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

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167 BIBLIOGRAPHY [108] R. L. Rivest. The RC4 encryption algorithm. RSA Data Security, Inc., 1992. [109] R. L. Rivest and A. Shamir. Efficient factoring based on partial information. In Proceedings of Eurocrypt’85, volume 219 of Lecture Notes in Computer Science, pages 31–34, 1986. [110] R. L. Rivest, A. Shamir, and L. M. Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communications of the Association for Computing Machinery, 21(2):120–126, 1978. [111] G. G. Rose and P. Hawkes. Turing: A fast stream cipher. In Proceedings of FSE’03, volume 2887 of Lecture Notes in Computer Science, pages 290–306, 2003. [112] S. Sarkar and S. Maitra. Approximate integer common divisor problem relates to implicit factorization. To appear in IEEE Transactions on Information Theory (accepted on 12th December, 2010). [113] S. Sarkar and S. Maitra. Further results on implicit factoring in polynomial time. Advances in Mathematics of Communications, 3(2):205–217, 2009. [114] S. Sarkar and S. Maitra. Cryptanalysis of RSA with more than one decryption exponent. Information Processing Letters, 110(8-9):336–340, 2010. [115] S. Sarkar and S. Maitra. Cryptanalysis of RSA with two decryption exponents. Information Processing Letters, 110(5):178–181, 2010. [116] S. Sarkar and S. Maitra. Some applications of lattice based root finding techniques. Advances in Mathematics of Communications, 4(4):519–531, 2010. [117] A. Shamir. A polynomial time algorithm for breaking the basic Merkle- Hellman cryptosystem. In Proceedings of Crypto’82, pages 279–288, 1982. [118] A. Shamir. A polynomial time algorithm for breaking the basic Merkle- Hellman cryptosystem. In Proceedings of FOCS’82, pages 145–152, 1982. [119] P. W. Shor. Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings of FOCS’94, pages 124–134, 1994. [120] P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5):1484–1509, 1997.
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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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Chapter 7 Approximate Integer Commo
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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 and 182: BIBLIOGRAPHY 164 [76] A. K. Lenstra
Page 183: BIBLIOGRAPHY 166 [97] A. Nitaj. Cry
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