메뉴 건너뛰기




Volumn 70, Issue 236, 2001, Pages 1575-1589

On the distribution of the power generator

Author keywords

Blum Blum Shub; Exponential sums; Pseudorandom numbers; RSA generator

Indexed keywords


EID: 0039923077     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-00-01283-7     Document Type: Article
Times cited : (33)

References (50)
  • 1
    • 0022716288 scopus 로고    scopus 로고
    • A simple unpredictable pseudorandom number generator
    • L. Blum, M. Blum and M. Shub, 'A simple unpredictable pseudorandom number generator', SIAM J. Comp., 15 (1986), 364-383. MR 87k:65007
    • (1986) SIAM J. Comp. , vol.15 , pp. 364-383
    • Blum, L.1    Blum, M.2    Shub, M.3
  • 2
    • 0022716288 scopus 로고    scopus 로고
    • L. Blum, M. Blum and M. Shub, 'A simple unpredictable pseudorandom number generator', SIAM J. Comp., 15 (1986), 364-383. MR 87k:65007
    • MR , vol.87 K , pp. 65007
  • 3
    • 0041182876 scopus 로고    scopus 로고
    • Analysis of iterated modular exponentiation: The orbit of xα mod N
    • J. J. Brennan and B. Geist, 'Analysis of iterated modular exponentiation: The orbit of xα mod N', Designs, Codes and Cryptography, 13 (1998), 229-245. MR 99b:11086
    • (1998) Designs, Codes and Cryptography , vol.13 , pp. 229-245
    • Brennan, J.J.1    Geist, B.2
  • 4
    • 0041182876 scopus 로고    scopus 로고
    • J. J. Brennan and B. Geist, 'Analysis of iterated modular exponentiation: The orbit of xα mod N', Designs, Codes and Cryptography, 13 (1998), 229-245. MR 99b:11086
    • MR , vol.99 B , pp. 11086
  • 6
    • 0000924324 scopus 로고    scopus 로고
    • On certain exponential sums and the distribution of Diffie-Hellman triples
    • R. Canetti, J. B. Friedlander and I. E. Shparlinski, 'On certain exponential sums and the distribution of Diffie-Hellman triples', J. London Math. Soc., 59 (1999), 799-812. MR 2000g:11079
    • (1999) J. London Math. Soc. , vol.59 , pp. 799-812
    • Canetti, R.1    Friedlander, J.B.2    Shparlinski, I.E.3
  • 7
    • 0000924324 scopus 로고    scopus 로고
    • R. Canetti, J. B. Friedlander and I. E. Shparlinski, 'On certain exponential sums and the distribution of Diffie-Hellman triples', J. London Math. Soc., 59 (1999), 799-812. MR 2000g:11079
    • MR , vol.2000 G , pp. 11079
  • 8
    • 0040072837 scopus 로고
    • The Vinogradov-Mordell-Tietäväinen inequalities
    • J. H. H. Chalk, 'The Vinogradov-Mordell-Tietäväinen inequalities', Indag. Math., 42 (1980), 367-374. MR 82d:10053
    • (1980) Indag. Math. , vol.42 , pp. 367-374
    • Chalk, J.H.H.1
  • 9
    • 49149142810 scopus 로고    scopus 로고
    • J. H. H. Chalk, 'The Vinogradov-Mordell-Tietäväinen inequalities', Indag. Math., 42 (1980), 367-374. MR 82d:10053
    • MR , vol.82 D , pp. 10053
  • 10
    • 0029345097 scopus 로고    scopus 로고
    • 2 mod N pseudorandom number generator
    • 2 mod N pseudorandom number generator', IEEE Trans. Inform. Theory, 41 (1995), 1155-1159. MR 96k:65006
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 1155-1159
    • Cusick, T.W.1
  • 11
    • 0029345097 scopus 로고    scopus 로고
    • 2 mod N pseudorandom number generator', IEEE Trans. Inform. Theory, 41 (1995), 1155-1159. MR 96k:65006
    • MR , vol.96 K , pp. 65006
  • 13
    • 0039403654 scopus 로고    scopus 로고
    • T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, Elsevier, Amsterdam, 1998. MR 99h:94045
    • MR , vol.99 H , pp. 94045
  • 14
    • 84957376046 scopus 로고    scopus 로고
    • Stronger security proofs for RSA and Rabin bits
    • Springer-Verlag, Berlin
    • R. Fischlin and C. P. Schnorr, 'Stronger security proofs for RSA and Rabin bits', Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1233 (1997), 267-279. CMP 98:09
    • (1997) Lect. Notes in Comp. Sci. , vol.1233 , pp. 267-279
    • Fischlin, R.1    Schnorr, C.P.2
  • 15
    • 84957376046 scopus 로고    scopus 로고
    • R. Fischlin and C. P. Schnorr, 'Stronger security proofs for RSA and Rabin bits', Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1233 (1997), 267-279. CMP 98:09
    • CMP , vol.98 , pp. 9
  • 18
    • 0007452303 scopus 로고    scopus 로고
    • Period of the power generator and small values of Carmichael's function
    • to appear
    • J. B. Friedlander, C. Pomerance and I. E. Shparlinski, 'Period of the power generator and small values of Carmichael's function', Math. Comp. (to appear).
    • Math. Comp.
    • Friedlander, J.B.1    Pomerance, C.2    Shparlinski, I.E.3
  • 20
    • 84957613068 scopus 로고    scopus 로고
    • On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders
    • Proc. the 13th Symp. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Hawaii, 1999, Springer-Verlag, Berlin
    • F. Griffin, H. Niederreiter and I. E. Shparlinski, On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders, Proc. the 13th Symp. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Hawaii, 1999, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1999, v.1719, 87-93.
    • (1999) Lect. Notes in Comp. Sci. , vol.1719 , pp. 87-93
    • Griffin, F.1    Niederreiter, H.2    Shparlinski, I.E.3
  • 21
    • 0002966966 scopus 로고    scopus 로고
    • On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period
    • J. Gutierrez, H. Niederreiter and I. E. Shparlinski, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatsh. Math. 129 (2000) 31-36. CMP 2000:08
    • (2000) Monatsh. Math. , vol.129 , pp. 31-36
    • Gutierrez, J.1    Niederreiter, H.2    Shparlinski, I.E.3
  • 22
    • 0002966966 scopus 로고    scopus 로고
    • J. Gutierrez, H. Niederreiter and I. E. Shparlinski, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatsh. Math. 129 (2000) 31-36. CMP 2000:08
    • CMP , vol.2000 , pp. 8
  • 24
    • 0000163126 scopus 로고    scopus 로고
    • On the distribution of digits in periodic fractions
    • N. M. Korobov, 'On the distribution of digits in periodic fractions', Math. USSR. - Sbornik, 18 (1972), 659-676. MR 54:12619
    • (1972) Math. USSR. - Sbornik , vol.18 , pp. 659-676
    • Korobov, N.M.1
  • 25
    • 0000163126 scopus 로고    scopus 로고
    • N. M. Korobov, 'On the distribution of digits in periodic fractions', Math. USSR. - Sbornik, 18 (1972), 659-676. MR 54:12619
    • MR , vol.54 , pp. 12619
  • 27
    • 0039995620 scopus 로고    scopus 로고
    • N. M. Korobov, Exponential sums and their applications, Kluwer Acad. Publ., Dordrecht, 1992. MR 93a:11068
    • MR , vol.93 A , pp. 11068
  • 29
    • 0039403645 scopus 로고    scopus 로고
    • J. C. Lagarias, 'Pseudorandom number generators in cryptography and number theory', Proc. Symp. in Appl. Math., Amer. Math. Soc., Providence, RI, 42 (1990), 115-143. MR 92f:11109
    • MR , vol.92 F , pp. 11109
  • 30
    • 0004127220 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge
    • R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997. MR 97i:11115
    • (1997) Finite Fields
    • Lidl, R.1    Niederreiter, H.2
  • 31
    • 0039403660 scopus 로고    scopus 로고
    • R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, Cambridge, 1997. MR 97i:11115
    • MR , vol.97 I , pp. 11115
  • 33
    • 84944878354 scopus 로고    scopus 로고
    • A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, FL, 1997. MR 99g:94015
    • MR , vol.99 G , pp. 94015
  • 34
    • 0000997571 scopus 로고
    • Quasi-Monte Carlo methods and pseudo-random numbers
    • H. Niederreiter, 'Quasi-Monte Carlo methods and pseudo-random numbers', Bull. Amer. Math. Soc., 84 (1978), 957-1041. MR 80d:65016
    • (1978) Bull. Amer. Math. Soc. , vol.84 , pp. 957-1041
    • Niederreiter, H.1
  • 35
    • 0040380008 scopus 로고    scopus 로고
    • H. Niederreiter, 'Quasi-Monte Carlo methods and pseudo-random numbers', Bull. Amer. Math. Soc., 84 (1978), 957-1041. MR 80d:65016
    • MR , vol.80 D , pp. 65016
  • 37
    • 0039195400 scopus 로고    scopus 로고
    • H. Niederreiter, Random number generation and Quasi-Monte Carlo methods, SIAM Press, Philadelphia, 1992. MR 93h:65008
    • MR , vol.93 H , pp. 65008
  • 38
    • 0007465177 scopus 로고    scopus 로고
    • On the distribution of inversive congruential pseudorandom numbers in parts of the period
    • to appear
    • H. Niederreiter and I. E. Shparlinski, 'On the distribution of inversive congruential pseudorandom numbers in parts of the period', Math. Comp. (to appear).
    • Math. Comp.
    • Niederreiter, H.1    Shparlinski, I.E.2
  • 39
    • 0033164169 scopus 로고    scopus 로고
    • On the distribution and lattice structure of nonlinear congruential pseudorandom numbers
    • H. Niederreiter and I. E. Shparlinski, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and Their Appl., 5 (1999), 246-253. CMP 99:17
    • (1999) Finite Fields and Their Appl. , vol.5 , pp. 246-253
    • Niederreiter, H.1    Shparlinski, I.E.2
  • 40
    • 0033164169 scopus 로고    scopus 로고
    • H. Niederreiter and I. E. Shparlinski, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and Their Appl., 5 (1999), 246-253. CMP 99:17
    • CMP , vol.99 , pp. 17
  • 41
    • 0039995623 scopus 로고    scopus 로고
    • On the distribution of inversive congruential pseudorandom numbers modulo a prime power
    • to appear
    • H. Niederreiter and I. E. Shparlinski, 'On the distribution of inversive congruential pseudorandom numbers modulo a prime power', Acta Arithm. (to appear).
    • Acta Arithm.
    • Niederreiter, H.1    Shparlinski, I.E.2
  • 42
    • 0033737044 scopus 로고    scopus 로고
    • On the distribution of pseudorandom numbers and vectors generated by inversive methods
    • H. Niederreiter and I. E. Shparlinski, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Appl. Algebra in Engin., Commun. and Computing, 10 (2000) 189-202. CMP 2000:11
    • (2000) Appl. Algebra in Engin., Commun. and Computing , vol.10 , pp. 189-202
    • Niederreiter, H.1    Shparlinski, I.E.2
  • 43
    • 0033737044 scopus 로고    scopus 로고
    • H. Niederreiter and I. E. Shparlinski, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Appl. Algebra in Engin., Commun. and Computing, 10 (2000) 189-202. CMP 2000:11
    • CMP , vol.2000 , pp. 11
  • 45
    • 0041182881 scopus 로고    scopus 로고
    • R. A. Rueppel, 'Stream ciphers', Contemporary cryptology: The science of information integrity, IEEE Press, NY, 1992, 65-134. CMP 93:08
    • CMP , vol.93 , pp. 8
  • 48
    • 0040588793 scopus 로고    scopus 로고
    • D. R. Stinson, Cryptography: Theory and Practice, CRC Press, Boca Raton, FL, 1995. MR 96k:94015
    • MR , vol.96 K , pp. 94015
  • 50
    • 4244161380 scopus 로고    scopus 로고
    • I. M. Vinogradov, Elements of Number Theory, Dover Publ., NY, 1954. MR 15:933e
    • MR , vol.15


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.