Groth proposes a shuffle-based scheme for an n-move honest verifier zero-knowledge (HVZK) argument, to shuffle known messages. The goal of this shuffle-based HVZK (SHVZK) scheme is to produce efficient HVZK arguments for the correctness of a shuffle. The author follows the Neff paradigm, where the shuffling is based on invariance of polynomials under permutation of their roots.

The author claims that the HVZK argument for correctness of the shuffle is the most efficient in terms of both computation and communication. This claim is proved through a thorough analysis of the overhead associated with the scheme, in section 6, and a subsequent comparison with other schemes, in section 7. The proposed scheme is applicable for multi-exponentiation and for randomized batch verification techniques.

The paper is written in the form of a thorough lead-through from questions such as why such a scheme is needed, to fine details of the scheme, in terms of arguments needed for homomorphic encryptions, and how verifiability is achieved for diverse applications such as mix servers (wherein voting is essential). Groth states that all arguments in the proposed scheme can be turned into HVZK proofs. The tone of the paper leads me to believe that it is intended for readers with a background in cryptography, but the language used makes it very easily accessible to any reader with a background in computing (particularly in network security).