Concrete security of the blum-blum-shub pseudorandom generator

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

Volumn 3796 LNCS, Issue , 2005, Pages 355-375

  Sidorenko, Andrey ^a   Schoenmakers, Berry ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA REDUCTION; INFORMATION DISSEMINATION; INTEGER PROGRAMMING; ITERATIVE METHODS; POLYNOMIAL APPROXIMATION;

BLUM-BLUM-SHUB (BBS) PSEUDORANDOM GENERATOR; CONCRETE SECURITY; FACTORIZATION RESULTS; INTEGER FACTORING;

SECURITY OF DATA;

EID: 33646853911     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11586821_24     Document Type: Conference Paper

References (16)

1. W. Alexi, B. Chor, O. Goldeich and C. P. Schnorr. RSA and Rabin functions: certain parts are as hard as the whole. SIAM Journal on Computing 17, 1988, pp. 194-209.
2. L. Blum, M. Blum and M. Shub. A Simple Unpredictable Pseudo-Random Number Generator. SIAM Journal on Computing 15, 1986, pp. 364-383.
3. M. Bellare and P. Rogaway. The exact security of digital signatures how to sign with RSA and Rabin. In Advances in Cryptology - Eurocrypt 1996, volume 1070 of Lecture Notes in Computer Science, pp. 399-416. Berlin: Springer-Verlag, 1996.
4. ECRYPT Yearly Report on Algorithms and Keysizes (2004). Available at http://www.ecrypt.eu.org/documents/D.SPA.10-1.1.pdf.
5. R. Fischlin and C. P. Schnorr. Stronger Security Proofs for RSA and Rabin Bits. Journal of Cryptology (2000) 13, pp. 221-244.
6. R. Gennaro. An improved pseudo-random generator based on discrete log. In Mihir Bellare, editor, Advances in Cryptology - Crypto 2000, volume 1880 of Lecture Notes in Computer Science, pp. 469-481. Springer-Verlag, 20-24 August 2000.
7. O. Goldreich. Three XOR-Lemmas - An Exposition. Technical report, ECCC TR95-056, 1995. Available at ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1995/ TR95-056/Paper.pdf.
8. W. Hoeffding. Probability in Equations for Sums of Bounded Random Variables. Journal of the American Statistical Association 56 (1963), pp. 13-30.
9. D. E. Knuth. Seminumerical Algorithms, 3rd edition. Addison-Wesley, Reading, MA, 1997.
10. J. Katz, N. Wang. Efficiency Improvements for Signature Schemes with Tight Security Reductions. CCS'03, October 27-30, 2003, Washington, DC, USA.
11. A. K. Lenstra, E. R. Verheul. Selecting Cryptographic Key Sizes. Journal of Cryptology (2001) 14: 255-293.
12. A. J. Menezes, P. C. van Oorschot, S. A. Vanstone. Handbook of Appied Cryptography. CRC Press series on discrete mathematics and its applications, 2000.
13. M. O. Rabin. Digitalized signatures and public-key functions as intractible as factorization. Technical report, TR-212, MIT Laboratory for Computer Science, 1979.
14. V. Shoup. On the security of a practical identification scheme. In Advances in Cryptology - Eurocrypt 1996, volume 1070 of Lecture Notes in Computer Science, pp. 344-353. Berlin: Springer-Verlag, 1996.
15. U. V. Vazirani, V. V. Vazirani. Efficient and Secure Pseudo-Random Number Generation. Proceedings 25th Symposium on Foundations of Computing Science IEEE, pp. 458-463, 1984.
16. A. C. Yao. Theory and Application of Trapdoor Functions. Proceedings of IEEE Symposium on Foundations of Computer Science, pp. 80-91, 1982.