Threshold Signatures with Private Accountability

Existing threshold signature schemes come in two flavors: (i) fully private, where the signature reveals nothing about the set of signers that generated the signature, and (ii) accountable, where the signature completely identifies the set of signers. In this paper we propose a new type of threshold signature, called TAPS, that is a hybrid of privacy and accountability. A TAPS signature is fully private from the public\u27s point of view. However, an entity that has a secret tracing key can trace a signature to the threshold of signers that generated it. A TAPS makes it possible for an organization to keep its inner workings private, while ensuring that signers are accountable for their actions. We construct a number of TAPS schemes. First, we present a generic construction that builds a TAPS from any accountable threshold signature. This generic construction is not efficient, and we next focus on efficient schemes based on standard assumptions. We build two efficient TAPS schemes (in the random oracle model) based on the Schnorr signature scheme. We conclude with a number of open problems relating to efficient TAPS

Walking Onions: Scaling Distribution of Information Safely in Anonymity Networks

Scaling anonymity networks offers unique security challenges, as attackers can exploit differing views of the network’s topology to perform epistemic and route capture attacks. Anonymity networks in practice, such as Tor, have opted for security over scalability by requiring participants to share a globally consistent view of all relays to prevent these kinds of attacks. Such an approach requires each user to maintain up-to-date information about every relay, causing the total amount of data each user must download every epoch to scale linearly with the number of relays. As the number of clients increases, more relays must be added to provide bandwidth, further exacerbating the total load on the network. In this work, we present Walking Onions, a set of protocols improving scalability for anonymity networks. Walking Onions enables constant-size scaling of the information each user must download in every epoch, even as the number of relays in the network grows. Furthermore, we show how relaxing the clients’ bandwidth growth from constant to logarithmic can enable an outsized improvement to relays’ bandwidth costs. Notably, Walking Onions offers the same security properties as current designs that require a globally consistent network view. We present two protocol variants. The first requires minimal changes from current onion-routing systems. The second presents a more significant design change, thereby reducing the latency required to establish a path through the network while providing better forward secrecy than previous such constructions. We evaluate Walking Onions against a generalized onion-routing anonymity network and discuss tradeoffs among the approaches

On End-to-End Encryption

End-to-end encryption (E2EE) is vitally important to security and privacy online, yet currently under-defined. In this note, we map intuitive notions of end-to-end encryption to existing notions of encryption. In particular, we introduce the notion of endness as an notion which end-to-end systems must achieve in addition to traditional security notions associated with encryption, and provide formalizations to capture practical requirements. We demonstrate how the notion of encryption plus endness relates to a variety of case studies that either meet normative security understanding of E2EE or are considered normative failures. Finally, we extend these observations to authentication, and real-world authenticated channel use variants, including authenticated encryption with associated data and message franking

FROST: Flexible Round-Optimized Schnorr Threshold Signatures

Unlike signatures in a single-party setting, threshold signatures require cooperation among a threshold number of signers each holding a share of a common private key. Consequently, generating signatures in a threshold setting imposes overhead due to network rounds among signers, proving costly when secret shares are stored on network-limited devices or when coordination occurs over unreliable networks. In this work, we present FROST, a Flexible Round-Optimized Schnorr Threshold signature scheme that reduces network overhead during signing operations while employing a novel technique to protect against forgery attacks applicable to similar schemes in the literature. FROST improves upon the state of the art in Schnorr threshold signature protocols, as it can be safely used without limiting concurrency of signing operations yet allows for true threshold signing, as only a threshold number of participants are required for signing operations. FROST can be used as either a two-round protocol where signers send and receive two messages in total, or optimized to a single-round signing protocol with a pre-processing stage. FROST achieves its efficiency improvements in part by allowing the protocol to abort in the presence of a misbehaving participant (who is then identified and excluded from future operations)---a reasonable model for practical deployment scenarios. We present proofs of security demonstrating that FROST is secure against chosen-message attacks assuming the discrete logarithm problem is hard and the adversary controls fewer participants than the threshold

How to Prove Schnorr Assuming Schnorr: Security of Multi- and Threshold Signatures

This work investigates efficient multi-party signature schemes in the discrete logarithm setting. We focus on a concurrent model, in which an arbitrary number of signing sessions may occur in parallel. Our primary contributions are: (1) a modular framework for proving the security of Schnorr multisignature and threshold signature schemes, (2) an optimization of the two-round threshold signature scheme $\mathsf{FROST}$ that we call $\mathsf{FROST2}$, and (3) the application of our framework to prove the security of $\mathsf{FROST2}$ as well as a range of other multi-party schemes. We begin by demonstrating that our framework is applicable to multisignatures. We prove the security of a variant of the two-round $\mathsf{MuSig2}$ scheme with proofs of possession and a three-round multisignature $\mathsf{SimpleMuSig}$. We introduce a novel three-round threshold signature $\mathsf{SimpleTSig}$ and propose an optimization to the two-round $\mathsf{FROST}$ threshold scheme that we call $\mathsf{FROST2}$. $\mathsf{FROST2}$ reduces the number of scalar multiplications required during signing from linear in the number of signers to constant. We apply our framework to prove the security of $\mathsf{FROST2}$ under the one-more discrete logarithm assumption and $\mathsf{SimpleTSig}$ under the discrete logarithm assumption in the programmable random oracle model

A Formal Treatment of Distributed Key Generation, and New Constructions

In this work, we present a novel generic construction for a Distributed Key Generation (DKG) scheme. Our generic construction relies on three modular cryptographic building blocks. The first is an aggregatable Verifiable Secret Sharing (AgVSS) scheme, the second is a Non-Interactive Key Exchange (NIKE) scheme, and the third is a secure hash function. We give formal definitions for the AgVSS and NIKE schemes, as well as concrete constructions. The utility of this generic construction is flexibility; i.e., any aggregatable VSS and NIKE scheme can be employed, and the construction will remain secure. To prove the security of our generic construction, we introduce formalized game based notions of security for DKGs, building upon existing notions in the literature. However, these prior security notions either were presented informally, omitted important requirements, or assumed certain algebraic structure of the underlying scheme. Our security notions make no such assumption of underlying algebraic structure, and explicitly consider details such as participant consistency, communication patterns, and key validity. Further, our security notions imply simulatability with respect to a target key generation scheme without rewinding. Hence, any construction that is proven secure using our security notions additionally imply UC security. We then present STORM, a concrete instantiation of our generic construction that is secure in the discrete logarithm setting in the random oracle model. STORM is more efficient than related DKG schemes in the literature. Because of its simple design and composability, it is a practical choice for real world settings and standardization efforts

Fully Adaptive Schnorr Threshold Signatures

We prove adaptive security of a simple three-round threshold Schnorr signature scheme, which we call Sparkle. The standard notion of security for threshold signatures considers a static adversary – one who must declare which parties are corrupt at the beginning of the protocol. The stronger adaptive adversary can at any time corrupt parties and learn their state. This notion is natural and practical, yet not proven to be met by most schemes in the literature. In this paper, we demonstrate that Sparkle achieves several levels of security based on different corruption models and assumptions. To begin with, Sparkle is statically secure under minimal assumptions: the discrete logarithm assumption (DL) and the random oracle model (ROM). If an adaptive adversary corrupts fewer than t/2 out of a threshold of t + 1 signers, then Sparkle is adaptively secure under a weaker variant of the one-more discrete logarithm assumption (AOMDL) in the ROM. Finally, we prove that Sparkle achieves full adaptive security, with a corruption threshold of t, under AOMDL in the algebraic group model (AGM) with random oracles. Importantly, we show adaptive security without requiring secure erasures. Ours is the first proof achieving full adaptive security without exponential tightness loss for any threshold Schnorr signature scheme; moreover, the reduction is tight

Towards Post-Quantum Updatable Public-Key Encryption via Supersingular Isogenies

We present the first post-quantum secure Key-Updatable Public-Key Encryption (UPKE) construction. UPKE has been proposed as a mechanism to improve the forward secrecy and post-compromise security of secure messaging protocols, but the hardness of all existing constructions rely on discrete logarithm assumptions. We focus our assessment on isogeny-based cryptosystems due to their suitability for performing a potentially unbounded number of update operations, a practical requirement for secure messaging where user conversations can occur over months, if not years. We begin by formalizing two UPKE variants in the literature as Symmetric and Asymmetric UPKE, which differ in how encryption and decryption keys are updated. We argue that Asymmetric UPKE constructions in the literature cannot be straightforwardly instantiated using SIDH nor CSIDH. We then describe a SIDH construction that partially achieves the required security notions for Symmetric UPKE, but due to existing mathematical limitations, cannot provide fine-grained forward secrecy. Finally, we present a CSIDH Symmetric UPKE construction that requires a parameter set in which the class group structure is fully known. We discuss open problems which are applicable to any cryptosystem with similar requirements for continuous operations over the secret domain

Snowblind: A Threshold Blind Signature in Pairing-Free Groups

Both threshold and blind signatures have, individually, received a considerable amount of attention. However little is known about their combination, i.e., a threshold signature which is also blind, in that no coalition of signers learns anything about the message being signed or the signature being produced. Several applications of blind signatures (e.g., anonymous tokens) would benefit from distributed signing as a means to increase trust in the service and hence reduce the risks of key compromise. This paper builds the first blind threshold signatures in pairing-free groups. Our main contribution is a construction that transforms an underlying blind non-threshold signature scheme with a suitable structure into a threshold scheme, preserving its blindness. The resulting signing protocol proceeds in three rounds, and produces signatures consisting of one group element and two scalars. The underlying non-threshold blind signature schemes are of independent interest, and improve upon the current state of the art (Tessaro and Zhu, EUROCRYPT ’22) with shorter signatures (three elements, instead of four) and simpler proofs of security. All of our schemes are proved secure in the Random Oracle and Algebraic Group Models, assuming the hardness of the discrete logarithm problem

Mind the Gap: Ceremonies for Applied Secret Sharing

Secret sharing schemes are desirable across a variety of real-world settings due to the security and privacy properties they can provide, such as availability and separation of privilege. However, transitioning secret sharing schemes from theoretical research to practical use must account for gaps in achieving these properties that arise due to the realities of concrete implementations, threat models, and use cases. We present a formalization and analysis, using Ellison’s notion of ceremonies, that demonstrates how simple variations in use cases of secret sharing schemes result in the potential loss of some security properties, a result that cannot be derived from the analysis of the underlying cryptographic protocol alone. Our framework accounts for such variations in the design and analysis of secret sharing implementations by presenting a more detailed user-focused process and defining previously overlooked assumptions about user roles and actions within the scheme to support analysis when designing such ceremonies. We identify existing mechanisms that, when applied to an appropriate implementation, close the security gaps we identified. We present our implementation including these mechanisms and a corresponding security assessment using our framework