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Counting Solutions To Discrete Non-Algebraic Equations Modulo Prime Powers, Abigail Mann
Counting Solutions To Discrete Non-Algebraic Equations Modulo Prime Powers, Abigail Mann
Mathematical Sciences Technical Reports (MSTR)
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is thought that the functions that such schemes use have inverses that are computationally intractable. In relation to this, we are interested in counting the solutions to a generalization of the discrete logarithm problem modulo a prime power. This is achieved by interpolating to p-adic functions, and using Hensel's lemma, or other methods in the case of singular lifting, and the Chinese Remainder Theorem.
Statistical Analysis Of Binary Functional Graphs Of The Discrete Logarithm, Mitchell Orzech
Statistical Analysis Of Binary Functional Graphs Of The Discrete Logarithm, Mitchell Orzech
Mathematical Sciences Technical Reports (MSTR)
The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively difficult. Therefore, we focus on the statistical analysis of certain properties of the graph of the discrete logarithm. We discovered the expected value and variance of a certain property of the graph and compare the expected value to experimental data. Our finding did not coincide with our intuition of the data following a Gaussian distribution given a large sample size. Thus, we found the …