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In cryptography, the computational complexity of the discrete logarithm problem, along with its application, was first proposed in the Diffie–Hellman problem. Several important algorithms in public-key cryptography , such as ElGamal , base their security on the hardness assumption that the discrete logarithm problem (DLP) over carefully ...
The computation solve DLP in the 1551-bit field GF(3 6 · 163), taking 1201 CPU hours. [ 21 ] [ 22 ] in 2012 by a joint Fujitsu, NICT, and Kyushu University team, that computed a discrete logarithm in the field of 3 6 · 97 elements and a size of 923 bits, [ 23 ] using a variation on the function field sieve and beating the previous record in a ...
Data loss prevention (DLP) software detects potential data breaches/data exfiltration transmissions and prevents them by monitoring, [1] detecting and blocking sensitive data while in use (endpoint actions), in motion (network traffic), and at rest (data storage).
For a given problem, average-case hardness implies worst-case hardness, so an average-case hardness assumption is stronger than a worst-case hardness assumption for the same problem. Furthermore, even for incomparable problems, an assumption like the Exponential Time Hypothesis is often considered preferable to an average-case assumption like ...
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.
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem.
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The decisional Diffie–Hellman (DDH) assumption is a computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the security of many cryptographic protocols, most notably the ElGamal and Cramer–Shoup cryptosystems.