Secure multi-party computation (MPC) allows participating parties to jointly compute a function over their inputs while keeping them private. In particular, MPC based on additive secret sharing has been widely studied as a tool to obtain efficient protocols secure against a dishonest majority, including the important two-party case. In this paper, we propose a two-party protocol for an exponentiation functionality based on an additive secret sharing scheme. Our proposed protocol aims to securely compute a public base exponentiation ax mod p for an odd prime p, where the exponent x ∈ ℤp is a (shared) secret and the base a ∈ ℤp is public. Our protocol is based on a new simple but efficient approach involving quotient transfer that allows the parties to perform the most expensive part of the computation locally, but requires the base a ∈ ℤp to be a quadratic residue. To address scenarios where the base does not fulfill this, we combine our exponentiation protocol with a new efficient modulus conversion protocol which might be of independent interest. Even taking into account a potential modulus conversion, our exponentiation protocol only requires 3 rounds and 4 invocations of multiplication.
Secure multi-party computation (MPC) allows participating parties to jointly compute a function over their inputs while keeping them private. In particular, MPC based on additive secret sharing has been widely studied as a tool to obtain efficient protocols secure against a dishonest majority, including the important two-party case. In this paper, we propose a two-party protocol for an exponentiation functionality based on an additive secret sharing scheme. Our proposed protocol aims to securely compute a public base exponentiation ax mod p for an odd prime p, where the exponent x ∈ ℤp is a (shared) secret and the base a ∈ ℤp is public. Our protocol is based on a new simple but efficient approach involving quotient transfer that allows the parties to perform the most expensive part of the computation locally, but requires the base a ∈ ℤp to be a quadratic residue. To address scenarios where the base does not fulfill this, we combine our exponentiation protocol with a new efficient modulus conversion protocol which might be of independent interest. Even taking into account a potential modulus conversion, our exponentiation protocol only requires 3 rounds and 4 invocations of multiplication.
In recent years, multi-party computation (MPC) frameworks based on replicated secret sharing schemes (RSSS) have attracted the attention as a method to achieve high efficiency among known MPCs. However, the RSSS-based MPCs are still inefficient for several heavy computations like algebraic operations, as they require a large amount and number of communication proportional to the number of multiplications in the operations (which is not the case with other secret sharing-based MPCs). In this paper, we propose RSSS-based three-party computation protocols for modular exponentiation, which is one of the most popular algebraic operations, on the case where the base is public and the exponent is private. Our proposed schemes are simple and efficient in both of the asymptotic and practical sense. On the asymptotic efficiency, the proposed schemes require O(n)-bit communication and O(1) rounds,where n is the secret-value size, in the best setting, whereas the previous scheme requires O(n2)-bit communication and O(n) rounds. On the practical efficiency, we show the performance of our protocol by experiments on the scenario for distributed signatures, which is useful for secure key management on the distributed environment (e.g., distributed ledgers). As one of the cases, our implementation performs a modular exponentiation on a 3,072-bit discrete-log group and 256-bit exponent with roughly 300ms, which is an acceptable parameter for 128-bit security, even in the WAN setting.
Modular exponentiation is a vital function in public key cryptography. Dozens of protocols, including encryption schemes, signature schemes, pseudorandom functions, and more, perform this operation on a secret base and/or a secret exponent. In a multiparty computation setting, these secret data might be shared over multiple parties who wish to compute this modular exponentiation in a secure and distributed way. However, whereas typical frameworks for secure multiparty computation based on secret sharing provide a basic tool box of secure distributed computation of, most importantly, randomness generation, addition, and multiplication, the status quo of secure distributed modular exponentiation is unsatisfactory. In this work, we provide a complete and comprehensive overview on existing protocols for perfectly secure distributed exponentiation differing depending on whether the inputs and outcomes are public or shared. We perform a detailed complexity computation of the currently existing protocols, observing that earlier authors have overestimated the complexity of their own protocols, and close the remaining open problem: protocols for secure distributed exponentiation with secret base, secret exponent, and public outcome. We prove that the presented protocol is universally composably secure in the presence of malicious adversaries. We finally exemplify the practical relevance of the new protocol by demonstrating how it can be used for pseudorandom generation and signing.
Secure multi-party computation (MPC) is a cryptographic tool that enables a set of parties to compute a function jointly while keeping each input secret. Since MPC based on secret sharing (SS) achieves high throughput and works fast, many applications have been developed. However, SS-based MPC requires many communication rounds in general, and this becomes a performance bottleneck in real-world applications under high-latency networks. In this paper, we propose SS-based secure three-party computation with almost no preprocessing based on our new (small-)constant-round fundamental gates, by revisiting a framework in a few previous works where a number of parties are assisted by another party who may partially learn secret information. Instead of ordinary logical gates, our fundamental gate is an efficient Equality, for which the result leaks to the third party, and we develop novel two-round constructions of secure building-block protocols (LessThan Comparison, RightShift, Table LookUp, etc.) from the insecure Equality. To show the practicality of our protocols, we implement a secure exact edit distance protocol for two genome strings. Our experiments show that in some network setting our protocol is about 2 times faster (14 times faster taking preprocessing into consideration) than the state-of-the-art SS-based protocol (Ohata and Nuida, FC 2020).
Protocols for secure multi-party computation (MPC) supporting mixed-mode computation have found a lot of applications in recent years due to their flexibility in representing the function to be evaluated. However, existing mixed-mode MPC protocols are only practical for a small number of parties: they are either tailored to the case of two/three parties, or scale poorly for a large number of parties.In this paper, we design and implement a new system for highly efficient and scalable mixed-mode MPC tolerating an arbitrary number of semi-honest corruptions. Our protocols allow secret data to be represented in Encrypted, Boolean, Arithmetic, or Yao form, and support efficient conversions between these representations.1)We design a multi-party table-lookup protocol, where both the index and the table can be kept private. The protocol is scalable even with hundreds of parties.2)Using the above protocol, we design efficient conversions between additive arithmetic secret sharings and Boolean secret sharings for a large number of parties. For 32 parties, our conversion protocols require 1184× to 8141× less communication compared to the state-of-the-art protocols MOTION and MP-SPDZ; this leads to up to 1275× improvement in running time under 1 Gbps network. The improvements are even larger with more parties.3)We also use new protocols to design an efficient multi-party distributed garbling protocol. The protocol could achieve asymptotically constant communication per party.Our implementation will be made public.
Secure multi-party computation (MPC) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits, some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. This is less than a half compared with the previous work. Moreover, the number of communication bits is also 38.4% fewer. As a result, total online execution time is 56.1% shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.
Bit-decomposition is an important primitive in multi-party computation (MPC). Given a sharing of secret x, it allows the parties to compute the sharings of the bits of x in constant rounds. With the help of bit-decomposition, we will be able to construct constant-rounds protocols for various MPC problems, such as equality test, comparison, public modulo reduction and private exponentiation, which are four main applications of bit-decomposition. However, when considering perfect security, bit-decomposition does not have a linear communication complexity. Thus any protocols involving bit-decomposition inherit this inefficiency, i.e. the communication complexity is non-linear. Constructing protocols for MPC problems without relying on bit-decomposition is a meaningful work because this may provide us with perfect secure protocols with linear communication complexity. It is already proved that equality test, comparison and public modulo reduction can be solved without involving bit-decomposition and the communication complexity can be reduced to linear. However, it remains an open problem whether private exponentiation could be done without relying on bit-decomposition. In this paper, maybe somewhat surprisingly, we show that it can. That is to say, we construct