Non-black-box Techniques Are Not Necessary for Constant Round Non-malleable Protocols

Recently, non-black-box techniques have enjoyed great success in cryptography. In particular, they have led to the construction of constant round protocols for two basic cryptographic tasks (in the plain model): non-malleable zero-knowledge (nmzk) arguments for np, and non-malleable commitments. Earlier protocols, whose security proofs relied only on black-box techniques, required non-constant (e.g., O(log n)) number of rounds. Given the inefficiency (and complexity) of existing non-black-box techniques, it is natural to ask whether they are necessary for achieving constant-round non-malleable cryptographic protocols. In this paper, we answer this question in the negative. Assuming the validity of a recently introduced assumption, namely the Gap Discrete Logarithm (gap-dl) assumption [MMY06], we construct a constant round simulation-extractable argument system for np, which implies nmzk. The gap-dl assumption also leads to a very simple and natural construction of non-interactive non-malleable commitments. In addition, plugging our simulation-extractable argument in the construction of Katz, Ostrovsky, and Smith [KOS03] yields the first O(1)-round secure multiparty computation with a dishonest majority using only black-box techniques. Although the gap-dl assumption is relatively new and non-standard, in addition to answering some long standing open questions, it brings a new approach to non-malleability which is simpler and very natural. We also demonstrate that gap-dl holds unconditionally against generic adversaries.