Publication

Abstract : The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, {DNA} cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, {AES} are not even proven to be computationally secure). In this work, we prove that the {OTP} encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the {GLS} that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that {OTP} encryption is related to Randomized Arithmetic Coding – a scheme for joint compression and encryption.