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2020 | OriginalPaper | Buchkapitel

11. Efficient Hardware Operations for the Residue Number System by Boolean Minimization

verfasst von : Danila Gorodecky, Tiziano Villa

Erschienen in: Advanced Boolean Techniques

Verlag: Springer International Publishing

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Abstract

Residue number systems (RNS) represent numbers by their remainders modulo a set of relatively prime numbers. This paper proposes an efficient hardware implementation of modular multiplication and of the modulo function (X(mod P)), based on Boolean minimization. We report experiments showing a performance advantage up to 30 times for our approach vs. the results obtained by state-of-the-art industrial tools.

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Literatur
1.
Zurück zum Zitat Bibilo, P., Cheremisinova, L., Kardash, S., Kirienko, N., Romanov, V., Cheremisinov, D.: Automatizations of the logic synthesis of CMOS circuits with low power consumption. Programnaia Ingeniria 8, 35–41 (2013) (in Russian) Bibilo, P., Cheremisinova, L., Kardash, S., Kirienko, N., Romanov, V., Cheremisinov, D.: Automatizations of the logic synthesis of CMOS circuits with low power consumption. Programnaia Ingeniria 8, 35–41 (2013) (in Russian)
2.
Zurück zum Zitat Butler, J.T., Sasao, T.: Fast hardware computation of x mod z. In: 25th IEEE International Parallel and Distributed Processing Symposium Anchorage, Alaska, May 16–17, pp. 289–292 (2011) Butler, J.T., Sasao, T.: Fast hardware computation of x mod z. In: 25th IEEE International Parallel and Distributed Processing Symposium Anchorage, Alaska, May 16–17, pp. 289–292 (2011)
3.
Zurück zum Zitat Cherviakov, N.I., et al.: Modular structures of parallel computing systems for neuroprocessor, Moscow, 288 pp. (2003) (in Russian) Cherviakov, N.I., et al.: Modular structures of parallel computing systems for neuroprocessor, Moscow, 288 pp. (2003) (in Russian)
4.
Zurück zum Zitat Ding, C., Pei, D., Pei, T., Salomaa, A.: Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography. Harbin Institute of Technology Press, Harbin (1996)CrossRef Ding, C., Pei, D., Pei, T., Salomaa, A.: Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography. Harbin Institute of Technology Press, Harbin (1996)CrossRef
5.
Zurück zum Zitat Dorf, R.C.: Computers, Software, Engineering and Digital Devices, 576 pp. Taylor and Francis, Boca Raton (2006)MATH Dorf, R.C.: Computers, Software, Engineering and Digital Devices, 576 pp. Taylor and Francis, Boca Raton (2006)MATH
6.
Zurück zum Zitat Flatt, H., Hesselbarth, S., Flugel, S., Pirsch, P.: A modular coprocessor architecture for embedded real-time image and video signal processing. In: Proceedings of Embedded Computer Systems: Architectures, Modeling, and Simulation, 7th International Workshop, Samos, pp. 241–250 (2007) Flatt, H., Hesselbarth, S., Flugel, S., Pirsch, P.: A modular coprocessor architecture for embedded real-time image and video signal processing. In: Proceedings of Embedded Computer Systems: Architectures, Modeling, and Simulation, 7th International Workshop, Samos, pp. 241–250 (2007)
7.
Zurück zum Zitat Gorodecky, D.: Hardware realization of X (mod P). In: Proceedings of the International scientific-practical conference “Actual problems of Radio Physics”, Tomsk, October 3–6, 2013. Izvestia VUZov. Physic., vol. 56. 9/2, pp. 198–199 Gorodecky, D.: Hardware realization of X (mod P). In: Proceedings of the International scientific-practical conference “Actual problems of Radio Physics”, Tomsk, October 3–6, 2013. Izvestia VUZov. Physic., vol. 56. 9/2, pp. 198–199
10.
Zurück zum Zitat Irhin, V.P.: Tabular implementation of modular arithmetic operations // Sb.nauch.tr. YUbilejnoj Mezhdunarodnoj nauchno-tekhnicheskoj konferencii 50 let modulyarnoj arifmetiki, pp. 268–273 (2005) (in Russian) Irhin, V.P.: Tabular implementation of modular arithmetic operations // Sb.nauch.tr. YUbilejnoj Mezhdunarodnoj nauchno-tekhnicheskoj konferencii 50 let modulyarnoj arifmetiki, pp. 268–273 (2005) (in Russian)
11.
Zurück zum Zitat Low, J.Y.S., Chang, C.H.: A new approach to the design of efficient residue generators for arbitrary moduli. IEEE Trans. Circuits Syst. I Reg. Pap. 60, 2366–2374 (2013)MathSciNetCrossRef Low, J.Y.S., Chang, C.H.: A new approach to the design of efficient residue generators for arbitrary moduli. IEEE Trans. Circuits Syst. I Reg. Pap. 60, 2366–2374 (2013)MathSciNetCrossRef
12.
Zurück zum Zitat Malashevich, B.M.: Unknown modular supercomputers. In: Proceedings of Conference for 50 Years of Modular Arithmetic, Nov. 23–25, pp. 50–70 (2005) (in Russian) Malashevich, B.M.: Unknown modular supercomputers. In: Proceedings of Conference for 50 Years of Modular Arithmetic, Nov. 23–25, pp. 50–70 (2005) (in Russian)
13.
Zurück zum Zitat Mohan, P.V.A.: Residue Number Systems. Theory and Applications. Birkhäuser (Springer), Basel (2016) Mohan, P.V.A.: Residue Number Systems. Theory and Applications. Birkhäuser (Springer), Basel (2016)
14.
Zurück zum Zitat Mohan, P.V.A.: Efficient design of binary to RNS converters. J. Circuit. Syst. Comput. 9, 145–154 (1999)CrossRef Mohan, P.V.A.: Efficient design of binary to RNS converters. J. Circuit. Syst. Comput. 9, 145–154 (1999)CrossRef
15.
Zurück zum Zitat Montgomery, P.L.: Modular multiplication without trial division mathematics of computation. Math. Comput. 44(170), 519–521 (1985)CrossRef Montgomery, P.L.: Modular multiplication without trial division mathematics of computation. Math. Comput. 44(170), 519–521 (1985)CrossRef
16.
Zurück zum Zitat Omondi, A.R., Premkumar, B.: Residue Number System: Theory and Implementation. Imperial College Press, London (2007)CrossRef Omondi, A.R., Premkumar, B.: Residue Number System: Theory and Implementation. Imperial College Press, London (2007)CrossRef
17.
Zurück zum Zitat Ozturk, E., Sunar, B., Savas, E.: Low-power elliptic curve cryptography using scaled modular arithmetic, In: Proceedings of the 6th International Workshop Cryptographic Hardware in Embedded Systems, Cambridge, Aug. 11–13, vol. 3156, pp. 92–106 (2004) Ozturk, E., Sunar, B., Savas, E.: Low-power elliptic curve cryptography using scaled modular arithmetic, In: Proceedings of the 6th International Workshop Cryptographic Hardware in Embedded Systems, Cambridge, Aug. 11–13, vol. 3156, pp. 92–106 (2004)
18.
Zurück zum Zitat Piestrak, S.J.: Design of residue generators and multi-operand modulo adders using carry save adders. In: Proceedings of the 10th Symposium on Computer Arithmetic, Grenoble, 26–28 June 1991, pp. 100–107 (1991) Piestrak, S.J.: Design of residue generators and multi-operand modulo adders using carry save adders. In: Proceedings of the 10th Symposium on Computer Arithmetic, Grenoble, 26–28 June 1991, pp. 100–107 (1991)
19.
Zurück zum Zitat Premkumar, A.B.: A formal framework for conversion from binary to residue numbers. IEEE Trans. Circuits Syst. 49, 135–144 (2002)CrossRef Premkumar, A.B.: A formal framework for conversion from binary to residue numbers. IEEE Trans. Circuits Syst. 49, 135–144 (2002)CrossRef
20.
Zurück zum Zitat Premkumar, A.B., Ang, E.L., Lai, E.M.K.: Improved memory-less RNS forward converter based on periodicity of residues. IEEE Trans. Circuits Syst. 53, 133–137 (2006)CrossRef Premkumar, A.B., Ang, E.L., Lai, E.M.K.: Improved memory-less RNS forward converter based on periodicity of residues. IEEE Trans. Circuits Syst. 53, 133–137 (2006)CrossRef
21.
Zurück zum Zitat Sousa, L., Chaves, R.: A universal architecture for designing efficient modulo 2n ± 1 multipliers. IEEE Trans. Circuits Syst. 52(6), 1166–1178 (2005)MathSciNetCrossRef Sousa, L., Chaves, R.: A universal architecture for designing efficient modulo 2n ± 1 multipliers. IEEE Trans. Circuits Syst. 52(6), 1166–1178 (2005)MathSciNetCrossRef
23.
Zurück zum Zitat Zimmermann, R.: Efficient VLSI implementation of modulo 2n + 1 addition and multiplication. In:14th IEEE Symposium on Computer Arithmetic, Adelaide, April 14–16, pp. 158–167 (1999) Zimmermann, R.: Efficient VLSI implementation of modulo 2n + 1 addition and multiplication. In:14th IEEE Symposium on Computer Arithmetic, Adelaide, April 14–16, pp. 158–167 (1999)
Metadaten
Titel
Efficient Hardware Operations for the Residue Number System by Boolean Minimization
verfasst von
Danila Gorodecky
Tiziano Villa
Copyright-Jahr
2020
DOI
https://doi.org/10.1007/978-3-030-20323-8_11

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