Category theory is a mathematical theory of composition, widely used in logic, computing, and physics. Here we apply it to give a theory of secure composition. In particular, we provide a categorical treatment of Canetti's Universal Composability (UC) framework for systems with a static number of parties and sessions, often termed UC for static systems, yielding four benefits. First, we present our results graphically yet retain rigor by applying a standard categorical technique known as string diagrams. In particular, our formulation of the composition theorem can be graphically verified with a short sequence of diagrams, while remaining translatable to equations and amenable to formal verification. Second, categories let us generalize so that our results extend beyond interactive Turing machines to other forms of computation, such as quantum computation or domain-specific languages. Third, categories help us drop some unnecessary restrictions of UC (e.g., our adversary can be a computational network rather than a single Turing machine); we prove equivalence between our variant and the usual UC, showing no expressiveness is lost. Finally, the categorical perspective leads us to identify and correct some minor technical oversights in the standard formulation of simple UC.

Threshold signatures have received considerable attention in recent years due to ongoing standardization efforts and deployment in real-world systems. In this work, we prove the universal composability of a wide range of threshold signature schemes, including state-of-the-art protocols compatible with standard signatures used in practice, such as BLS and Schnorr signatures, as well as emerging post-quantum solutions. Importantly, we show UC security without any modifications to the existing protocols. To this end, we design natural game-based definitions to capture different combinations of main threshold signature scheme properties, such as different levels of unforgeability, adaptive corruption, robustness, and different degrees of preprocessing. These definitions generalize prior definitional work, such as Bellare et al. (CRYPTO’22), and cover a wide range of existing schemes. Moreover, we identify and resolve gaps in prior work. We then express these properties in terms of a UC ideal functionality ℱ- . We prove that a threshold signature scheme UC-realizes ℱ- if and only if it satisfies our game-based definitions. This opens up the usage of (existing) threshold signature schemes in a UC setting, enabling scheme designers to formulate their protocols relative to an ideal threshold signature functionality and use the UC composition theorem to argue security given any concrete instantiation. To further support UC scheme designers and to give further guidance on UC modeling for threshold signatures, we provide additional ideal threshold signature functionalities ℱ- , This opens up the usage of (existing) threshold signature schemes in a UC setting, enabling scheme designers to formulate their protocols relative to an ideal threshold signature functionality and use the UC composition theorem to argue security given any concrete instantiation. To further support UC scheme designers and to give further guidance on UC modeling for threshold signatures, we provide additional ideal threshold signature functionalities ℱ- , ℱ- , ℱ- , and ℱ- , which capture fewer properties than ℱ- but are more convenient to use. ℱ-,ℱ-,ℱ-,ℱ- can also be UC-realized by schemes proven secure according to our game-based definitions. Through this work, we show that composable security does not require sacrificing performance, but it does require rigor when setting up game-based definitions and ideal functionalities.

Introduced by Kohlweiss, Lysyanskaya, and Nguyen (Eurocrypt’23), a privacy-preserving blueprint (PPB) allows an auditor of a privacy system, on input x, to create a public encoding of the function f(x,· ) that reveals nothing about x. Yet, a user who knows and a y that corresponds to a commitment to y, C_y , can compute an escrow Z of the value f(x, y); Z will verifiably correspond to and C_y . The auditor will be able to recover f(x, y) from Z , but will learn no other information about y. For example, let f(x, y) be the “watchlist” function that outputs y iff y is on the list x; a PPB for such a function (which we call an f-PPB) allows the auditor to trace watchlisted users in an otherwise anonymous system. PPBs are a—socially important and potentially controversial—instance of the actively secure non-interactive secure computation (NISC) problem. As such, they can be naturally constructed from homomorphic encryption and efficient proof systems. In this work, we present a framework for additively homomorphic encryption (AHE) with efficient proof systems that yields a dramatically improved PPB both in efficiency and security. In our setting, AHE allows one to compute an encryption, c_f , of a polynomial f(x_1,… ,x_n,y_1,… , y_k) on input the values: y_1,… ,y_k and only the (additively homomorphic) encryptions of x_1,… ,x_n . For AHE that satisfies a set of natural requirements, we give a NIZK proof system for showing the correct computation of c_f and proves that the y_1,… ,y_k values used in the computation of c_f correspond to public commitments C_1,… ,C_k . The resulting proof’s size is O(klog d) (independent of n) where d is the maximum degree of any variable in f. Critically, the proof can be computed without knowledge of x_1,… ,x_n only requiring the encryptions of these values. We show how our proof system can be instantiated both with ElGamal-based encryption (under DDH) and with a variant of the Camenisch-Shoup cryptosystem (under DCR and Strong RSA). Applying our proof system to Camenisch-Shoup ciphertexts is novel and extends previous work to apply to more general polynomials. Using our NIZK proof system for additively homomorphic computation we achieve the following results: (1) We provide efficient schemes for a useful class of functions f; for example, we show how to realize f that would allow the auditor to trace all private payment transactions of a suspect user in a central bank digital currency (CBDC). (2) For the watchlist and related functions, we reduce the size of the escrow Z from linear in the size of the auditor’s input x, to logarithmic. Additionally, (3) we define and satisfy a stronger notion of security for f-PPBs, where a malicious auditor cannot frame a user in a transaction in which the user was not involved in.

Project Everest began at Microsoft Research in 2016, aiming to spur research in program verification to produce industrial-grade software. In collaboration with INRIA and Carnegie Mellon University, Project Everest’s goal was to produce drop-in verified replacements of secure communications software used in the HTTPS ecosystem, including TLS, the underlying cryptography, and related subprotocols. Now, almost a decade later, we reflect on the project, sharing both its successes and failures, and look ahead to the next decade of program verification research.

We study Sybil-Resilient Anonymous (SyRA) signatures, a cryptographic primitive that enables credentialed users to generate, on demand, unlinkable pseudonyms tied to any given context, and issue signatures on behalf of these pseudonyms. Concretely, SyRA allows a distributed issuer to turn any legacy identity or personhood identifier, possibly of low entropy, into a unique associated cryptographic key of high pseudoentropy, for use in generating signatures for any given context. Sybil-resilient anonymous signatures achieve three main objectives: 1) Sybil resilience: every user is entitled to at most one digital identity, 2) anonymity: no information about the user's real identity is leaked, and 3) non-interactive context switching: users can create on their own at most one credential for any given context in a manner that is unlinkable across contexts. We conceptualize the SyRA primitive as an ideal functionality in the Universal Composition (UC) setting and put forth SASSI, an efficient, pairing-based construction that realizes it by utilizing two levels of verifiable random functions (VRFs), a design which may be of independent interest. The first level consists of threshold VRF issuance of a user's unique secret key tied to their real-world identifier. The second level allows a user to create signatures for each context, under a unique pseudonym per context. Compared to prior cryptographic tools capable of realizing SyRA, SASSI has the unique feature that issuers are stateless and hence do not need to retain any information about past user interactions, a relevant property for a decentralized implementation. We overview various applications of SASSI in multiparty systems, such as cryptocurrency account management and airdrops, e-voting (e.g., for decentralized governance), and privacy-preserving regulatory compliance (e.g., AML/CFT checks). In the context of creating addresses for digital assets, SyRA signatures enable users to embed their legacy identity into their address in a manner that protects their privacy for each application with which they interact. We demonstrate the practicality of SASSI by providing an implementation and performance evaluation of our construction.

A Trusted Execution Environment (TEE) is a security technology, implemented by CPU manufacturers, which guarantees integrity and confidentiality on a restricted execution environment to any remote verifier through attestation. TEEs are deployed on various consumer and commercial hardware platforms, and have been widely adopted as a component in the design of cryptographic protocols both theoretical and practical. Within the provable security community, the use of TEEs as a setup assumption has converged to a standard ideal definition in the Universal Composability setting (G(att), defined by Pass et al., Eurocrypt '17). However, it is unclear whether any real TEE design can actually realise such a level of security, or whether the diverse capabilities of today's TEE implementations will in fact converge to a single standard. Therefore, it is necessary for cryptographers and protocol designers to specify what assumptions are necessary for the TEE they are using to support the correctness and security of their protocol. To this end, this paper provides a more careful treatment of trusted execution than the existing literature, focusing on the capabilities of enclaves and adversaries. Our goal is to provide meaningful patterns for comparing different classes of TEEs, particularly how a weaker TEE functionality can implement a stronger one given an appropriate mechanism to bridge the two. We introduce a new, "modular" definition of TEEs that captures a broad range of pre-existing functionalities defined in the literature while maintaining their high level of abstraction. While our goal is not directly to model implementations of specific commercial TEE providers, our modular definition provides a way to capture more meaningful and realistic hardware capabilities. We propose to characterise TEE capabilities along the following terms: the set of trusted features available to the enclave; the set of possible attacks on an enclave; the content of attestation signatures. We then define various possible ideal modular G(att) functionality instantiations that capture existing variants in the literature. Finally, we conclude the paper by constructing a protocol template to realise stronger G(att) setups from weaker ones, and provide an example of removing an attack.

In today’s systems, privacy is often at odds with utility: users that reveal little information about themselves get restricted functionality, and service providers mistrust them. In practice, systems tip to either full anonymity (e.g. Monero), or full utility (e.g. Bitcoin). Well-known cryptographic primitives for bridging this gap exist: anonymous credentials (AC) let users disclose a subset of their credentials’ attributes, revealing to service providers “just what they need”; group signatures (GS) allow users to authenticate anonymously, to be de-anonymized “just when deemed necessary”. However, these primitives are hard to deploy. Current AC and GS variants reach specific points in the privacy-utility tradeoff, which we point as counter-productive engineering-wise, as it requires full and error-prone re-engineering to adjust the tradeoff. Also, so far, GS and AC have been studied separately by theoretical research. We take the first steps toward unifying and generalizing both domains, with the goal of bringing their benefits to practice, in a flexible way. We give a common model capturing their core properties, and use functional placeholders to subsume intermediate instantiations of the privacy-utility tradeoff under the same model. To prove its flexibility, we show how concrete variants of GS, AC (and others, like ring signatures) can be seen as special cases of our scheme – to which we refer as universal anonymous signatures (UAS). In practice, this means that instantiations following our construction can be configured to behave as variant X of a GS scheme, or as variant Y of an AC scheme, by tweaking a few functions.

In blockchain systems, Merkle trees represent a fundamental cryptographic structure for verifying the validity of public keys in digital signatures. However, the verification process presents significant computational challenges, particularly when dealing with large-scale public key participation in signing operations. This paper focuses on addressing the efficiency bottlenecks in public key validity verification within Merkle tree commitments, with particular emphasis on their application in trustless cross-chain bridge protocols. While existing crosschain solutions predominantly rely on zero-knowledge proofs for blockchain state validation, the inherent computational cost of proof generation remains prohibitive. We present a novel batch opening scheme for Merkle tree commitments that synergistically integrates Merkle tree construction from permutation arguments to verify the membership of extensive leaf sets. Our approach demonstrates remarkable proof generation efficiency advantages, particularly maintaining consistent performance regardless of the number of opened leaves, given a fixed tree depth. Our methods significantly reduce the computational overhead associated with public key validity verification. Meanwhile, it is fully applicable to the existing classical Merkle tree structure without any modifications and has universality. To demonstrate the practicality and efficiency of our scheme, We implemented the Merkle tree opening circuit for three hash functions (Poseidon, Rescue and Keccak) based on our scheme. Our evaluation shows that the batch opening scheme achieves better performance: proof generation time begins to shorten from an opening ratio of 0.25, achieving a 3.5 to 7.1x improvement at a ratio of 0.75 (with tree depth = 9). Similar improvements are also reflected in the proof size and verification time. Moreover, as tree depth increases, our method's performance advantages become more pronounced.

The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts. We establish the UC security of Groth16 without any significant overhead. In the spirit of global random oracles, we design a global (restricted) observable generic group functionality that models a natural notion of observability: computations that trace back to group elements derived from generators of other sessions are observable. This notion turns out to be surprisingly subtle to formalize. We provide a general framework for proving protocols secure in the presence of global generic groups, which we then apply to Groth16.

Privacy-preserving blueprint schemes (Kohlweiss et al., EUROCRYPT’23) offer a mechanism for safeguarding user’s privacy while allowing for specific legitimate controls by a designated auditor agent. These schemes enable users to create escrows encrypting the result of evaluating a function y=P(t,x) , with P being publicly known, t a secret used during the auditor’s key generation, and x the user’s private input. Crucially, escrows only disclose the blueprinting result y=P(t,x) to the designated auditor, even in cases where the auditor is fully compromised. The original definition and construction only support the evaluation of functions P on an input x provided by a single user. We address this limitation by introducing updatable privacy-preserving blueprint schemes (UPPB), which enhance the original notion with the ability for multiple users to non-interactively update the private user input x while blueprinting. Moreover, UPPBs contain a proof that y is the result of a sequence of valid updates, while revealing nothing else about the private inputs {x_i} of updates. As in the case of privacy-preserving blueprints, we first observe that UPPBs can be realized via a generic construction for arbitrary predicates P based on FHE and NIZKs. Our main result is , an efficient instantiation for a specific predicate comparing the values x and t, where x is the cumulative sum of users’ private inputs and t is a fixed private value provided by the auditor in the setup phase. This rather specific setting already finds interesting applications such as privacy-preserving anti-money laundering and location tracking, and can be extended to support more generic predicates. From the technical perspective, we devise a novel technique to keep the escrow size concise, independent of the number of updates, and reasonable for practical applications. We achieve this via a novel characterization of malleability for the algebraic NIZK by Couteau and Hartmann (CRYPTO’20) that allows for an additive update function.

Stablecoins are digital assets designed to maintain a consistent value relative to a reference point, serving as a vital component in Blockchain, and Decentralized Finance (DeFi) ecosystem. Typical implementations of stablecoins via smart contracts come with important downsides such as a questionable level of privacy, potentially high fees, and lack of scalability. We put forth a new design, , for a Privacy-preserving, Auditable, and Regulation-friendly Stablecoin that mitigates these issues while enabling high performance both in terms of speed of settlement and for scaling to large numbers of users as our performance analysis demonstrates. Our construction is blockchain-agnostic and is analyzed in the Universal Composition (UC) framework, offering a secure and modular approach for its integration into the broader blockchain ecosystem.

If everyone were to use anonymous credentials for all access control needs, it would be impossible to trace wrongdoers, by design. This would make legitimate controls, such as tracing illicit trade and terror suspects, impossible to carry out. Here, we propose a privacy-preserving blueprint capability that allows an auditor to publish an encoding _ of the function f(x,· ) for a publicly known function f and a secret input x. For example, x may be a secret watchlist, and f(x, y) may return y if y∈ x . On input her data y and the auditor’s _ , a user can compute an escrow Z such that anyone can verify that Z was computed correctly from the user’s credential attributes, and moreover, the auditor can recover f(x, y) from Z . Our contributions are:

Structure-preserving signatures (SPS) are an important building block for privacy-preserving cryptographic primitives, such as electronic cash, anonymous credentials, and delegatable anonymous credentials. In this work, we introduce the first threshold structure-preserving signature scheme (TSPS). This enables multiple parties to jointly sign a message, resulting in a standard, single-party SPS signature, and can thus be used as a replacement for applications based on SPS. We begin by defining and constructing SPS for indexed messages, which are messages defined relative to a unique index. We prove its security in the random oracle model under a variant of the generalized Pointcheval-Sanders assumption (PS). Moreover, we generalize this scheme to an indexed multi-message SPS for signing vectors of indexed messages, which we prove secure under the same assumption. We then formally define the notion of a TSPS and propose a construction based on our indexed multi-message SPS. Our TSPS construction is fully non-interactive, meaning that signers simply output partial signatures without communicating with the other signers. Additionally, signatures are short: they consist of 2 group elements and require 2 pairing product equations to verify. We prove the security of our TSPS under the security of our indexed multi-message SPS scheme. Finally, we show that our TSPS may be used as a drop-in replacement for UC-secure Threshold-Issuance Anonymous Credential (TIAC) schemes, such as Coconut, without the overhead of the Fischlin transform.

Transport Layer Security (TLS) is the cryptographic backbone of secure communication on the Internet. In its latest version 1.3, the standardization process has taken formal analysis into account both due to the importance of the protocol and the experience with conceptual attacks against previous versions. To manage the complexity of TLS (the specification exceeds 100 pages), prior reduction-based analyses have focused on some protocol features and omitted others, e.g., included session resumption and omitted agile algorithms or vice versa. This article is a major step towards analysing the TLS 1.3 key establishment protocol as specified at the end of its rigorous standardization process. Namely, we provide a full proof of the TLS key schedule, a core protocol component which produces output keys and internal keys of the key exchange protocol. In particular, our model supports all key derivations featured in the standard, including its negotiated modes and algorithms that combine an optional Diffie-Hellman exchange for forward secrecy with optional pre-shared keys supplied by the application or recursively established in prior sessions. Technically, we rely on state-separating proofs (Asiacrypt ’18) and introduce techniques to model large and complex derivation graphs. Our key schedule analysis techniques have been used subsequently to analyse the key schedule of Draft 11 of the MLS protocol (S &P ’22) and to propose improvements.

Most succinct arguments (SNARKs) are initially only proven knowledge sound (KS). We show that the commonly employed compilation strategy from polynomial interactive oracle proofs (PIOP) via polynomial commitments to knowledge sound SNARKS actually also achieves other desirable properties: weak unique response (WUR) and trapdoorless zero-knowledge (TLZK); and that together they imply simulation extractability (SIM-EXT). The factoring of SIM-EXT into KS + WUR + TLZK is becoming a cornerstone of the analysis of non-malleable SNARK systems. We show how to prove WUR and TLZK for PIOP compiled SNARKs under mild falsifiable assumptions on the polynomial commitment scheme. This means that the analysis of knowledge soundness from PIOP properties that inherently relies on non-falsifiable or idealized assumption such as the algebraic group model (AGM) or generic group model (GGM) need not be repeated. While the proof of WUR requires only mild assumptions on the PIOP, TLZK is a different matter. As perfectly hiding polynomial commitments sometimes come at a substantial performance premium, SNARK designers prefer to employ deterministic commitments with some leakage. This results in the need for a stronger zero-knowledge property for the PIOP. The modularity of our approach implies that any analysis improvements, e.g. in terms of tightness, credibility of the knowledge assumption and model of the KS analysis, or the precision of capturing real-world optimizations for TLZK also benefits the SIM-EXT guarantees.

We study sufficient conditions to compile simulation-extractable zkSNARKs from information-theoretic interactive oracle proofs (IOP) using a simulation-extractable commit-and-prove system for its oracles. Specifically, we define simulation extractability for opening and evaluation proofs of polynomial commitment schemes, which we then employ to prove the security of zkSNARKS obtained from polynomial IOP proof systems. To instantiate our methodology, we additionally prove that KZG commitments satisfy our simulation extractability requirement, despite being naturally malleable. To this end, we design a relaxed notion of simulation extractability that matches how KZG commitments are used and optimized in real-world proof systems. The proof that KZG satisfies this relaxed simulation extractability property relies on the algebraic group model and random oracle model.

Self sovereign identity is a form of decentralised credential management. During credential verification, data exchange only happens between the data owner and the verifier without passing through any third parties. While this approach offers a privacy-centric solution, it poses a challenge. How do verifiers trust that the credential is vouched by a trusted source? More specifically, how do verifiers know that the issuer has the reputation or is authorised to issue the credential? In this paper, we propose a trust registry design that handles the aspect of human trust in self sovereign identity. We also introduce an incentivisation mechanism for the trust registry in order to motivate each stakeholder to participate actively and honestly.

Central Bank Digital Currencies (CBDCs) aspire to offer a digital replacement for physical cash and as such need to tackle two fundamental requirements that are in conflict. On the one hand, it is desired they are private so that a financial "panopticon'' is avoided, while on the other, they should be regulation friendly in the sense of facilitating any threshold-limiting, tracing, and counterparty auditing functionality that is necessary to comply with regulations such as Know Your Customer (KYC), Anti Money Laundering (AML) and Combating Financing of Terrorism (CFT) as well as financial stability considerations. In this work, we put forth a new model for CBDCs and an efficient construction that, for the first time, fully addresses these issues simultaneously. Moreover, recognizing the importance of avoiding a single point of failure, our construction is distributed so that all its properties can withstand a suitably bounded minority of participating entities getting corrupted by an adversary. Achieving all the above properties efficiently is technically involved; among others, our construction uses suitable cryptographic tools to thwart man-in-the-middle attacks, it showcases a novel traceability mechanism with significant performance gains compared to previously known techniques and, perhaps surprisingly, shows how to obviate Byzantine agreement or broadcast from the optimistic execution path of a payment, something that results in an essentially optimal communication pattern and communication overhead when the sender and receiver are honest. Going beyond "simple'' payments, we also discuss how our scheme can facilitate one-off large transfers complying with Know Your Transaction (KYT) disclosure requirements. Our CBDC concept is expressed and realized in the Universal Composition (UC) framework providing in this way a modular and secure way to embed it within a larger financial ecosystem.