Counting Solutions to Discrete Non-Algebraic Equations Modulo Prime Powers
This addresses cryptographic security by analyzing a foundational problem in encryption schemes, but appears incremental as it builds on existing mathematical techniques.
The paper tackles the problem of counting solutions to a generalization of the discrete logarithm problem modulo prime powers, using methods like p-adic interpolation and Hensel's lemma, but does not report concrete numerical results.
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.