Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IACR Communications in Cryptology

Simple Three-Round Multiparty Schnorr Signing with Full Simulatability

Yehuda Lindell

Published Apr 9, 2024• 22 citations
Publisher

Abstract

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.

DOI
10.62056/a36c0l5vt

Related papers

Bounded-concurrent secure multi-party computation with a dishonest majority

Rafael Pass

We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.

ACM Symposium on Theory of Computing (STOC)•Jun 13, 2004•183 citations

Broadcast-Efficient Secure Multiparty Computation.

Juan A. Garay, Clint Givens, Rafail Ostrovsky

Secure multiparty computation (MPC) is perhaps the most popular paradigm in the area of cryptographic protocols. It allows several mutually untrustworthy parties to jointly compute a function of their private inputs, without revealing to each other information about those inputs. In the case of unconditional (information-theoretic) security, protocols are known which tolerate a dishonest minority of players, who may coordinate their attack and deviate arbitrarily from the protocol specification. It is typically assumed in these results that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Broadcast allows one party to send a consistent message to all other parties, guaranteeing consistency even if the broadcaster is corrupted. Because broadcast cannot be simulated on the point-to-point network when more than a third of the parties are corrupt, it is impossible to construct general MPC protocols in this setting without using a broadcast channel (or some equivalent addition to the model). A great deal of research has focused on increasing the efficiency of MPC, primarily in terms of round complexity and communication complexity. In this work we propose a refinement of the round complexity which we term broadcast complexity. We view the broadcast channel as an expensive resource

•Jan 1, 2012•3 citations

Efficient threshold multiparty computation schemes

Schuyler Rosefield

Multiparty Computation (hereafter MPC) is a technique for allowing a set ofparticipants to run a secure computation with the assurance that the output is (1) correct, and (2) that a malicious party did not learn anything about the inputs of the honest parties besides what it can glean from the output. Impor- tantly much of cryptography is based on the assumption that an honest party has a private and secret input, and if the adversary learns this input the security of the scheme is broken. Then naturally the techniques of MPC can be applied to create threshold protocols for these cryptographic schemes to ensure that the secret inputs are not leaked and moreover that no group of parties smaller than the threshold know the input at all. While we have known how to generically evaluate MPC for any function since the 80s the question of efficiency still drives progress to this day. This thesis looks at two approaches for making secure com- putation more practical to deploy: developing specialized protocols for appli- cations such as distributed key generation and signing with RSA and ECDSA; and improving the state of the art of maliciously secure generic boolean-circuit MPC. We first look at work that produced a distributed key generation protocol for RSA that utilizes a novel candidate sampling mechanism to reduce waste in primality testing. The second work builds a threshold scheme for symmetric cryptographic primitives such as AES and SHA where there is limited algebraic structure to exploit by efficiently converting a generic n-of-n MPC protocol into a threshold t-of-n MPC protocol. Future directions in this thesis are in combin- ing techniques from the prior works to create a blind signature scheme for the Elliptic Curve Digital Signature Algorithm (ECDSA) that requires both alge- braic operations over elliptic curves and additionally symmetric evaluations of the SHA2 hash function.--Author's abstract

•Jan 1, 2024•0 citations

Scalable Multiparty Garbling

Gabrielle Beck, Aarushi Goel, Aditya Hegde +3 more

Multiparty garbling is the most popular approach for constant-round secure multiparty computation (MPC). Despite being the focus of significant research effort, instantiating prior approaches to multiparty garbling results in constant-round MPC that can not realistically accommodate large numbers of parties. In this work we present the first global-scale multiparty garbling protocol. The per-party communication complexity of our protocol decreases as the number of parties participating in the protocol increases - for the first time matching the asymptotic communication complexity of non-constant round MPC protocols. Our protocol achieves malicious security in the honest-majority setting and relies on the hardness of the Learning Party with Noise assumption.

ACM SIGSAC Conference on Computer and Communications Security (CCS)•Nov 15, 2023•15 citations

Two-round Multiparty Secure Computation from Minimal Assumptions

Sanjam Garg, Akshayaram Srinivasan

We provide new two-round multiparty secure computation (MPC) protocols in the dishonest majority setting assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions.

Journal of the ACM•Oct 7, 2022•12 citations

Ringtail: Practical Two-Round Threshold Signatures from Learning with Errors

Cecilia Boschini, Darya Kaviani, Russell W. F. Lai +3 more

A threshold signature scheme splits the signing key among$\ell$parties, such that any$t$-subset of parties can jointly generate signatures on a given message. Designing concretely efficient post-quantum threshold signatures is a pressing question, as evidenced by NIST's recent call. In this work, we propose, implement, and evaluate a lattice-based threshold signature scheme, Ringtail, which is the first to achieve a combination of desirable properties: (i) The signing protocol consists of only two rounds, where the first round is message-independent and can thus be preprocessed offline. (ii) The scheme is concretely efficient and scalable to$t\leq 1024$parties. For 128-bit security and$t=1024$parties, we achieve 13.4 KB signature size and 10.5 KB of online communication. (iii) The security is based on the standard learning with errors (LWE) assumption in the random oracle model. This improves upon the state-of-the-art (with comparable efficiency) which either has a three-round signing protocol [Eurocrypt'24] or relies on a new non-standard assumption [Crypto'24]. To substantiate the practicality of our scheme, we conduct the first WAN experiment deploying a lattice-based threshold signature, across 8 countries in 5 continents. We observe that an overwhelming majority of the end-to-end latency is consumed by network latency, underscoring the need for round-optimized schemes.

IEEE Symposium on Security and Privacy (S&P)•May 12, 2025•17 citations
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.
We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.
Secure multiparty computation (MPC) is perhaps the most popular paradigm in the area of cryptographic protocols. It allows several mutually untrustworthy parties to jointly compute a function of their private inputs, without revealing to each other information about those inputs. In the case of unconditional (information-theoretic) security, protocols are known which tolerate a dishonest minority of players, who may coordinate their attack and deviate arbitrarily from the protocol specification. It is typically assumed in these results that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Broadcast allows one party to send a consistent message to all other parties, guaranteeing consistency even if the broadcaster is corrupted. Because broadcast cannot be simulated on the point-to-point network when more than a third of the parties are corrupt, it is impossible to construct general MPC protocols in this setting without using a broadcast channel (or some equivalent addition to the model). A great deal of research has focused on increasing the efficiency of MPC, primarily in terms of round complexity and communication complexity. In this work we propose a refinement of the round complexity which we term broadcast complexity. We view the broadcast channel as an expensive resource
Multiparty Computation (hereafter MPC) is a technique for allowing a set ofparticipants to run a secure computation with the assurance that the output is (1) correct, and (2) that a malicious party did not learn anything about the inputs of the honest parties besides what it can glean from the output. Impor- tantly much of cryptography is based on the assumption that an honest party has a private and secret input, and if the adversary learns this input the security of the scheme is broken. Then naturally the techniques of MPC can be applied to create threshold protocols for these cryptographic schemes to ensure that the secret inputs are not leaked and moreover that no group of parties smaller than the threshold know the input at all. While we have known how to generically evaluate MPC for any function since the 80s the question of efficiency still drives progress to this day. This thesis looks at two approaches for making secure com- putation more practical to deploy: developing specialized protocols for appli- cations such as distributed key generation and signing with RSA and ECDSA; and improving the state of the art of maliciously secure generic boolean-circuit MPC. We first look at work that produced a distributed key generation protocol for RSA that utilizes a novel candidate sampling mechanism to reduce waste in primality testing. The second work builds a threshold scheme for symmetric cryptographic primitives such as AES and SHA where there is limited algebraic structure to exploit by efficiently converting a generic n-of-n MPC protocol into a threshold t-of-n MPC protocol. Future directions in this thesis are in combin- ing techniques from the prior works to create a blind signature scheme for the Elliptic Curve Digital Signature Algorithm (ECDSA) that requires both alge- braic operations over elliptic curves and additionally symmetric evaluations of the SHA2 hash function.--Author's abstract
Multiparty garbling is the most popular approach for constant-round secure multiparty computation (MPC). Despite being the focus of significant research effort, instantiating prior approaches to multiparty garbling results in constant-round MPC that can not realistically accommodate large numbers of parties. In this work we present the first global-scale multiparty garbling protocol. The per-party communication complexity of our protocol decreases as the number of parties participating in the protocol increases - for the first time matching the asymptotic communication complexity of non-constant round MPC protocols. Our protocol achieves malicious security in the honest-majority setting and relies on the hardness of the Learning Party with Noise assumption.
We provide new two-round multiparty secure computation (MPC) protocols in the dishonest majority setting assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions.
A threshold signature scheme splits the signing key amongℓ\ellℓparties, such that anyttt-subset of parties can jointly generate signatures on a given message. Designing concretely efficient post-quantum threshold signatures is a pressing question, as evidenced by NIST's recent call. In this work, we propose, implement, and evaluate a lattice-based threshold signature scheme, Ringtail, which is the first to achieve a combination of desirable properties: (i) The signing protocol consists of only two rounds, where the first round is message-independent and can thus be preprocessed offline. (ii) The scheme is concretely efficient and scalable tot≤1024t\leq 1024t≤1024parties. For 128-bit security andt=1024t=1024t=1024parties, we achieve 13.4 KB signature size and 10.5 KB of online communication. (iii) The security is based on the standard learning with errors (LWE) assumption in the random oracle model. This improves upon the state-of-the-art (with comparable efficiency) which either has a three-round signing protocol [Eurocrypt'24] or relies on a new non-standard assumption [Crypto'24]. To substantiate the practicality of our scheme, we conduct the first WAN experiment deploying a lattice-based threshold signature, across 8 countries in 5 continents. We observe that an overwhelming majority of the end-to-end latency is consumed by network latency, underscoring the need for round-optimized schemes.