Post-Quantum Zero-Knowledge Proofs for Accumulators with Applications to Ring Signatures from Symmetric-Key Primitives

In this paper we address the construction of privacy-friendly cryptographic primitives for the post-quantum era and in particular accumulators with zero-knowledge membership proofs and ring signatures. This is an important topic as it helps to protect the privacy of users in online authentication or emerging technologies such as cryptocurrencies. Recently, we have seen first such constructions, mostly based on assumptions related to codes and lattices. We, however, ask whether it is possible to construct such primitives without relying on structured hardness assumptions, but solely based on symmetric-key primitives such as hash functions or block ciphers. This is interesting because the resistance of latter primitives to quantum attacks is quite well understood. In doing so, we choose a modular approach and firstly construct an accumulator (with one-way domain) that allows to efficiently prove knowledge of (a pre-image of) an accumulated value in zero-knowledge. We, thereby, take care that our construction can be instantiated solely from symmetric-key primitives and that our proofs are of sublinear size. Latter is non trivial to achieve in the symmetric setting due to the absence of algebraic structures which are typically used in other settings to make these efficiency gains. Regarding efficient instantiations of our proof system, we rely on recent results for constructing efficient non-interactive zero-knowledge proofs for general circuits. Based on this building block, we then show how to construct logarithmic size ring signatures solely from symmetric-key primitives. As constructing more advanced primitives only from symmetric-key primitives is a very recent field, we discuss some interesting open problems and future research directions. Finally, we want to stress that our work also indirectly impacts other fields: for the first time it raises the requirement for collision resistant hash functions with particularly low AND count

Post-Quantum EPID Signatures from Symmetric Primitives

EPID signatures are used extensively in real-world systems for hardware enclave attestation. As such, there is a strong interest in making these schemes post-quantum secure. In this paper we initiate the study of EPID signature schemes built only from symmetric primitives, such as hash functions and PRFs. We present two constructions in the random oracle model. The first is a scheme satisfying the EPID signature syntax and security definitions needed for private hardware attestation used in Intel’s SGX. The second achieves significantly shorter signatures for many applications, including the use case of remote hardware attestation. While our EPID signatures for attestation are longer than standard post-quantum signatures, they are short enough for applications where the data being signed is large, such as analytics on large private data sets, or streaming media to a trusted display. We evaluate several instantiations of our schemes so that the costs and benefits of these constructions are clear. Along the way we also give improvements to the zero-knowledge Merkle inclusion proofs of Derler et al. (2017)

Efficient Set Membership Proofs using MPC-in-the-Head

Set membership proofs are an invaluable part of privacy preserving systems. These proofs allow a prover to demonstrate knowledge of a witness $w$ corresponding to a secret element $x$ of a public set, such that they jointly satisfy a given NP relation, {\em i.e.} $\mathcal{R}(w,x)=1$ and $x$ is a member of a public set $\{x_1, \ldots, x_\ell\}$. This allows the identity of the prover to remain hidden, eg. ring signatures and confidential transactions in cryptocurrencies. In this work, we develop a new technique for efficiently adding logarithmic-sized set membership proofs to any MPC-in-the-head based zero-knowledge protocol (Ishai et al. [STOC\u2707]). We integrate our technique into an open source implementation of the state-of-the-art, post quantum secure zero-knowledge protocol of Katz et al. [CCS\u2718]. We find that using our techniques to construct ring signatures results in signatures (based only on symmetric key primitives) that are between 5 and 10 times smaller than state-of-the-art techniques based on the same assumptions. We also show that our techniques can be used to efficiently construct post-quantum secure RingCT from only symmetric key primitives

Improved Non-Interactive Zero Knowledge with Applications to Post-Quantum Signatures

Recent work, including ZKBoo, ZKB++, and Ligero, has developed efficient non-interactive zero-knowledge proofs of knowledge (NIZKPoKs) for arbitrary Boolean circuits based on symmetric- key primitives alone using the “MPC-in-the-head” paradigm of Ishai et al. We show how to instantiate this paradigm with MPC protocols in the preprocessing model; once optimized, this results in an NIZKPoK with shorter proofs (and comparable computation) as in prior work for circuits containing roughly 300–100,000 AND gates. In contrast to prior work, our NIZKPoK also supports witness-independent preprocessing, which allows the prover to move most of its work to an offline phase before the witness is known. We use our NIZKPoK to construct a signature scheme based only on symmetric-key primitives (and hence with “post-quantum” security). The resulting scheme has shorter signatures than the scheme built using ZKB++ (with comparable signing/verification time), and is even competitive with hash-based signature schemes. To further highlight the flexibility and power of our NIZKPoK, we also use it to build efficient ring and group signatures based on symmetric-key primitives alone. To our knowledge, the resulting schemes are the most efficient constructions of these primitives that offer post-quantum security

Logarithmic-Size (Linkable) Threshold Ring Signatures in the Plain Model

Ring signatures are a cryptographic primitive that allow a signer to anonymously sign messages on behalf of an ad-hoc group of $N$ potential signers (the so-called ring). This primitive has attracted significant research since its introduction by Rivest et al. (ASIACRYPT\u2701), but until recently, no construction was known that was both (i) compact, i.e., the signature size is sub-linear in $N$, and (ii) in the plain model, i.e., secure under standard hardness assumptions without requiring heuristic or setup assumptions. The first construction in this most desirable setting, where reducing trust in external parties is the primary goal, was only recently presented by Backes et al. (EUROCRYPT\u2719). An interesting generalization of ring signatures are $t$-out-of-$N$ ring signatures for $t\geq 1$, also known as threshold ring (thring) signatures (Bresson et al., CRYPTO\u2702). For threshold ring signatures, non-linkable sub-linear-size constructions are not even known under heuristic or setup assumptions. In this work, we propose the first sub-linear thring signatures and prove them secure in the plain model. While our constructions are inspired by the template underlying the Backes et al. construction, they require novel ideas and techniques. Our scheme is non-interactive, and has strong inter-signer anonymity, meaning that signers do not need to know the other signers that participate in a threshold signing. We then present a linkable counterpart to our non-linkable construction. Our thring signatures can easily be adapted to achieve the recently introduced notions of flexibility (Okamoto et al., EPRINT\u2718) as well as claimability and repudiability (Park and Sealfon, CRYPTO\u2719). (Th)Ring signatures and, in particular, their linkable versions have recently drawn significant attention in the field of privacy-friendly cryptocurrencies. We discuss applications that are enabled by our strong inter-signer anonymity, demonstrating that thring signatures are interesting from a practical perspective also

Efficient FPGA Implementations of LowMC and Picnic

Post-quantum cryptography has received increased attention in recent years, in particular, due to the standardization effort by NIST. One of the second-round candidates in the NIST post-quantum standardization project is Picnic, a post-quantum secure signature scheme based on efficient zero-knowledge proofs of knowledge. In this work, we present the first FPGA implementation of Picnic. We show how to efficiently calculate LowMC, the block cipher used as a one-way function in Picnic, in hardware despite the large number of constants needed during computation. We then combine our LowMC implementation and efficient instantiations of Keccak to build the full Picnic algorithm. Additionally, we conform to recently proposed hardware interfaces for post-quantum schemes to enable easier comparisons with other designs. We provide evaluations of our Picnic implementation for both, the standalone design and a version wrapped with a PCIe interface, and compare them to the state-of-the-art software implementations of Picnic and similar hardware designs. Concretely, signing messages on our FPGA takes 0.25 ms for the L1 security level and 1.24 ms for the L5 security level, beating existing optimized software implementations by a factor of 4

Generic Double-Authentication Preventing Signatures and a Post-Quantum Instantiation

Double-authentication preventing signatures (DAPS) are a variant of digital signatures which have received considerable attention recently (Derler et al. EuroS&P 2018, Poettering AfricaCrypt 2018). They are unforgeable signatures in the usual sense and sign messages that are composed of an address and a payload. Their distinguishing feature is the property that signing two different payloads with respect to the same address allows to publicly extract the secret signing key from two such signatures. DAPS are known in the factoring, the discrete logarithm and the lattice setting. The majority of the constructions are ad-hoc. Only recently, Derler et al. (EuroS&P 2018) presented the first generic construction that allows to extend any discrete logarithm based secure signatures scheme to DAPS. However, their scheme has the drawback that the number of potential addresses (the address space) used for signing is polynomially bounded (and in fact small) as the size of secret and the public keys of the resulting DAPS are linear in the address space. In this paper we overcome this limitation and present a generic construction of DAPS with constant size keys and signatures. Our techniques are not tailored to a specific algebraic setting and in particular allow us to construct the first DAPS without structured hardness assumptions, i.e., from symmetric key primitives, yielding a candidate for post-quantum secure DAPS

SoK: Privacy-Preserving Signatures

Modern security systems depend fundamentally on the ability of users to authenticate their communications to other parties in a network. Unfortunately, cryptographic authentication can substantially undermine the privacy of users. One possible solution to this problem is to use privacy-preserving cryptographic authentication. These protocols allow users to authenticate their communications without revealing their identity to the verifier. In the non-interactive setting, the most common protocols include blind, ring, and group signatures, each of which has been the subject of enormous research in the security and cryptography literature. These primitives are now being deployed at scale in major applications, including Intel\u27s SGX software attestation framework. The depth of the research literature and the prospect of large-scale deployment motivate us to systematize our understanding of the research in this area. This work provides an overview of these techniques, focusing on applications and efficiency

A Survey on Exotic Signatures for Post-Quantum Blockchain: Challenges & Research Directions

Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this paper, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and which are crucial cryptographic tools used in the blockchain ecosystem for (i) account management, (ii) consensus efficiency, (iii) empowering scriptless blockchain, and (iv) privacy. The exotic signatures that we particularly focus on in this work are the following: multi-/aggregate, threshold, adaptor, blind and ring signatures. Herein the term exotic refers to signatures with properties which are not just beyond the norm for signatures e.g. unforgeability, but also imbue new forms of functionalities. Our treatment of such exotic signatures includes discussions on existing challenges and future research directions in the post-quantum space. We hope that this article will help to foster further research to make post-quantum cryptography more accessible so that blockchain systems can be made ready in advance of the approaching quantum threats