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

List of Tables
3.1 The numerical upper bounds of γ (in each cell) following Theorem
3.2, given different values of α and τ. . . . . . . . . . . . . . . 51
3.2 The numerical values of γ given α found by experiment when N
is of 1000 bits and p,q are as in Example 3.3. The lattice has the
parameters m = 7,t = 3,w = 60. . . . . . . . . . . . . . . . . . . . 55
3.3 Values of γ for τ = 0.552, 100 bit N, and p,q as in Example 3.3. . . 58
3.4 Numerical values of ǫ 3 following Theorem 3.2 where α = 1. . . . . . 61
4.1 Comparison of our theoretical bounds with that of [62]. . . . . . . . 68
4.2 Comparison of theoretical and experimental results for n = 2. . . . 72
5.1 Experimental results corresponding to Algorithm 7. . . . . . . . . . 83
5.2 Experimental runs of the Lattice Based Technique with dimension
64. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3 Percentage of success of Algorithm 8 with 512-bit p,q, i.e., l N = 1024. 93
6.1 Values of α,β for which N 1 ,N 2 can be factored efficiently. . . . . . . 100
6.2 Comparison of experimental results when α = 0.35. . . . . . . . . . 104
6.3 Theoretical and experimental values of α,β for which N 1 ,N 2 ,N 3
can be factored efficiently. Results using our technique are obtained
with the lattice dimension 20. . . . . . . . . . . . . . . . . . . . . . 107
6.4 Values of α,γ 1 ,γ 2 for which N 1 ,N 2 can be factored efficiently. . . . 110
6.5 Effect of knowing a few MSBs of q 2 . . . . . . . . . . . . . . . . . . . 112
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