Parallel FPGA Implementation of RSA with Residue Number Systems - Can side-channel threats be avoided?

Midwest Symposium on Circuits and Systems

Volumn 2, Issue , 2003, Pages 806-810

  Ciet, Mathieu ^a   Neve, Michael ^b   Peeters, Eric ^b   Quisquater, Jean Jacques ^b  

^a INNOVA CARD   (France)

^b Microelectronics Laboratory   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

FIELD PROGRAMMABLE GATE ARRAYS (FPGA); NUMBERING SYSTEMS; SIDE CHANNEL ATTACK;

DIFFERENTIAL POWER ANALYSIS; ELECTROMAGNETIC ANALYSIS; FAULT INDUCTION ATTACKS; FPGA IMPLEMENTATIONS; FPGAS IMPLEMENTATION; RESIDUE NUMBER SYSTEM; RSA SIGNATURES; SIDE-CHANNEL; SIDE-CHANNEL ANALYSIS; SIMPLE++;

PARALLEL ARCHITECTURES;

EID: 84894447348     PISSN: 15483746     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/mwscas.2003.1562409     Document Type: Conference Paper

References (41)

1. IEEE Std 1363-2000. IEEE Standard Specifications for Public-Key Cryptography. IEEE Computer Society, August 29, 2000.
2. Mehdi-Laurent Akkar, Régis Bevan, Paul Dischamp, Didier Moyart. Power analysis, What is now possible... In T. Okamoto, Ed., Advances in Cryptology - ASIACRYPT 2000, volume 1976 of Lecture Notes in Computer Science, pp. 489-502. Springer-Verlag, 2000.
3. Dakshi Agrawal, Bruce Archambeault, Josyula R. Rao and Pankaj Rohatgi The EM side-channel (s). In B. S. Kaliski Jr. and Ç. K. Koç, Ed., Cryptographic Hardware and Embedded Systems (CHES 2002), volume 2523 of Lecture Notes in Computer Science, pp. 29-45. Springer, 2002.
4. Christian Aumülier, Peter Bier, Wieland Fischer, Peter Hofreiter and Jean-Pierre Seifert. Fault attacks on RSA with CRT: Concrete results and practical countermeasures In B. S. Kaliski Jr. and Ç. K. Koç, Ed., Cryptographic Hardware and Embedded Systems (CHES 2002), volume 2523 of Lecture Notes in Computer Science, pp. 260-275. Springer, 2002.
5. Jean-Claude Bajard, Laurent-Stéphane Didier and Peter Kornerup, Modular Multiplication and Base Extensions in Residue Number Systems, IEEE Symposium on Computer Arithmetic (2001).
6. Jean-Claude Bajard, Laurent-Stéphane Didier and Peter Kornerup, An RNS Montgomery modular multiplication algorithm, IEEE Transactions on Computers, vol. 47, pp. 766-76, July 1998.
7. Régis Bevan and Erik Knudsen. Ways to enhance differential power analysis. In P. J. Lee and C. H. Lim, Ed., Information Security and Cryptology (ICISC 2002), volume 2587 of Lecture Notes in Computer Science, pp. 327-342. Springer-Verlag, 2002.
8. Johannes Blömer, Martin Otto and Jean-Pierre Seifert. A new CRT-RSA algorithm secure against bellcore attacks. newblock ACM conference on Computer and communication security (ACM-CCS), pp. 311-320. ACM Press, 2003.
9. Dan R. Boneh, Richard A. DeMillo, and Richard J. Lipton, On the importance of checking cryptographic protocols for faults. In W. Fumy, Ed., Advances in Cryptology - EVROCRYPT '97, volume 1233 of Lecture Notes in Computer Science, pp. 37-51. Springer, 1997.
10. Dan R. Boneh, Richard A. DeMillo, and Richard J. Lipton. On the importance of eliminating errors in cryptographic computations. Journal of Cryptology, 14(2):101-119, 2001. An earlier version appears in EURO-CRYPT'97 [9].
11. Eli Biham and Adi Shamir. Differential fault analysis of secret key cryptosystems. In B. S. Kaliski Jr., Ed., Advances in Cryptology - CRYPTO '97, volume 1294 of Lecture Notes in Computer Science, pp. 513-525. Springer, 1997.
12. Eric Brier, Christophe Clavier, and Francis Olivier. Optimal statistical power analysis. Cryptology ePrint Archive, Report 2003/152, 2003. http://eprint.iacr.org/2003/152.
13. Jaewook Chung and Anwar Hasan. More generalized mersenne numbers. Selected Areas in Cryptography (SAC 2003), August 14 & 15, 2003, Carleton University, Ottawa, Ontario, Canada.
14. Jean-François Dhem. Design of an efficient public-key cryptographic library for RISC-based smart cards. PhD thesis, Université catholique de Louvain, May 1998.
15. Karine Gandolfi, Christophe Mourtel, and Francis Olivier. Electromagnetic analysis: Concrete results. In Ç. K. Koç, D. Naccache, and C. Paar, Ed., Cryptographic Hardware and Embedded Systems (CHES 2001), volume 2162 of Lecture Notes in Computer Science, pp. 251-261. Springer, 2001.
16. Gael Hachez and Jean-Jacques Quisquater. Montgomery exponentiation with no final subtractions: Improved results. In Ç. K. Koç and C. Paar, Ed., Cryptographic Hardware and Embedded Systems (CHES 2000), volume 1965 of Lecture Notes in Computer Science, pp. 293-301, 2000.
17. Markus A. Hitz and Erich Kaltofen. Integer division in residue number systems. IEEE Transaction on Computers 44(8), pp. 983-989, (1995).
18. Ching Yu Hung and Behrooz Parhami. Fast RNS division algorithms for fixed divisors with application to RSA encryption Information Processing Utters, Vol. 51, pp. 163-169, 1994.
19. Laurent Imbert, Jean-Claude Bajard. A full RNS implementation of RSA Research Report 02068, LIRMM, available at: http://www.lirmm.fr/bibli/GEIDEFile.PDF?Archive=191917991919&File=RR\%2D02068_PDF, May 2002.
20. Shinichi Kawamura, Masanobu Koike, Fumihiko Sano, and Atsushi Shimbo, Cox-Rower Architecture for Fast Parallel Montgomery Multiplication, In B. Preneel Ed. Advances in Cryptology - EVROCRYPT 2000, volume 1807 of Lecture Notes in Computer Science, Springer-Verlag, 2000, pp. 523-538.
21. Paul C. Kocher. Timing attacks on implementations cf Diffie-Hellman, RSA, DSS, and other systems. In N. Koblitz, Ed., Advances in Cryptology-CRYPTO '96, volume 1109 of Lecture Notes in Computer Science, pp. 104-113. Springer, 1996.
22. Paul C. Kocher, Joshua Jafffe, and Benjamin Jun. Differential power analysis. In M. Wiener, Ed., Advances in Cryptology - CRYPTO '99, volume 1666 of Lecture Notes in Computer Science, pp. 388-397. Springer, 1999.
23. Olivier Kömmerling and Markus G. Kuhn, Design principles for tamperresistant smartcard processors, USENIX Workshop on Snuirtcard Technology (Smarcard'99), pp. 9-20. USENIX Association, 1999
24. Peter L. Montgomery. Modular multiplication without trial division. Math. Comp., 44(170):519-521, April 1985.
25. Jean-Jacques Quisquater and Chantai Couvreur. Fast Decipherment Algorithm for RSA Public-Key Cryptosystem. Electronics Utters, 18(21):905-907, 1982.
26. Jean-Jacques Quisquater and David Samyde. Electromagnetic analysis (EMA): Measures and counter-measures for smart cards In I. Attali and T. P. Jensen, Ed., Smart Card Programming and Security (E-smart 2001), volume 2140 of Ucture Notes in Computer Science, pp 200-210. Springer, 2001.
27. Hanae Nozaki, Masahiko Motoyama, Atsushi Shimbo, and Shinichi Kawamura, Implementation of RSA algorithm based on RNS Mont gomery multiplication, In C. Paar ed. Cryptographic Hardware and Embedded Systems - CHES 2001, pp. 364-376, Springer-Verlag. Berlin. Germany.
28. Karl C. Posh and Reinhard Posh. Modulo reduction in Residue Number Systems. IEEE Transactions on Parallel and Distributed Systems, Vol. 6, No. 5, May 1995, pp. 449-454.
29. Werner Schindler. A timing attack against RSA with the Chinese remainder theorem. In Ç. K. Koç and C. Paar, Ed., Cryptographic Hardware and Embedded Systems (CHES 2000), volume 1965 of Ucture Notes in Computer Science, pages 109-124. Springer, 2000.
30. J. Schwemmlein, Karl C. Posch, Reinhard Posch. RNS-modulo reduction upon a restricted base value set and its applicability to RSA cryptography. Computer & Security, Vol. 17, No. 7, pp. 637-650, 1998
31. A. Shamir. How to check modular exponentiation. Presented at Eurocrypt'97 rump session, 1997.
32. A. Shamir. Method and apparatus for protecting public key schemes from timing and fault attacks. United States Patent 5991415, 1999.
33. A. P. Shenoy and R. Kumaresan. Fast base extension using a redundant modulus in RNS. IEEE Transactions on Computers, 38(1989), pp. 292-297.
34. Alex Skavantzos and Mohammad Abdallah. Implementation issues of the two-level residue number system with pairs of conjugate moduli IEEE Transactions on Signal Processing, vol. 47, no. 3, pp. 826-838, 1999.
35. Jérôme A. Solinas Generalized Mersenne numbers. Technical report, The centre for applied cryptographic research, University of Waterloo, 1999. CORR 99-39.
36. Nicholas S. Szabó and Richard I. Tanaka. Residue nrithemtic and its application to computer technology. McGraw-Hill, 1967
37. Colin D. Walter. An overview of Montgomery multiplication technique: How to make it smaller and faster. In Ç. K. Koç and C. Paar, editors, Cryptographic Hardware and Embedded Systems (CHES '99), volume 1717 of Ucture Note in Computer Science, pp. 80-93 1999.
38. Colin D. Walter. Montgomery exponentiation needs no final subtractions. Electronics Utters, 35(21):1831-1832, October 1999.
39. Huapeng Wu. On modular reduction Technical report, CACR. University of Waterloo, 2000. CORR 2000-36.
40. Sung-Ming Yen, Setingjoo Kim, Seongan Lim, and Scongan Moon RSA Speedup with Residue Number System Immune against Hardware Failli Cryptanalysis. In K. Kim, Ed., Information Security and Cryptology ICISC2001, volume 2288 of Ucture Notes in Computer Science, pp. 397-413. Springer-Verlag, 2001.
41. Sung-Ming Yen, Seungjoo Kim, Seongan Lim and Sang-Jac Moon. newblock RSA Speedup with Chinese Remainder Theorem Immune against Hardware Fault Cryptanalys newblock IEEE Transactions on Computers 52 (4): pp. 461-472, 2003.