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Structure And Randomness Of The Discrete Lambert Map, Jingjing Chen, Mark Lotts
Structure And Randomness Of The Discrete Lambert Map, Jingjing Chen, Mark Lotts
Mathematical Sciences Technical Reports (MSTR)
We investigate the structure and cryptographic applications of the Discrete Lambert Map (DLM). 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.
The Square Discrete Exponentiation Map, A Wood
The Square Discrete Exponentiation Map, A Wood
Mathematical Sciences Technical Reports (MSTR)
We will examine the square discrete exponentiation map and its properties. The square discrete exponentiation map is a variation on a commonly seen problem in cryptographic algorithms. This paper focuses on understanding the underlying structure of the functional graphs generated by this map. Specifically, this paper focuses on explaining the in-degree of graphs of safe primes, which are primes of the form p = 2q + 1, where q is also prime.
Algebraic Solutions To Overdefined Systems With Applications To Cryptanalysis, Eric Crockett
Algebraic Solutions To Overdefined Systems With Applications To Cryptanalysis, Eric Crockett
Mathematical Sciences Technical Reports (MSTR)
Cryptographic algorithms are based on a wide variety of difficult problems in mathematics. One of these problems is finding a solution to a system of multivariate quadratic equations (MQ). A generalization of this problem is to find a solution to a system of higher order non-linear equations. Both of these problems are NP-hard over any field. Many cryptosystems such as AES, Serpent, Toyocrypt, and others can be reduced to some form of the MQ problem. In this paper we analyze the relinearization and XL algorithms for solving overdetermined systems of non-linear equations, as well as two variations of the XL …