Towards Practical Lattice-Based One-Time Linkable Ring Signatures

Ring signatures, as introduced by Rivest, Shamir, and Tauman (Asiacrypt ’01), allow to generate a signature for a message on be half of an ad-hoc set of parties. To sign a message, only the public keys must be known and these can be generated independently. It is furthermore not possible to identify the actual signer based on the signature. Ring signatures have recently gained attention due to their applicability in the construction of practical anonymous cryptocurrencies, where they are used to secure transactions while hiding the identity of the actual spender. To be applicable in that setting, ring signatures must allow to determine when a party signed multiple transactions, which is done using a property called linkability. This work presents a linkable ring signature scheme constructed from a lattice-based collision-resistant hash function. We follow the idea of existing schemes which are secure based on the hardness of the discrete logarithm problem, but adapt and optimize ours to the lattice setting. In comparison to other designs for (lattice-based) linkable ring signatures, our approach avoids the standard solution for achieving linkability, which involves proofs about correct evaluation of a pseudorandom function using heavy zero-knowledge machinery

A Survey on Exotic Signatures for Post-quantum Blockchain: Challenges and Research Directions

Blockchain technology provides efficient and secure solutions to various online activities by utilizing a wide range of cryptographic tools. In this article, we survey the existing literature on post-quantum secure digital signatures that possess exotic advanced features and that are crucial cryptographic tools used in the blockchain ecosystem for (1) account management, (2) consensus efficiency, (3) empowering scriptless blockchain, and (4) 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 that 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

Efficient Linkable Ring Signatures: New Framework and Post-Quantum Instantiations

In this paper, we introduce a new framework for constructing linkable ring signatures (LRS). Our framework is based purely on signatures of knowledge (SoK) which allows one to issue signatures on behalf of any NP-statement using the corresponding witness. Our framework enjoys the following advantages: (1) the security of the resulting LRS depends only on the security of the underlying SoK; (2) the resulting LRS naturally supports online/offline signing (resp. verification), where the output of the offline signing (resp. verification) can be re-used across signatures of the same ring. For a ring size $n$, our framework requires an SoK of the NP statement with size $\log n$. To instantiate our framework, we adapt the well-known post-quantum secure non-interactive argument of knowledge (NIAoK), ethSTARK, into an SoK. This SoK is inherently post-quantum secure and has a signature size poly-logarithmic in the size of the NP statement. Thus, our resulting LRS has a signature size of $O(\text{polylog}(\log n))$. By comparison, existing post-quantum ring signatures, regardless of linkability considerations, have signature sizes of $O(\log n)$ at best. Furthermore, leveraging online/offline verification, part of the verification of signatures on the same ring can be shared, resulting in a state-of-the-art amortized verification cost of $O(\text{polylog}(\log n))$. Our LRS also performs favourably against existing schemes in practical scenarios. Concretely, our scheme has the smallest signature size among all post-quantum linkable ring signatures with non-slanderability for ring size larger than $32$. In our experiment, at $128$-bit security and ring size of $1024$, our LRS has a size of $29$KB, and an amortized verification cost of $0.3$ ms, surpassing the state-of-the-art by a significant margin. Even without considering amortization, the verification time for a single signature is $128$ ms, comparable to those featuring linear signature size. A similar performance advantage can also be seen at signing. Furthermore, our LRS has extremely short public keys ($32$ bytes), while public keys of existing constructions are in the order of kilobytes

(Linkable) Ring Signature from Hash-Then-One-Way Signature

In this paper, we revisit the generic construction of ring signatures from hash-then-one-way type ($\mathsf{Type-H}$) signatures proposed by Abe et al. (AOS) in 2004 and made the following contributions. First, we give a proof for the generic construction, in a strengthened security model. Previously, this was only done for concrete instantiations, in a weaker model. Second, we extend AOS\u27s framework to generically construct one-time linkable ring signatures from $\mathsf{Type-H}$ signatures and one-time signatures. Lastly, we instantiate the generic construction with an NTRU-based $\mathsf{Type-H}$ signature: Falcon~and obtain a post-quantum linkable ring signature scheme. Our analysis shows that the resulting linkable signature is more efficient than any existing lattice based solutions for small to moderate number of users

Raptor: A Practical Lattice-Based (Linkable) Ring Signature

We present Raptor, the first practical lattice-based (linkable) ring signature scheme with implementation. Raptor is as fast as classical solutions; while the size of the signature is roughly $1.3$ KB per user. Prior to our work, all existing lattice-based solutions are analogues of their discrete-log or pairing-based counterparts. We develop a generic construction of (linkable) ring signatures based on the well-known generic construction from Rivest et al., which is not fully compatible with lattices. We show that our generic construction is provably secure in random oracle model. We also give instantiations from both standard lattice, as a proof of concept, and NTRU lattice, as an efficient instantiation. We showed that the latter construction, called Raptor, is almost as efficient as the classical RST ring signatures and thus may be of practical interest

Adding Linkability to Ring Signatures with One-Time Signatures

We propose a generic construction that adds linkability to any ring signature scheme with one-time signature scheme. Our construction has both theoretical and practical interest. In theory, the construction gives a formal and cleaner description for constructing linkable ring signature from ring signature directly. In practice, the transformation incurs a tiny overhead in size and running time. By instantiating our construction using the ring signature scheme (ACNS 2019) and the one-time signature scheme (TCHES 2018), we obtain a lattice-based linkable ring signature scheme whose signature size is logarithmic in the number of ring members. This scheme is practical, especially the signature size is very short: for $2^{30}$ ring members and 100 bit security, our signature size is only 4 MB. In addition, when proving the linkability we develop a new proof technique in the random oracle model, which might be of independent interes

One-time Traceable Ring Signatures

A ring signature allows a party to sign messages anonymously on behalf of a group, which is called ring. Traceable ring signatures are a variant of ring signatures that limits the anonymity guarantees, enforcing that a member can sign anonymously at most one message per tag. Namely, if a party signs two different messages for the same tag, it will be de-anomymized. This property is very useful in decentralized platforms to allow members to anonymously endorse statements in a controlled manner. In this work we introduce one-time traceable ring signatures, where a member can sign anonymously only one message. This natural variant suffices in many applications for which traceable ring signatures are useful, and enables us to design a scheme that only requires a few hash evaluations and outperforms existing (non one-time) schemes. Our one-time traceable ring signature scheme presents many advantages: it is fast, with a signing time of less than 1 second for a ring of $2^{10}$ signers (and much less for smaller rings); it is {\em post-quantum resistant}, as it only requires hash evaluations; it is extremely simple, as it requires only a black-box access to a generic hash function (modeled as a random oracle) and no other cryptographic operation is involved. From a theoretical standpoint our scheme is also the first anonymous signature scheme based on a black-box access to a symmetric-key primitive. All existing anonymous signatures are either based on specific hardness assumptions (e.g., LWE, SIS, etc.) or use the underlying symmetric-key primitive in a non-black-box way, i.e., they leverage the circuit representation of the primitive

Lattice-Based Linkable Ring Signature in the Standard Model

Ring signatures enable a user to sign messages on behalf of an arbitrary set of users, called the ring. The anonymity property guarantees that the signature does not reveal which member of the ring signed the message. The notion of linkable ring signatures (LRS) is an extension of the concept of ring signatures such that there is a public way of determining whether two signatures have been produced by the same signer. Lattice-based LRS is an important and active research line since lattice-based cryptography has attracted more attention due to its distinctive features, especially the quantum-resistant. However, all the existing lattice-based LRS relied on random oracle heuristics, i.e., no lattice-based LRS in the standard model has been introduced so far. In this paper, we present a lattice-based LRS scheme in the standard model. Toward our goal, we present a lattice basis extending algorithm which is the key ingredient in our construction, that may be of indepen- dent interes