DLOG is a hard problem in mathematics which is the inverse problem of exponentiation of a number modulo# \(p\). For instance, to find \(x\) in \(y = g^x (\mod p)\), it is written as \(x = \log_g y (\mod p)\). If \(g\) is a Primitive Root#, then DLOG always exists, otherwise it may not.
Discrete Logarithms (DLOG)
- Trapdoor One-Way Function
- TAC3121 Chapter 2: Finite Fields and Computational Number Theory
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El Gamal Encryption
El Gamal is a variant of Diffie-Hellman Key Exchange# based on the difficulty of Discrete Logarithms (DLOG)# problem invented by El Gamal in 1985*. It consists of three components: key generation, encryption, and decryption.
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Computational Diffie-Hellman (CDH) Problem
CDH Problem states that given \((g, g^x \mod p, g^y \mod p)\), find \(g^{xy} \mod p\). Based on the CDH assumption, it is generally a hard problem to solve (other than being solved by Discrete Logarithms (DLOG)#). Many asymmetric cryptographic scheme depends on CDH security guarantee.