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

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161 BIBLIOGRAPHY [42] M. K. Franklin and M. K. Reiter. A linear protocol failure for RSA with exponent three. Crypto’95 Rump Session, 1995. [43] Free Software Foundation, Inc. GMP: The GNU Multiple Precision Arithmetic Library. Available at http://gmplib.org/. [44] S. Goldwasser and J. Kilian. Primality testing using elliptic curves. Journal of the ACM, 46(4):450–472, 1999. [45] S. Goldwasser and S. Micali. Probabilistic encryption. Journal of Computer and System Sciences, 28:450–472, 1984. [46] J. A. Halderman, S. D. Schoen, N. Heninger, W. Clarkson, W. Paul, J. A. Calandrino, A. J. Feldman, J. Appelbaum, and E. W. Felten. Lest we remember: cold-boot attacks on encryption keys. Commun. ACM, 52(5):91– 98, 2009. [47] G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. Oxford University Press, USA, 1960. [48] J. Håstad. On using RSA with low exponent in a public key network. In Proceedings of Crypto’85, volume 218 of Lecture Notes in Computer Science, pages 403–408, 1986. [49] J. Håstad. Solving simultaneous modular equations of low degree. SIAM Journal on Computing, 17(2):336–341, 1988. [50] N.HeningerandH.Shacham. ReconstructingRSAprivatekeysfromrandom key bits. In Proceedings of Crypto’09, volume 5677 of Lecture Notes in Computer Science, pages 1–17, 2009. [51] M. Herrmann and A. May. Solving linear equations modulo divisors: On factoring given any bits. In Proceedings of Asiacrypt’08, volume 5350 of Lecture Notes in Computer Science, pages 406–424, 2008. [52] M. J. Hinek. Another look at small RSA exponents. In Proceedings of CT- RSA’06, volume 3860 of Lecture Notes in Computer Science, pages 82–98, 2006. [53] M.J.Hinek. On the security of some variants of RSA. PhDthesis,University of Waterloo, Canada, 2007. Available at http://uwspace.uwaterloo.ca/ handle/10012/2988.
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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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107 6.2 Two Primes with Shared Cont
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109 6.2 Two Primes with Shared Cont
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Page 169 and 170: Chapter 8: Conclusion 152 p 1 ,p 2
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Page 173 and 174: Chapter 8: Conclusion 156 Final Wor
Page 175 and 176: BIBLIOGRAPHY 158 [9] J. Blömer and
Page 177: BIBLIOGRAPHY 160 [31] B. de Weger.
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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