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 image of order n.

Suppose q is a generator of image and m = imageimageimage; the exponent x of y = qx has a representation x = im + j where 0 ≤ i, j < m. Write yqim = qj and construct a table of size O(image) whose entries (j, qj) are sorted according to the second term. The cost of the sort is O(image log image) = O(image log n) comparisons.

Proposition 14.4 (Shank's Baby-Step, Giant-Step Algorithm):

Initialization: Compute qm and set γ = y.

For i = 0 to m − 1 ...

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