altera Corporation. Stratix Device Handbook, July 2005. ver. 3.4. [19] Altera Corporation. Stratix II Device Handbook, PLLs in Stratix II De- vices, Mar. 2005. ver. 2.2. [20] Altera Corporation. Stratix II Device Handbook, Volume 2, Chapter 2, TriMatrix Embedded Memory Blocks in Stratix II & Stratix II GX Devices, Apr. 2006. ver. 4.2. [21] Altera Corporation. Stratix II Device Handbook, Volume 1, Chapter 5, DC & Switching Characteristics, May 2007. ver. 4.3. [22] AMI Semiconductors Company. XpressArray High Density 0.18 um Structured ASIC. [23] ARM Limited. ARM7TDMI (Rev 3) — Technical Reference Manual. Avail- able at http://www.arm.com/pdfs/DDI0029G_7TDMI_R3_trm.pdf, 2001. [24] Bagini, V., and Bucci, M. A design of reliable true random number generator for cryptographic applications. In Cryptographic Hardware and Embedded Systems – CHES’99 (Berlin, Germany, Aug. 1999), Ç. K. Koç and C. Paar, Eds., no. 1717 in Lecture Notes in Computer Science, Springer-Verlag, pp. 204– 218. [25] Barrett, P. Implementating the rivest, shamir and aldham public-key en- cryption algorithm on standard digital signal processor. In Proceedings of CRYPTO’86 (1986), vol. 263 of Lecture Notes in Computer Science, pp. 311– 323. [26] Baudet, M., Lubicz, D., Micolod, J., and Tassiaux, A. On the secu- rity of oscillator-based random number generators. Cryptology ePrint Archive, Report 2009/299, 2009. http://eprint.iacr.org/. 128
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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
Page 95 and 96: FEI KEMT control also all the syste
Page 97 and 98: FEI KEMT we can mention a generator
Page 99 and 100: 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
Page 107 and 108: FEI KEMT For R it holds that the in
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: FEI KEMT Curriculum vitae Professio
Page 149 and 150: FEI KEMT [37] Bundesamt für Sicher
Page 151 and 152: FEI KEMT [54] Federal Information P
Page 153 and 154: FEI KEMT [71] Gura, N., Chang, S.,
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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