January 2007
Beginner
544 pages
14h 21m
English
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14.4 THE BABY-STEP, GIANT-STEP ALGORITHM
The baby-step, giant-step algorithm (Shank's Algorithm) [Shanks, 1962] makes a time/memory tradeoff to solve the DLP in the cyclic group 
of order n.
Suppose q is a generator of and m = 
; the exponent x of y = qx has a representation x = im + j where 0 ≤ i, j < m. Write yq−im = qj and construct a table of size O() whose entries (j, qj) are sorted according to the second term. The cost of the sort is O( log ) = O( log n) comparisons.
Proposition 14.4 (Shank's Baby-Step, Giant-Step Algorithm):
Initialization: Compute q−m and set γ = y.
For i = 0 to m − 1 ...
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