International Association
for Cryptologic Research

In the past decades, user authentication has been dominated by server-side password-based solutions that rely on ``what users know". This approach is susceptible to breaches and phishing attacks, and poses usability challenges. As a result, the industry is gradually moving to biometric-based client-side solutions that do not store any secret information on servers. This shift necessitates the safe storage of biometric templates and private keys, which are used to generate tokens, on user devices. We propose a new generic framework called Biometric Enabled Threshold Authentication (BETA) to protect sensitive client-side information like biometric templates and cryptographic keys. Towards this, we formally introduce the notion of Fuzzy Threshold Tokenizer (FTT) where an initiator can use a ``close'' biometric measurement to generate an authentication token if at least t (the threshold) devices participate. We require that the devices only talk to the initiator, and not to each other, to capture the way user devices are connected in the real world. We use the universal composability (UC) framework to model the security properties of FTT, including the unforgeability of tokens and the privacy of the biometric values (template and measurement), under a malicious adversary. We construct three protocols that meet our definition. Our first two protocols are general feasibility results that work for any distance function, any threshold t and tolerate the maximal (i.e. t-1) amount of corruption. They are based on any two round UC-secure multi-party computation protocol in the standard model (with a CRS) and threshold fully homomorphic encryption, respectively. We show how to effectively use these primitives to build protocols in a constrained communication model with just four rounds of communication. For the third protocol, we consider inner-product based distance metrics (cosine similarity, Euclidean distance, etc.) specifically, motivated by the recent interest in its use for face recognition. We use Paillier encryption, efficient NIZKs for specific languages, and a simple garbled circuit to build an efficient protocol for the common case of n=3 devices with one compromised.

Private set intersection reveals the intersection of two private sets, but many real-world applications require the parties to learn $\textit{only}$ partial information} about the intersection. In this paper, we introduce a new approach for computing arbitrary functions of the intersection, provided that it is safe to also reveal the cardinality of the intersection. In the most general case, our new protocol provides the participants with secret shares of the intersection, which can be fed into any generic 2PC protocol. Certain computations on the intersection can also be done even more directly and efficiently, avoiding this secret-sharing step. These cases include computing $\textit{only}$ the cardinality of the intersection, or the ``cardinality-sum'' application proposed in Ion $\textit{et al.}$ (ePrint 2017). Compared to the state-of-the-art protocol for computing on the intersection (Pinkas et al., Eurocrypt 2019), our protocol has about $2.5-3\times$ less communication and has faster running time on slower (50Mbps) networks. Our new techniques can also be used to privately compute the {\em union} of two sets as easily as computing the intersection. Our protocol concretely improves the leading private set union protocol (Kolesnikov et al., Asiacrypt 2020) by a factor of $2-2.5\times$, depending on the network speed. We then show how private set union can be used in a simple way to realize the ``Private-ID'' functionality suggested by Buddhavarapu et al.~(ePrint 2020). Our protocol is significantly faster than the prior Private-ID protocol, especially on fast networks. All of our protocols are in the two-party setting and are secure against semi-honest adversaries.

Schnorr's signature scheme permits an elegant threshold signing protocol due to its linear signing equation. However each new signature consumes fresh randomness, which can be a major attack vector in practice. Sources of randomness in deployments are frequently either unreliable, or require state continuity, i.e. reliable fresh state resilient to rollbacks. State continuity is a notoriously difficult guarantee to achieve in practice, due to system crashes caused by software errors, malicious actors, or power supply interruptions (Parno et al., S&P '11). This is a non-issue for Schnorr variants such as EdDSA, which is specified to derive nonces deterministically as a function of the message and the secret key. However, it is challenging to translate these benefits to the threshold setting, specifically to construct a threshold Schnorr scheme where signing neither requires parties to consume fresh randomness nor update long-term secret state. In this work, we construct a dishonest majority threshold Schnorr protocol that enables such stateless deterministic nonce derivation using standardized block ciphers. Our core technical ingredients are new tools for the zero-knowledge from garbled circuits (ZKGC) paradigm to aid in verifying correct nonce derivation: - A mechanism based on UC Commitments that allows a prover to commit once to a witness, and prove an unbounded number of statements online with only cheap symmetric key operations. - A garbling gadget to translate intermediate garbled circuit wire labels to arithmetic encodings. A proof per our scheme requires only a small constant number of exponentiations.

The two most common ways to design non-interactive zero-knowledge (NIZK) proofs are based on Sigma protocols and QAP-based SNARKs. The former is highly efficient for proving algebraic statements while the latter is superior for arithmetic representations.   Motivated by applications such as privacy-preserving credentials and privacy-preserving audits in cryptocurrencies, we study the design of NIZKs for composite statements that compose algebraic and arithmetic statements in arbitrary ways. Specifically, we provide a framework for proving statements that consist of ANDs, ORs and function compositions of a mix of algebraic and arithmetic components. This allows us to explore the full spectrum of trade-offs between proof size, prover cost, and CRS size/generation cost. This leads to proofs for statements of the form: knowledge of x such that $$SHA(g^x)=y$$SHA(gx)=y for some public y where the prover’s work is 500 times fewer exponentiations compared to a QAP-based SNARK at the cost of increasing the proof size to 2404 group and field elements. In application to anonymous credentials, our techniques result in 8 times fewer exponentiations for the prover at the cost of increasing the proof size to 298 elements.