Дискретті логарифмді шешу алгоритмі: Shanks әдісі

Algorithm for solving the discrete logarithm problem
In group theory, a branch of mathematics, the baby step giant step is a meet in the middle algorithm for computing the discrete logarithm or order of an element in a finite abelian group by Daniel Shanks. The discrete log problem is of fundamental importance to the area of public key cryptography. Many of the most commonly used cryptography systems are based on the assumption that the discrete log is extremely difficult to compute; the more difficult it is, the more security it provides a data transfer. One way to increase the difficulty of the discrete log problem is to base the cryptosystem on a larger group.

The best way to speed up the baby step giant step algorithm is to use an efficient table lookup scheme. The best in this case is a hash table. The hashing is done on the second component, and to perform the check in step 1 of the main loop, γ is hashed and the resulting memory address checked. Since hash tables can retrieve and add elements in time (constant time), this does not slow down the overall baby step giant step algorithm. The space complexity of the algorithm is , while the time complexity of the algorithm is This running time is better than the running time of the naive brute force calculation. The Baby step giant step algorithm could be used by an eavesdropper to derive the private key generated in the Diffie Hellman key exchange, when the modulus is a prime number that is not too large. If the modulus is not prime, the Pohlig–Hellman algorithm has a smaller algorithmic complexity, and potentially solves the same problem.