Cryptanalysis of RSA Factorization - Library(ISI Kolkata) - Indian ...

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Bibliography [1] Advanced Encryption Standard. National Institute of Standards and Technology, 2001. Available at http://csrc.nist.gov/CryptoToolkit/aes/ rijndael/. [2] D. Aggarwal and U. M. Maurer. Breaking RSA generically is equivalent to factoring. In Proceedings of Eurocrypt’09, volume 5479 of Lecture Notes in Computer Science, pages 36–53, 2009. [3] M. Agrawal, N. Kayal, and N. Saxena. Primes is in P. Annals of Mathematics, 2:781–793, 2002. [4] M.AjtaiandC.Dwork. Apublic-keycryptosystemwithworst-case/averagecase equivalence. Electronic Colloquium on Computational Complexity (ECCC), 3(65), 1996. [5] M.AjtaiandC.Dwork. Apublic-keycryptosystemwithworst-case/averagecase equivalence. In Proceedings of STOC’97, pages 284–293, 1997. [6] A. O. L. Atkin and F. Morain. Elliptic curves and primality proving. Mathematics of Computation, 61:29–68, 1993. [7] A. Bauer and A. Joux. Toward a rigorous variation of Coppersmith’s algorithm on three variables. In Proceedings of Eurocrypt’07, volume 4515 of Lecture Notes in Computer Science, pages 361–378, 2007. [8] J. Blömer and A. May. New partial key exposure attacks on RSA. In Proceedings of Crypto’03,volume2729ofLecture Notes in Computer Science, pages 27–43, 2003. 157
BIBLIOGRAPHY 158 [9] J. Blömer and A. May. A generalized Wiener attack on RSA. In Proceedings of PKC’04, volume 2947 of Lecture Notes in Computer Science, pages 1–13, 2004. [10] J. Blömer and A. May. A tool kit for finding small roots of bivariate polynomials over the integers. In Proceedings of Eurocrypt’05, volume 3494 of Lecture Notes in Computer Science, pages 251–267, 2005. [11] D. Boneh. Twenty years of attacks on the RSA cryptosystem. Notices of the AMS, 46:203–213, 1999. [12] D. Boneh. Finding smooth integers in short intervals using CRT decoding. In Proceedings of STOC’00, pages 265–272, 2000. [13] D. Boneh. Finding smooth integers in short intervals using CRT decoding. Journal of Computer and System Sciences, 64(4):768–784, 2002. [14] D. Boneh and G. Durfee. Cryptanalysis of RSA with private key less than N 0.292 . In Proceedings of Eurocrypt’99, volume 1592 of Lecture Notes in Computer Science, pages 1–11, 1999. [15] D. Boneh and G. Durfee. Cryptanalysis of RSA with private key d less than N 0.292 . IEEE Transactions on Information Theory, 46:1339–1349, 2000. [16] D. Boneh, G. Durfee, and Y. Frankel. An attack on RSA given a small fraction of the private key bits. In Proceedings of Asiacrypt’98, volume 1514 of Lecture Notes in Computer Science, pages 25–34, 1998. [17] D. Boneh, G. Durfee, and N. Howgrave-Graham. Factoring n = p r q for large r. In Proceedings of Crypto’99, volume 1666 of Lecture Notes in Computer Science, pages 326–337, 1999. [18] D. Boneh and R. Venkatesan. Breaking RSA may not be equivalent to factoring. In Proceedings of Eurocrypt’98, volume 1403 of Lecture Notes in Computer Science, pages 59–71, 1998. [19] D. R. L. Brown. Breaking RSA may be as difficult as factoring. Cryptology ePrint Archive, Report 2005/380, 2005. Available at http://eprint.iacr. org/.
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some results on Cryptanalysis of RS
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Abstract In this thesis, we propose
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Acknowledgements There are many peo
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To Thaakuma (Grandmother), the firs
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2.3.7 Small Decryption Exponent Att
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7.4 The General Solution for EPACDP
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List of Figures 1.1 Communication o
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Chapter 1: Introduction 2 The motiv
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Chapter 1: Introduction 4 there is
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Chapter 1: Introduction 6 Discrete
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Chapter 1: Introduction 8 Chapter 5
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Chapter 2 Mathematical Preliminarie
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13 2.2 RSA Cryptosystem are impleme
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15 2.2 RSA Cryptosystem • private
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17 2.2 RSA Cryptosystem istic prima
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19 2.2 RSA Cryptosystem Afterfindin
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21 2.2 RSA Cryptosystem integer x <
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23 2.3 Cryptanalysis of RSA to be h
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25 2.3 Cryptanalysis of RSA The att
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27 2.4 Lattice and LLL Algorithm No
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29 2.4 Lattice and LLL Algorithm Wh
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31 2.5 Solving Modular Polynomials
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39 2.6 Solving Integer Polynomials
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41 2.6 Solving Integer Polynomials
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43 2.7 Analysis of the Root Finding
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45 2.9 Conclusion 2.9 Conclusion No
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Chapter 3: A class of Weak Encrypti
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Chapter 4: Cryptanalysis of RSA wit
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Chapter 5 Reconstruction of Primes
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77 5.1 LSB Case: Combinatorial Anal
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85 5.2 LSB Case: Lattice Based Tech
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87 5.3 MSB Case: Our Method and its
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Chapter 6 Implicit Factorization In
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97 6.1 Implicit Factoring of Two La
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99 6.1 Implicit Factoring of Two La
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101 6.1 Implicit Factoring of Two L
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Page 124 and 125: 107 6.2 Two Primes with Shared Cont
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Page 130 and 131: 113 6.3 Exposing a Few MSBs of One
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Page 134 and 135: 117 7.1 Finding q −1 mod p ≡ Fa
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Page 138 and 139: 121 7.3 Extension of Approximate Co
Page 140 and 141: 123 7.4 The General Solution for EP
Page 150 and 151: 133 7.5 Sublattice and Generalized
Page 156 and 157: 139 7.6 Improved Results for Larger
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Page 160 and 161: 143 7.7 EGACDP The approach in this
Page 162 and 163: 145 7.7 EGACDP Sinceinthiscasethema
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Page 169 and 170: Chapter 8: Conclusion 152 p 1 ,p 2
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Page 173: Chapter 8: Conclusion 156 Final Wor
Page 177 and 178: BIBLIOGRAPHY 160 [31] B. de Weger.
Page 179 and 180: BIBLIOGRAPHY 162 [54] M.J.Hinek. Cr
Page 181 and 182: BIBLIOGRAPHY 164 [76] A. K. Lenstra
Page 183 and 184: BIBLIOGRAPHY 166 [97] A. Nitaj. Cry
Page 185: BIBLIOGRAPHY 168 [121] C. L. Siegel
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Cryptanalysis of RSA Factorization - Library(ISI Kolkata) - Indian ...

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