Fast generation of prime numbers on portable devices: An update

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4249 LNCS, Issue , 2006, Pages 160-173

  Joye, Marc ^a   Paillier, Pascal ^b  

^a Thomson R and D France   (France)

^b GEMALTO   (France)

Author keywords

Cryptoprocessors; Efficient implementations; Embedded software; PDAs; Primality testing; Prime number generation; Public key cryptography; RSA; Smart cards

Indexed keywords

ALGORITHMS; EMBEDDED SYSTEMS; PERSONAL DIGITAL ASSISTANTS; PUBLIC KEY CRYPTOGRAPHY; SECURITY OF DATA; SMART CARDS;

CRYPTOGRAPHIC COPROCESSOR; EFFICIENT IMPLEMENTATIONS; ELECTRONIC CASH; EMBEDDED SOFTWARE; MOBILE COMMERCE; PRIMALITY TESTING; PRIME NUMBER GENERATION; RSA;

PORTABLE EQUIPMENT;

EID: 33750736029     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11894063_13     Document Type: Conference Paper

References (25)

1. ANSI X9.31. Public-key cryptography using RSA for the financial services industry. American National Standard for Financial Services, draft, 1995.
2. A.O.L. Atkin and F. Morain. Elliptic curves and primality proving. Mathematics of Computation, vol. 61, pp. 29-68, 1993.
3. D. Boneh and M. Franklin. Efficient generation of shared RSA keys. In Advances in Cryptology - CRYPTO '97, vol. 1294 of Lecture Notes in Computer Science, pp. 425-439, Springer-Verlag, 1997.
4. W. Bosma and M.-P. van der Hulst. Faster primality testing. In Advances in Cryptology - CRYPTO '89, vol. 435 of Lecture Notes in Computer Science, pp. 652-656, Springer-Verlag, 1990.
5. J. Brandt and I. Damgård. On generation of probable primes by incremental search. In Advances in Cryptology - CRYPTO '92, vol. 740 of Lecture Notes in Computer Science, pp. 358-370, Springer-Verlag, 1993.
6. J. Brandt, I. Damgård, and P. Landrock. Speeding up prime number generation. In Advances in Cryptology - ASIACRYPT '91, vol. 739 of Lecture Notes in Computer Science, pp. 440-449, Springer-Verlag, 1991.
7. R.D. Carmichael. Introduction to the Theory of Groups of Finite Order, Dover, 1956.
8. C. Couvreur and J.-J. Quisquater. An introduction to fast generation of large prime numbers. Philips Journal of Research, vol. 37, pp. 231-264, 1982.
9. C. Ding, D. Pei, and A. Salomaa. Chinese Remainder Theorem, Word Scientific, 1996.
10. P.X. Gallagher. On the distribution of primes in short intervals. Mathematica, vol. 23, pp. 4-9, 1976.
11. G.H. Hardy and J.E. Littlewood. Some problems of 'Partitio Numerorum' III: On the expression of a number as a sum of primes. Acta Mathematica, vol. 44, pp. 1-70, 1922.
12. M. Joye and P. Paillier. Fast generation of prime numbers on portable devices: An update. Extended version of this work. Available on http://eprint.iacr.org.
13. M. Joye, P. Paillier, and S. Vaudenay. Efficient generation of prime numbers. In Cryptographic Hardware and Embedded Systems -CHES 2000, vol. 1965 of Lecture Notes in Computer Science, pp. 340-354, Springer-Verlag, 2000.
14. D.E. Knuth. The Art of Computer Programming - Seminumerical Algorithms, vol. 2, Addison-Wesley, 2nd ed., 1981.
15. C. Lu and A.L.M. Dos Santos. A note on efficient implementation of prime generation in small portable devices. Computer Networks, vol. 49, pp. 476-491, 2005.
16. C. Lu, A.L.M. Dos Santos, and F.R. Pimentel. Implementation of fast RSA key generation on smart cards. In 17th ACM Symposium on Applied Computing, pp. 214-221, ACM Press, 2002.
17. U. Maurer. Fast generation of prime numbers and secure public-key cryptographic parameters. Journal of Cryptology, vol. 8, pp. 123-155, 1995.
18. A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone. Handbook of Applied Cryptography, CRC Press, 1997.
19. L. Monier. Evaluation and comparison of two efficient probabilistic primality testing algorithms. Theoretical Computer Science, vol. 12, pp. 97-108, 1980.
20. H.C. Pocklington. The determination of the prime or composite nature of large numbers by Fermat's theorem. Proc. of the Cambridge Philosophical Society, vol. 18, pp. 29-30, 1914.
21. J.-J. Quisquater and C. Couvreur. Fast decipherment algorithm for RSA public-key cryptosystem. Electronics Letters, vol. 18, pp. 905-907, 1982.
22. H. Riesel. Prime Numbers and Computer Methods for Factorization, Birkhäuser, 1985.
23. R.L. Rivest, A. Shamir, and L.M. Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, vol. 21, pp. 120-126, 1978.
24. R.D. Silverman. Fast generation of random, strong RSA primes. Cryptobytes, vol. 3, pp. 9-13, 1997.
25. R. Solovay and V. Strassen. A fast Monte-Carlo test for primality. SIAM Journal on Computing, vol. 6, pp. 84-85, 1977.