Provably Secure Encryption Schemes With Zero Setup and Linear Speed by Using Rubik’s Cubes

Recently, new paradigms for designing modern cryptographic schemes were proposed based on Rubik's rotations. However, most of them lack rigorous provable security reductions. Enlightened by this interesting progress, we present a novel method for designing encryption schemes by using Rubik's groups. Different from most naive designs of permutation ciphers based on Rubik's cubes, our proposals are probabilistic encryption schemes that combine some of the newest cryptographic primitives with modern coding theory. More specifically, under the intractability assumption of the conjugacy decision problem over Rubik's groups, the proposed schemes have provable security reductions (in the random oracle model). Furthermore, the proposed schemes have two remarkable performance advantages: zero setup and linear encryption/decryption speed. In addition, the processes of encoding/encryption and decryption/decoding are demonstrated graphically.