A CCA2 Secure Key Encapsulation Scheme Based on 3rd Order Shift Registers

Abstract

In 1998, Cramer and Shoup proposed the first practical and provable cryptosystem against adaptive chosen ciphertext attack under the standard assumption in the standard model, that is, decisional Diffie-Hellman assumption. Recently, Lucks extended the Cramer-Shoup cryptosystem to a group of quadratic residues modulo a composite number and showed that the scheme is provably secure in the standard model. In this paper, we extend Lucks’ key encapsulation scheme to a third order linear feedback shift register and is based on a new assunmption which is called shift register based decisional Diffie-Hellman assumptions (SR-DDH). The proposed scheme is provably secure against adaptive chosen ciphertext attack based on the hardness of shift register based decisional Diffie-Hellman assumption in the standard model and not in random oracle model. Furthermore, the size of public key and ciphertext are shorter than Cramer-Shoup cryptosystem and the computational complexity is also more efficient than Cramer-Shoup cryptosystem and Lucks scheme.KeywordsPublic key cryptosystemshift registersadaptive chosen-ciphertext attack