Distributing Any Elliptic Curve Based Protocol

Smart, Nigel P.; Alaoui, Younes Talibi

doi:10.1007/978-3-030-35199-1_17

Cited by 23 publications

(7 citation statements)

References 19 publications

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“…Other related works. The multiplication in the exponent approach we adopt bears similarity with [50], [47]. However, there are crucial differences.…”

Section: Related Workmentioning

confidence: 99%

“…However, there are crucial differences. Both [50] and [47] consider security-with-abort, albeit differently. For example, [47] does not verify shares from parties while computing the KZG evaluation proof and uses properties of the KZG polynomial commitment to check the correctness of the final proof.…”

Section: Related Workmentioning

confidence: 99%

“…For example, [47] does not verify shares from parties while computing the KZG evaluation proof and uses properties of the KZG polynomial commitment to check the correctness of the final proof. Similarly, [50] validates the reconstructed values using MACs and outputs a default value upon unsuccessful verification. Moreover, [50] assumes synchrony as it uses a broadcast channel to verify the MACs.…”

Section: Related Workmentioning

confidence: 99%

“…Similarly, [50] validates the reconstructed values using MACs and outputs a default value upon unsuccessful verification. Moreover, [50] assumes synchrony as it uses a broadcast channel to verify the MACs. Contrary to both, our approach ensures guaranteed output delivery in asynchrony with 1/3 failures.…”

Section: Related Workmentioning

confidence: 99%

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Das,

Xiang,

Ren

2024

Proceedings 2024 Network and Distributed System Security Symposium

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The q-Strong Diffie-Hellman (q-SDH) parameters are foundational to efficient constructions of many cryptographic primitives such as zero-knowledge succinct non-interactive arguments of knowledge, polynomial/vector commitments, verifiable secret sharing, and randomness beacon. The only existing method to generate these parameters securely is highly sequential, requires synchrony assumptions, and has very high communication and computation costs. For example, to generate parameters for any given q, each party incurs a communication cost of Ω(nq) and requires Ω(n) rounds. Here n is the number of parties in the secure multiparty computation protocol. Since q is typically large, i.e., on the order of billions, the cost is highly prohibitive.In this paper, we present a distributed protocol to generate q-SDH parameters in an asynchronous network. In a network of n parties, our protocol tolerates up to one-third of malicious parties. Each party incurs a communication cost of O(q+n 2 log q) and the protocol finishes in O(log q + log n) expected rounds. We provide a rigorous security analysis of our protocol. We implement our protocol and evaluate it with up to 128 geographically distributed parties. Our evaluation illustrates that our protocol is highly scalable and results in a 2-6× better runtime and 4-13× better per-party bandwidth usage compared to the state-of-theart synchronous protocol for generating q-SDH parameters.

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“…Other related works. The multiplication in the exponent approach we adopt bears similarity with [50], [47]. However, there are crucial differences.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Das,

Xiang,

Ren

2024

Proceedings 2024 Network and Distributed System Security Symposium

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“…Finally, as related work in the area of threshold cryptography, we note that several papers on threshold signatures [13,14], threshold Σ-proofs [15], and verifiable (or auditable) MPC [16,17] implicitly implement some form of secure groups for F * q or elliptic curves, but these papers do not treat secure groups in general terms.…”

Section: Introductionmentioning

confidence: 99%

Secure Groups for Threshold Cryptography and Number-Theoretic Multiparty Computation

Schoenmakers,

Segers

2023

Cryptography

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In this paper, we introduce secure groups as a cryptographic scheme representing finite groups together with a range of operations, including the group operation, inversion, random sampling, and encoding/decoding maps. We construct secure groups from oblivious group representations combined with cryptographic protocols, implementing the operations securely. We present both generic and specific constructions, in the latter case specifically for number-theoretic groups commonly used in cryptography. These include Schnorr groups (with quadratic residues as a special case), Weierstrass and Edwards elliptic curve groups, and class groups of imaginary quadratic number fields. For concreteness, we develop our protocols in the setting of secure multiparty computation based on Shamir secret sharing over a finite field, abstracted away by formulating our solutions in terms of an arithmetic black box for secure finite field arithmetic or for secure integer arithmetic. Secure finite field arithmetic suffices for many groups, including Schnorr groups and elliptic curve groups. For class groups, we need secure integer arithmetic to implement Shanks’ classical algorithms for the composition of binary quadratic forms, which we will combine with our adaptation of a particular form reduction algorithm due to Agarwal and Frandsen. As a main result of independent interest, we also present an efficient protocol for the secure computation of the extended greatest common divisor. The protocol is based on Bernstein and Yang’s constant-time 2-adic algorithm, which we adapt to work purely over the integers. This yields a much better approach for multiparty computation but raises a new concern about the growth of the Bézout coefficients. By a careful analysis, we are able to prove that the Bézout coefficients in our protocol will never exceed 3max(a,b) in absolute value for inputs a and b. We have integrated secure groups in the Python package MPyC and have implemented threshold ElGamal and threshold DSA in terms of secure groups. We also mention how our results support verifiable multiparty computation, allowing parties to jointly create a publicly verifiable proof of correctness for the results accompanying the results of a secure computation.

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Bandwidth-Efficient Threshold EC-DSA

Castagnos

Catalano

Laguillaumie

et al. 2020

Lecture Notes in Computer Science

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Threshold Signatures allow n parties to share the power of issuing digital signatures so that any coalition of size at least t+1 can sign, whereas groups of t or less players cannot. Over the last few years many schemes addressed the question of realizing efficient threshold variants for the specific case of EC-DSA signatures. In this paper we present new solutions to the problem that aim at reducing the overall bandwidth consumption. Our main contribution is a new variant of the Gennaro and Goldfeder protocol from ACM CCS 2018 that avoids all the required range proofs, while retaining provable security against malicious adversaries in the dishonest majority setting. Our experiments show that-for all levels of security-our signing protocol reduces the bandwidth consumption of best previously known secure protocols for factors varying between 4.4 and 9, while key generation is consistently two times less expensive. Furthermore compared to these same protocols, our signature generation is faster for 192-bits of security and beyond.

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Distributing Any Elliptic Curve Based Protocol

Cited by 23 publications

References 19 publications

Powers of Tau in Asynchrony

Powers of Tau in Asynchrony

Secure Groups for Threshold Cryptography and Number-Theoretic Multiparty Computation

Bandwidth-Efficient Threshold EC-DSA

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