Ulianov Elliptic Cryptography: A Real-Number-Based Asymmetric Encryption Model

Abstract

Traditional cryptographic algorithms such as RSA and ECC rely on the computational difficulty of problems like prime factorization and discrete logarithms. However, these systems are increasingly vulnerable in the face of emerging quantum computing technologies, which can efficiently solve these problems using algorithms like Shor’s. Ulianov Elliptic Cryptography (UEC) introduces a fundamentally new approach based on non-invertible real-number functions and high-entropy embedding techniques, offering resistance to both classical and quantum attacks. This paper presents the theoretical foundation of UEC, its key components, and a security analysis that demonstrates its robustness.