We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM), the mapping x --> xgx mod p, for p a prime and some fixed g \in (Z/pZ)* The mapping is closely related to the Discrete Log Problem, but has received far less attention since it is considered to be a more complicated map that is likely even harder to invert. However, this mapping is quite important because it underlies the security of the ElGamal Digital Signature Scheme. Using functional graphs induced by this mapping, we were able to find non-random properties that could potentially be used to exploit the ElGamal DSS.
Chen, JingJing and Lotts, Mark
"Structure and Randomness of the Discrete Lambert Map,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 5.
Available at: http://scholar.rose-hulman.edu/rhumj/vol13/iss1/5