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

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165 BIBLIOGRAPHY [86] A. May and M. Ritzenhofen. Implicit factoring: On polynomial time factoring given only an implicit hint. In Proceedings of PKC’09, volume 5443 of Lecture Notes in Computer Science, pages 1–14, 2009. [87] A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, 2001. Available at http://www.cacr.math. uwaterloo.ca/hac/. [88] R. C. Merkle and M. E. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Transactions on Information Theory, 24:525– 530, 1978. [89] D. Micciancio and S. Goldwasser. Complexity of Lattice Problems: A Cryptographic Perspective. Springer International Series in Engineering and Computer Science, 2002. [90] G. L. Miller. Riemann’s hypothesis and tests for primality. Journal of Computer and System Sciences, 13(3):300–317, December 1976. (Invited publication). [91] V. S. Miller. Use of elliptic curves in cryptography. In Proceedings of Crypto’85, volume 218 of Lecture Notes in Computer Science, pages 417– 426, 1986. [92] H. Minkowski. Geometrie der Zahlen. Teubner Verlag, 1896. [93] P. Q. Nguyen and D. Stehlé. Floating-point LLL revisited. In Proceedings of Eurocrypt’05, volume 3494 of Lecture Notes in Computer Science, pages 215–233, 2005. [94] P. Q. Nguyen and J. Stern. The two faces of lattices in cryptology. In Proceedings of CaLC’01, volume 2146 of Lecture Notes in Computer Science, pages 146–180, 2001. [95] P. Q. Nguyen and B. Vallée. The LLL Algorithm: Survey and Applications, chapter 2, pages 19–69. Information Security and Cryptography. Springer, 2009. [96] A. Nitaj. Another generalization of Wiener’s attack on RSA. In Proceedings of Africacrypt’08, volume 5023 of Lecture Notes in Computer Science, pages 174–190, 2008.
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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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111 6.3 Exposing a Few MSBs of One
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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 175 and 176: BIBLIOGRAPHY 158 [9] J. Blömer and
Page 177 and 178: BIBLIOGRAPHY 160 [31] B. de Weger.
Page 179 and 180: BIBLIOGRAPHY 162 [54] M.J.Hinek. Cr
Page 181: BIBLIOGRAPHY 164 [76] A. K. Lenstra
Page 185: BIBLIOGRAPHY 168 [121] C. L. Siegel
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