Secure symmetric ciphers over the real field
This addresses the lack of known secure cryptosystems over real numbers, which could impact cryptography and security fields, though it appears incremental as it builds on prior work.
The paper tackles the problem of constructing secure symmetric ciphers over the real numbers, demonstrating feasibility by extending previous designs into composite ciphers with multiple encryptions and showing security enhancements through entropy-based uncertainty estimates.
Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field of real numbers are known. In this work, we demonstrate the feasibility of constructing secure symmetric key ciphers defined over the field of real numbers. We consider the security of ciphers introduced in a previous work and based on solving linear and non-linear equations numerically. We complement the design of those ciphers to satisfy the requirements of secure systems and, consequently, extend them into composite ciphers with multiple encryptions. We show security enhancements by estimating the uncertainty in finding the keys using a measure based on Shannon's entropy function.