메뉴 건너뛰기




Volumn 70, Issue 236, 2001, Pages 1591-1605

Period of the power generator and small values of Carmichael's function

Author keywords

Blum Blum Shub generator; Carmichael's function; RSA generator

Indexed keywords


EID: 0035647482     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-00-01282-5     Document Type: Article
Times cited : (54)

References (44)
  • 1
    • 0001725847 scopus 로고
    • There are infinitely many Carmichael numbers
    • W. R. Alford, A. Granville and C. Pomerance, 'There are infinitely many Carmichael numbers', Annals Math. 140 (1994), 703-722. MR 95k:11114
    • (1994) Annals Math. , vol.140 , pp. 703-722
    • Alford, W.R.1    Granville, A.2    Pomerance, C.3
  • 2
    • 0040096851 scopus 로고    scopus 로고
    • W. R. Alford, A. Granville and C. Pomerance, 'There are infinitely many Carmichael numbers', Annals Math. 140 (1994), 703-722. MR 95k:11114
    • MR , vol.95 K , pp. 11114
  • 3
    • 0032441756 scopus 로고    scopus 로고
    • Shifted primes without large prime factors
    • R. C. Baker and G. Harman, 'Shifted primes without large prime factors', Acta Arith. 83 (1998), 331-361. MR 99b:11104
    • (1998) Acta Arith. , vol.83 , pp. 331-361
    • Baker, R.C.1    Harman, G.2
  • 4
    • 0032441756 scopus 로고    scopus 로고
    • R. C. Baker and G. Harman, 'Shifted primes without large prime factors', Acta Arith. 83 (1998), 331-361. MR 99b:11104
    • MR , vol.99 B , pp. 11104
  • 5
    • 0040207816 scopus 로고
    • The prime k-tuplets conjecture on average
    • Analytic Number Theory, Birkhäuser, Boston
    • A. Balog, 'The prime k-tuplets conjecture on average', Analytic Number Theory, Progress in Mathematics 85, Birkhäuser, Boston, 1990, 47-75. MR 92e:11105
    • (1990) Progress in Mathematics , vol.85 , pp. 47-75
    • Balog, A.1
  • 6
    • 0041182872 scopus 로고    scopus 로고
    • A. Balog, 'The prime k-tuplets conjecture on average', Analytic Number Theory, Progress in Mathematics 85, Birkhäuser, Boston, 1990, 47-75. MR 92e:11105
    • MR , vol.92 E , pp. 11105
  • 7
    • 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
  • 8
    • 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
  • 10
    • 0041182876 scopus 로고    scopus 로고
    • α mod N', Designs, Codes and Cryptography, 13 (1998), 229-245. MR 99b:11086
    • MR , vol.99 B , pp. 11086
  • 11
    • 0002768224 scopus 로고    scopus 로고
    • On a problem of Oppenheim concerning "factorisatio Numerorum"
    • E. R. Canfield, P. Erdos and C. Pomerance, 'On a problem of Oppenheim concerning "Factorisatio Numerorum"', J. Number Theory, 17 (1983), 1-28. MR 85j:11012
    • (1983) J. Number Theory , vol.17 , pp. 1-28
    • Canfield, E.R.1    Erdos, P.2    Pomerance, C.3
  • 12
    • 0002768224 scopus 로고    scopus 로고
    • E. R. Canfield, P. Erdos and C. Pomerance, 'On a problem of Oppenheim concerning "Factorisatio Numerorum"', J. Number Theory, 17 (1983), 1-28. MR 85j:11012
    • MR , vol.85 J , pp. 11012
  • 13
    • 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
  • 14
    • 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
  • 16
    • 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
  • 17
    • 0000980020 scopus 로고
    • Carmichael's lambda function
    • P. Erdos, C. Pomerance and E. Schmutz, 'Carmichael's lambda function', Acta Arith., 58 (1991), 363-385. MR 92g:11093
    • (1991) Acta Arith. , vol.58 , pp. 363-385
    • Erdos, P.1    Pomerance, C.2    Schmutz, E.3
  • 18
    • 0041182871 scopus 로고    scopus 로고
    • P. Erdos, C. Pomerance and E. Schmutz, 'Carmichael's lambda function', Acta Arith., 58 (1991), 363-385. MR 92g:11093
    • MR , vol.92 G , pp. 11093
  • 19
    • 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. 267279
    • Fischlin, R.1    Schnorr, C.P.2
  • 20
    • 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
  • 25
    • 0039403648 scopus 로고    scopus 로고
    • H. Halberstam and H.-E. Richert, Sieve methods, Academic Press, London 1974. MR 54:12689
    • MR , vol.54 , pp. 12689
  • 28
    • 0039403647 scopus 로고    scopus 로고
    • A. Hildebrand and G. Tenenbaum, 'Integers without large prime factors', J. de Théorie des Nombres de Bordeaux, 5 (1993), 411-484. MR 95d:11116
    • MR , vol.95 D , pp. 11116
  • 29
    • 0001632721 scopus 로고
    • Pseudorandom number generators in cryptography and number theory
    • Providence, RI
    • 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
    • (1990) Proc. Symp. in Appl. Math., Amer. Math. Soc. , vol.42 , pp. 115-143
    • Lagarias, J.C.1
  • 30
    • 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
  • 31
    • 0029325653 scopus 로고    scopus 로고
    • Fast generation of prime numbers and secure public-key cryptographic parameters
    • U. M. Maurer, 'Fast generation of prime numbers and secure public-key cryptographic parameters', J. Cryptology, 8 (1995), 123-155. MR 96i:94021
    • (1995) J. Cryptology , vol.8 , pp. 123-155
    • Maurer, U.M.1
  • 32
    • 0029325653 scopus 로고    scopus 로고
    • U. M. Maurer, 'Fast generation of prime numbers and secure public-key cryptographic parameters', J. Cryptology, 8 (1995), 123-155. MR 96i:94021
    • MR , vol.96 I , pp. 94021
  • 34
    • 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
  • 35
    • 0002386392 scopus 로고    scopus 로고
    • On the distribution of amicable numbers
    • C. Pomerance, 'On the distribution of amicable numbers', J. Reine Angew. Math., 293/294 (1977), 217-222. MR 56:5402
    • (1977) J. Reine Angew. Math. , vol.293-294 , pp. 217-222
    • Pomerance, C.1
  • 36
    • 0002386392 scopus 로고    scopus 로고
    • C. Pomerance, 'On the distribution of amicable numbers', J. Reine Angew. Math., 293/294 (1977), 217-222. MR 56:5402
    • MR , vol.56 , pp. 5402
  • 38
    • 24244480937 scopus 로고    scopus 로고
    • K. Prachar, Primzahlverteilung, Springer-Verlag, Berlin, 1957. MR 19:393b
    • MR , vol.19
  • 39
    • 0039995586 scopus 로고
    • Remarks on a proposed cryptanalytic attack on the M.I.T. Public-key cryptosystem
    • R. L. Rivest, 'Remarks on a proposed cryptanalytic attack on the M.I.T. public-key cryptosystem', Cryptologia, 2 (1978), 62-65.
    • (1978) Cryptologia , vol.2 , pp. 62-65
    • Rivest, R.L.1
  • 44
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.