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Arrays over roots of unity with perfect autocorrelation and good ZCZ cross-correlation
Improved bounds for the implicit factorization problem
1. | State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China, China, China |
References:
[1] |
H. Cohn and N. Heninger, Approximate common divisors via lattices, preprint, arXiv:1108.2714 |
[2] |
D. Coppersmith, Small solutions to polynomial equations, and low exponent RSA vulnerabilities, J. Cryptology, 10 (1997), 233-260.
doi: 10.1007/s001459900030. |
[3] |
J. C. Faugère, R. Marinier and G. Renault, Implicit factoring with shared most significant and middle bits, in "Public Key Cryptography-PKC 2010,'' (2010), 70-87.
doi: 10.1007/978-3-642-13013-7_5. |
[4] |
M. Herrmann and A. May, Solving linear equations modulo divisors: On factoring given any bits in "Advances in Cryptology-ASIACRYPT 2008,'' (2008), 406-424.
doi: 10.1007/978-3-540-89255-7_25. |
[5] |
N. Howgrave-Graham, Finding small roots of univariate modular equations revisited, in "Crytography and Coding,'' Springer, Berlin, (1997), 131-142.
doi: 10.1007/BFb0024458. |
[6] |
A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Annalen, 261 (1982), 515-534.
doi: 10.1007/BF01457454. |
[7] |
A. May, "New RSA Vulnerabilities Using Lattice Reduction Methods,'' Ph.D thesis, University of Paderborn, 2003. |
[8] |
A. May and M. Ritzenhofen, Implicit factoring: On polynomial time factoring given only an implicit hint, in "Public Key Cryptography-PKC 2009,'' (2009), 1-14.
doi: 10.1007/978-3-642-00468-1_1. |
[9] |
S. Sarkar and S. Maitra, Approximate integer common divisor problem relates to implicit factorization, IEEE Trans. Inform. Theory, 57 (2011), 4002-4013.
doi: 10.1109/TIT.2011.2137270. |
[10] |
S. Sarkar and S. Maitra, Further results on implicit factoring in polynomial time, Adv. Math. Commun., 3 (2009), 205-217.
doi: 10.3934/amc.2009.3.205. |
show all references
References:
[1] |
H. Cohn and N. Heninger, Approximate common divisors via lattices, preprint, arXiv:1108.2714 |
[2] |
D. Coppersmith, Small solutions to polynomial equations, and low exponent RSA vulnerabilities, J. Cryptology, 10 (1997), 233-260.
doi: 10.1007/s001459900030. |
[3] |
J. C. Faugère, R. Marinier and G. Renault, Implicit factoring with shared most significant and middle bits, in "Public Key Cryptography-PKC 2010,'' (2010), 70-87.
doi: 10.1007/978-3-642-13013-7_5. |
[4] |
M. Herrmann and A. May, Solving linear equations modulo divisors: On factoring given any bits in "Advances in Cryptology-ASIACRYPT 2008,'' (2008), 406-424.
doi: 10.1007/978-3-540-89255-7_25. |
[5] |
N. Howgrave-Graham, Finding small roots of univariate modular equations revisited, in "Crytography and Coding,'' Springer, Berlin, (1997), 131-142.
doi: 10.1007/BFb0024458. |
[6] |
A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Annalen, 261 (1982), 515-534.
doi: 10.1007/BF01457454. |
[7] |
A. May, "New RSA Vulnerabilities Using Lattice Reduction Methods,'' Ph.D thesis, University of Paderborn, 2003. |
[8] |
A. May and M. Ritzenhofen, Implicit factoring: On polynomial time factoring given only an implicit hint, in "Public Key Cryptography-PKC 2009,'' (2009), 1-14.
doi: 10.1007/978-3-642-00468-1_1. |
[9] |
S. Sarkar and S. Maitra, Approximate integer common divisor problem relates to implicit factorization, IEEE Trans. Inform. Theory, 57 (2011), 4002-4013.
doi: 10.1109/TIT.2011.2137270. |
[10] |
S. Sarkar and S. Maitra, Further results on implicit factoring in polynomial time, Adv. Math. Commun., 3 (2009), 205-217.
doi: 10.3934/amc.2009.3.205. |
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