Research Article
Sieve Method for Polynomial Linear Equivalence
Algorithm 4
The sieve algorithm for PLE:
SieAlg .
(1) Randomly choose n linearly independent vectors . Store | the n row vectors as an invertible n-dimensional matrix X. | (2) for do | (3) Compute and the pre-image set . | (4) Store the set . | (5) end for //Algorithm Initialization. | (6) for do | (7) Run MulSieve and assign the output to . | (8) end for //Multiplicative Sieve. | (9) for do | (10) for do | (11) Run AddSieve and assign the output to | and . | (12) end for | (13) end for //Additive Sieve. | (14) for do | (15) Run DifSieve and assign the output to . | (16) end for //Differential Sieve. | (17) for do | (18) Randomly choose a vector from and assign the vector to . | (19) end for | (20) Denote the set of vectors as a matrix Y. | (21) Compute . | (22) if then | (23) return M. | (24) else | (25) return . | (26) end if |
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