VTBPEKE: Verifier-based Two-Basis Password Exponential Key Exchange

PAKE protocols, for Password-Authenticated Key Exchange, enable two parties to establish a shared cryptographically strong key over an insecure network using a short common secret as authentication means. After the seminal work by Bellovin and Merritt, with the famous EKE, for Encrypted Key Exchange, various settings and security notions have been defined, and many protocols have been proposed. In this paper, we revisit the promising SPEKE, for Simple Password Exponential Key Exchange, proposed by Jablon. The only known security analysis works in the random oracle model under the CDH assumption, but in the multiplicative groups of finite fields only (subgroups of Zp*), which means the use of large elements and so huge communications and computations. Our new instantiation (TBPEKE, for Two-Basis Password Exponential Key Exchange) applies to any group, and our security analysis requires a DLIN-like assumption to hold. In particular, one can use elliptic curves, which leads to a better efficiency, at both the communication and computation levels. We additionally consider server corruptions, which immediately leak all the passwords to the adversary with symmetric PAKE. We thus study an asymmetric variant, also known as VPAKE, for Verifier-based Password Authenticated Key Exchange. We then propose a verifier-based variant of TBPEKE, the so-called VTBPEKE, which is also quite efficient, and resistant to server-compromise.