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

More documents

Recommendations

Info

163 BIBLIOGRAPHY [65] E. Jochemsz and A. May. A strategy for finding roots of multivariate polynomials with new applications in attacking RSA variants. In Proceedings of Asiacrypt’06, volume 4284 of Lecture Notes in Computer Science, pages 267–282, 2006. [66] E. Jochemsz and A. May. A polynomial time attack on RSA with private CRT-exponents smaller than N 0.073 . In Proceedings of Crypto’07, volume 4622 of Lecture Notes in Computer Science, pages 395–411, 2007. [67] A. Joux, D. Naccache, and E. Thomé. When e-th roots become easier than factoring. In Proceedings of Asiacrypt’07, volume 4833 of Lecture Notes in Computer Science, pages 13–28, 2007. [68] A. Joux and J. Stern. Lattice reduction: A toolbox for the cryptanalyst. Journal of Cryptology, 11(3):161–185, 1998. [69] T. Kleinjung, K. Aoki, J. Franke, A. K. Lenstra, E. Thomé, J. W. Bos, P. Gaudry, A. Kruppa, P. L. Montgomery, D. A. Osvik, H. J. J. te Riele, A. Timofeev, and P. Zimmermann. Factorization of a 768-bit RSA modulus. In Proceedings of Crypto’10, volume 6223 of Lecture Notes in Computer Science, pages 333–350, 2010. [70] D. E. Knuth. The Art of Computer Programming: Seminumerical Algorithms, volume 2. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 3 edition, 1997. [71] N. Koblitz. Elliptic curve cryptosystems. Mathematics of Computation, 48:203–209, 1987. [72] P. C. Kocher. Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In Proceedings of Crypto’96, volume 1109 of Lecture Notes in Computer Science, pages 104–113, 1996. [73] J. C. Lagarias. The computational complexity of simultaneous Diophantine approximation problems. In Proceedings of FOCS’82, pages 32–39, 1982. [74] J. C. Lagarias. The computational complexity of simultaneous Diophantine approximationproblems. SIAM Journal on Computing, 14(1):196–209, 1985. [75] A. K. Lenstra. Integer factoring. In Encyclopedia of Cryptography and Security, pages 290–297. Springer, 2005.
BIBLIOGRAPHY 164 [76] A. K. Lenstra and H. W. Lenstra, Jr., editors. The Development of the Number Field Sieve, volume1554ofLecture Notes in Mathematics. Springer- Verlag, Berlin, 1993. [77] A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen, 261:515–534, 1982. [78] A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, and J. M. Pollard. The factorization of the ninth Fermat number. Mathematics of Computation, 61(203):319–349, 1993. [79] H. W. Lenstra, Jr. Factoring integers with elliptic curves. Annals of Mathematics, 126:649–673, 1987. [80] F. Luca and P. Stănică. On the prime power factorization of n!. Journal of Number Theory, 102/2:298–305, 2003. [81] S. Maitra and S. Sarkar. A new class of weak encryption exponents in RSA. In Proceedings of Indocrypt’08, volume 5365 of Lecture Notes in Computer Science, pages 337–349, 2008. [82] S. Maitra, S. Sarkar, and S. Sen Gupta. Factoring RSA modulus using prime reconstruction from random known bits. In Proceedings of Africacrypt’10, volume 6055 of Lecture Notes in Computer Science, pages 82–99, 2010. [83] A. May. New RSA Vulnerabilities Using Lattice Reduction Methods. PhD thesis, University of Paderborn, Germany, 2003. Available at http://www. cs.uni-paderborn.de/uploads/tx_sibibtex/bp.pdf. [84] A. May. Using LLL-reduction for solving RSA and factorization problems. Technical report, LLL+25 Conference in honour of the 25th birthday of the LLL algorithm, Technische Universität Darmstadt, 2007. Available at http://www.informatik.tu-darmstadt.de/KP/alex.html. [85] A. May and M. Ritzenhofen. Solving systems of modular equations in one variable: How many RSA-encrypted messages does Eve need to know? In Proceedings of PKC’08, volume 4939 of Lecture Notes in Computer Science, pages 37–46, 2008.
Page 1:
some results on Cryptanalysis of RS
Page 5 and 6:
Abstract In this thesis, we propose
Page 7 and 8:
Acknowledgements There are many peo
Page 9:
To Thaakuma (Grandmother), the firs
Page 12 and 13:
2.3.7 Small Decryption Exponent Att
Page 14 and 15:
7.4 The General Solution for EPACDP
Page 17 and 18:
List of Figures 1.1 Communication o
Page 19 and 20:
Chapter 1: Introduction 2 The motiv
Page 21 and 22:
Chapter 1: Introduction 4 there is
Page 23 and 24:
Chapter 1: Introduction 6 Discrete
Page 25 and 26:
Chapter 1: Introduction 8 Chapter 5
Page 28 and 29:
Chapter 2 Mathematical Preliminarie
Page 30 and 31:
13 2.2 RSA Cryptosystem are impleme
Page 32 and 33:
15 2.2 RSA Cryptosystem • private
Page 34 and 35:
17 2.2 RSA Cryptosystem istic prima
Page 36 and 37:
19 2.2 RSA Cryptosystem Afterfindin
Page 38 and 39:
21 2.2 RSA Cryptosystem integer x <
Page 40 and 41:
23 2.3 Cryptanalysis of RSA to be h
Page 42 and 43:
25 2.3 Cryptanalysis of RSA The att
Page 44 and 45:
27 2.4 Lattice and LLL Algorithm No
Page 46 and 47:
29 2.4 Lattice and LLL Algorithm Wh
Page 48 and 49:
31 2.5 Solving Modular Polynomials
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
39 2.6 Solving Integer Polynomials
Page 58 and 59:
41 2.6 Solving Integer Polynomials
Page 60 and 61:
43 2.7 Analysis of the Root Finding
Page 62:
45 2.9 Conclusion 2.9 Conclusion No
Page 65 and 66:
Chapter 3: A class of Weak Encrypti
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Chapter 4: Cryptanalysis of RSA wit
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 92 and 93:
Chapter 5 Reconstruction of Primes
Page 94 and 95:
77 5.1 LSB Case: Combinatorial Anal
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
85 5.2 LSB Case: Lattice Based Tech
Page 104 and 105:
87 5.3 MSB Case: Our Method and its
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Chapter 6 Implicit Factorization In
Page 114 and 115:
97 6.1 Implicit Factoring of Two La
Page 116 and 117:
99 6.1 Implicit Factoring of Two La
Page 118 and 119:
101 6.1 Implicit Factoring of Two L
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
107 6.2 Two Primes with Shared Cont
Page 126 and 127:
109 6.2 Two Primes with Shared Cont
Page 128 and 129:
111 6.3 Exposing a Few MSBs of One
Page 130 and 131: 113 6.3 Exposing a Few MSBs of One
Page 132 and 133: Chapter 7 Approximate Integer Commo
Page 134 and 135: 117 7.1 Finding q −1 mod p ≡ Fa
Page 136 and 137: 119 7.2 Finding Smooth Integers in
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
Page 158 and 159: 141 7.6 Improved Results for Larger
Page 160 and 161: 143 7.7 EGACDP The approach in this
Page 162 and 163: 145 7.7 EGACDP Sinceinthiscasethema
Page 164: 147 7.8 Conclusion poly{loga,k}. Th
Page 167 and 168: Chapter 8: Conclusion 150 Chapter 3
Page 169 and 170: Chapter 8: Conclusion 152 p 1 ,p 2
Page 171 and 172: Chapter 8: Conclusion 154 represent
Page 173 and 174: Chapter 8: Conclusion 156 Final Wor
Page 175 and 176: BIBLIOGRAPHY 158 [9] J. Blömer and
Page 177 and 178: BIBLIOGRAPHY 160 [31] B. de Weger.
Page 179: BIBLIOGRAPHY 162 [54] M.J.Hinek. Cr
Page 183 and 184: BIBLIOGRAPHY 166 [97] A. Nitaj. Cry
Page 185: BIBLIOGRAPHY 168 [121] C. L. Siegel
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?