Constructing Variable-Length PRPs and SPRPs from Fixed-Length PRPs

We create variable-length pseudorandompermutations (PRPs) and strong PRPs (SPRPs) accepting inputs of any length in the range of b to 2b bits from fixed-length, b-bit PRPs.We utilize the elastic network that underlies the recently introduced concrete design of elastic block ciphers, exploiting it as a network of PRPs. We prove that three and four-round elastic networks are variable-length PRPs and five-round elastic networks are variable-length SPRPs, accepting any input length in the range of b to 2b bits, when the round functions are independently chosen fixed-length PRPs on b bits.We also prove that these are the minimal number of rounds required.