Some Analogue of Cramer-Shoup - Md. Said, Mohamad Rushdan; Muslim, Norliana (Institute for Mathematical Research, 2008)
LUCELG and Cramer-Shoup are examples of public key cryptosystem. LUCELG uses a special group based on the Lucas function, also known as second order linear recurrence relation but the first practical Lucas function in a cryptosystem is LUC. Cramer-Shoup is a practical public key cryptosystem provably secure against adaptive chosen ciphertext attack that requires a universal one-way hash function. Based on LUCELG and Cramer-Shoup cryptosystems, analogous systems based on Lucas function and its extension are proposed and analyzed.