Fully-simulatable multiparty computation

Bernardo David, Ryo Nishimaki, Samuel Ranellucci +1 more

Dennis Hofheinz, Jörn Müller‐Quade, Dominique Unruh

We elaborate on the problem of polynomial runtime in simulatability definitions for multiparty computation. First, the need for a new definition is demonstrated by showing which problems occur with common definitions of polynomial runtime. Then, we give a definition which captures in an intuitive manner what it means for a protocol or an adversary to have polynomial runtime. We show that this notion is suitable for simulatability definitions for multiparty computation. In particular, a composition theorem is shown for this notion.

Albrecht Beutelspacher, Klaus-Dieter Wolfenstetter, Jörg Schwenk

Yehuda Lindell

In a multiparty signing protocol, also known as a threshold signature scheme, the private signing key is shared amongst a set of parties and only a quorum of those parties can generate a signature. Research on multiparty signing has been growing in popularity recently due to its application to cryptocurrencies. Most work has focused on reducing the number of rounds to two, and as a result: (a) are not fully simulatable in the sense of MPC real/ideal security definitions, and/or (b) are not secure under concurrent composition, and/or (c) utilize non-standard assumptions of different types in their proofs of security. In this paper, we describe a simple three-round multiparty protocol for Schnorr signatures that is secure for any number of corrupted parties; i.e., in the setting of a dishonest majority. The protocol is fully simulatable, secure under concurrent composition, and proven secure in the standard model or random-oracle model (depending on the instantiations of the commitment and zero-knowledge primitives). The protocol realizes an ideal Schnorr signing functionality with perfect security in the ideal commitment and zero-knowledge hybrid model (and thus the only assumptions needed are for realizing these functionalities). In our presentation, we do not assume that all parties begin with the message to be signed, the identities of the participating parties and a unique common session identifier, since this is often not the case in practice. Rather, the parties achieve consensus on these parameters as the protocol progresses.

Kaoru Kurosawa, Ryo Nojima

Abstract. Adaptive oblivious transfer (adaptive OT) schemes have wide applications such as oblivious database searches, secure multiparty computation and etc. It is a two-party protocol which simulates an ideal world such that the sender sends M1, · · · , Mn to the trusted third party (TTP) first, and then the receiver receives Mσi from TTP adaptively for i = 1, 2, · · · k. In the standard model, however, the fully simulatable schemes known so far had to rely on dynamic assumptions such as q-strong DH assumption, q-PDDH assumption and q-hidden LRSW assumption. This paper shows two fully simulatable adaptive OT schemes which do not rely on dynamic assumptions in the standard model. Our first scheme holds under the DDH assumption and our second scheme holds under the Paillier’s decisional Nth residuosity assumption, respectively.

Albrecht Beutelspacher, Jörg Schwenk, Klaus-Dieter Wolfenstetter