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The algorithm was introduced by Roland Silver, but first published by Stephen Pohlig and Martin Hellman, who credit Silver with its earlier independent but unpublished discovery. Pohlig and Hellman also list Richard Schroeppel and H. Block as having found the same algorithm, later than Silver, but again without publishing it. [2]
Download QR code; Print/export Download as PDF; Printable version ... If used together with the Pohlig–Hellman algorithm, the running time of the combined algorithm ...
The extended Euclidean algorithm finds k quickly. With Diffie–Hellman, a cyclic group modulo a prime p is used, allowing an efficient computation of the discrete logarithm with Pohlig–Hellman if the order of the group (being p−1) is sufficiently smooth, i.e. has no large prime factors.
Stephen C. Pohlig (1952/1953 in Washington, D.C. – April 14, 2017) was an American electrical engineer who worked in the MIT Lincoln Laboratory.As a graduate student of Martin Hellman's at Stanford University in the mid-1970s, he helped develop the underlying concepts of Diffie-Hellman key exchange, [1] including the Pohlig–Hellman exponentiation cipher and the Pohlig–Hellman algorithm ...
The first practical implementations followed the 1976 introduction of the Diffie-Hellman cryptosystem which relies on the discrete logarithm. Merkle's Stanford University dissertation (1979) was credited by Pohlig (1977) and Hellman and Reyneri (1983), who also made improvements to the implementation.
Used in Python 2.3 and up, and Java SE 7. ... Pohlig–Hellman algorithm; ... Sethi-Ullman algorithm: generates optimal code for arithmetic expressions;
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. [2]
As n increases, the performance of the algorithm or method in question degrades rapidly. For example, the Pohlig–Hellman algorithm for computing discrete logarithms has a running time of O ( n 1/2 )—for groups of n -smooth order .