Pre-computation Table for Discrete Logarithm Computation

The patent applies preliminary action by pre-computing and storing chains of function values in a table before the actual discrete logarithm problem needs to be solved. The pre-computation table stores values of the form (g^i mod p, i) where g is a generator and i ranges from 0 to a predetermined maximum. When a discrete logarithm problem y = g^x mod p needs to be solved, the system only needs to compute g^y mod p and look up the result in the pre-computed table, significantly reducing computation time at the cost of storing the pre-computed values in memory.

The patent applies segmentation by dividing the pre-computation table into multiple segments or chains, where each chain corresponds to a different starting value or generator. Instead of storing all possible discrete logarithm values in a single large table, the system creates multiple smaller chains that can be independently managed and searched. This segmentation reduces the complexity of individual table structures while maintaining comprehensive coverage for solving discrete logarithm problems.