Security and Composition of Multiparty Cryptographic Protocols

Vipul Goyal

Vipul Goyal

Daniel Simón

Koji Nuida

Secure multiparty computation (MPC) is a cryptographic technology to perform some computation on multiple parties' input data while concealing the individual inputs from other parties. For the case of semi-honest adversaries, the security definition in Goldreich's famous book is widely used as a standard definition. In this paper, however, we point out that there is an MPC protocol where a semi-honest adversary receives only a ciphertext of one-time pad with unknown key but the protocol is not secure under the standard security definition, which may look inconsistent with the perfect secrecy of one-time pad that its ciphertext leaks no information at all. We propose a variant of the security definition that resolves this issue. We also show that a somewhat restrictive version of the Composition Theorem holds for our modified security definition.

Carmit Hazay, Gert Læssøe Mikkelsen, Tal Rabin +1 more

The problem of generating an RSA composite in a distributed manner without leaking its factorization is particularly challenging and useful in many cryptographic protocols. Our first contribution is the first non-generic fully simulatable protocol for distributively generating an RSA composite with security against malicious behavior. Our second contribution is complete Paillier [Pai99] threshold encryption scheme in the two-party setting with security against malicious behavior. Furthermore, we describe how to extend our protocols to the multiparty setting with dishonest majority. Our RSA key generation is comprised of the following: (i) a distributed protocol for generation of an RSA composite, and (ii) a biprimality test for verifying the validity of the generated composite. Our Paillier threshold encryption scheme uses the RSA composite as public key and is comprised of: (i) a distributed generation of the corresponding secret-key shares and, (ii) a distributed decryption protocol for decrypting according to Paillier.

Yael Tauman Kalai, Yehuda Lindell, Manoj Prabhakaran

In the setting of secure multiparty computation, a set of mutually distrustful parties wish to securely compute some joint function of their inputs. In the stand-alone case, it has been shown that every efficient function can be securely computed. However, in the setting of concurrent composition, broad impossibility results have been proven for the case of no honest majority and no trusted setup phase. These results hold both for the case of general composition (where a secure protocol is run many times concurrently with arbitrary other protocols) and self composition (where a single secure protocol is run many times concurrently). In this paper, we investigate the feasibility of obtaining security in the concurrent setting, assuming that each party has a local clock and that these clocks proceed at approximately the same rate. We show that under this mild timing assumption, it is possible to securely compute any multiparty functionality under concurrent self composition. Loosely speaking, we also show that it is possible to securely compute any multiparty functionality under concurrent general composition, as long as the secure protocol is run only with protocols whose messages are delayed by a specified amount of time. On the negative side, we show that it is impossible to achieve security under concurrent general composition with no restrictions whatsoever on the network (like the aforementioned delays), even in the timing model.