An Equivalence Between Attribute-Based Signatures and Homomorphic Signatures, and New Constructions for Both

In Attribute-Based Signatures (ABS; first defined by Maji, Prabhakaran and Rosulek, CT-RSA 2011) an authority can generate multiple signing keys, where each key is associated with a constraint $f$. A key respective to $f$ can sign a message $x$ only if $f(x) = 0$. The security requirements are unforgeability and key privacy (signatures should not expose the specific signing key used). In Homomorphic Signatures (HS; first defined by Boneh and Freeman, PKC 2011), given a signature for a data-set $x$, one can evaluate a signature for the pair $(f(x),f)$, for functions $f$. In context-hiding HS, evaluated signatures do not reveal information about the pre-evaluated signature. In this work we start by showing that these two notions are in fact equivalent. The first implication of this equivalence is a new lattice-based ABS scheme for polynomial-depth circuits, based on the HS construction of Gorbunov, Vaikuntanathan and Wichs (GVW; STOC 2015). We then construct a new ABS candidate from a worst case lattice assumption (SIS), with different parameters. Using our equivalence again, now in the opposite direction, our new ABS implies a new lattice-based HS scheme with different parameter trade-off, compared to the aforementioned GVW

Verifiably Encrypted Signatures with Short Keys based on the Decisional Linear Problem and Obfuscation for Encrypted VES

Verifiably encrypted signatures (VES) are signatures encrypted by a public key of a trusted third party and we can verify their validity without decryption. This paper proposes a new VES scheme which is secure under the decisional linear (DLIN) assumption in the standard model. We also propose new obfuscators for encrypted signatures (ES) and encrypted VES (EVES) which are secure under the DLIN assumption. All previous efficient VES schemes in the standard model are either secure under standard assumptions (such as the computational Diffie-Hellman assumption) with large verification (or secret) keys or secure under \emph{(non-standard) dynamic $q$-type assumptions} (such as the $q$-strong Diffie-Hellman extraction assumption) with short verification keys. Our construction is the first efficient VES scheme with short verification (and secret) keys secure under \emph{a standard assumption (DLIN)}. As by-products of our VES scheme, we construct new obfuscators for ES/EVES based on our new VES scheme. They are more efficient than previous obfuscators with respect to the public key size. Previous obfuscators for EVES are secure under non-standard assumption and use zero-knowledge (ZK) proof systems and Fiat-Shamir heuristics to obtain non-interactive ZK, i.e., its security is considered in the random oracle model. Thus, our construction also has an advantage with respect to assumptions and security models. Our new obfuscator for ES is obtained from our new obfuscator for EVES

Homomorphic Trapdoors for Identity-based and Group Signatures

Group signature (GS) schemes are an important primitive in cryptography that provides anonymity and traceability for a group of users. In this paper, we propose a new approach to constructing GS schemes using the homomorphic trapdoor function (HTDF). We focus on constructing an identity-based homomorphic signature (IBHS) scheme using the trapdoor, providing a simpler scheme that has no zero-knowledge proofs. Our scheme allows packing more data into the signatures by elevating the existing homomorphic trapdoor from the SIS assumption to the MSIS assumption to enable packing techniques. Compared to the existing group signature schemes, we provide a straightforward and alternate construction that is efficient and secure under the standard model. Overall, our proposed scheme provides an efficient and secure solution for GS schemes using HTDF

Semi-Quantum Copy-Protection and More

Properties of quantum mechanics have enabled the emergence of quantum cryptographic protocols achieving important goals which are proven to be impossible classically. Unfortunately, this usually comes at the cost of needing quantum power from every party in the protocol, while arguably a more realistic scenario would be a network of classical clients, classically interacting with a quantum server. In this paper, we focus on copy-protection, which is a quantum primitive that allows a program to be evaluated, but not copied, and has shown interest especially due to its links to other unclonable cryptographic primitives. Our main contribution is to show how to dequantize existing quantum copy-protection from hidden coset states, by giving a construction for classically-instructed remote state preparation for coset states. We then apply this dequantizer to obtain semi-quantum cryptographic protocols for copy-protection and tokenized signatures with strong unforgeability. In the process, we present the first secure copy-protection scheme for point functions in the plain model and a new direct product hardness property of coset states which immediately implies a strongly unforgeable tokenized signature scheme

SoK: Signatures With Randomizable Keys

Digital signature schemes with specific properties have recently seen various real-world applications with a strong emphasis on privacy-enhancing technologies. They have been extensively used to develop anonymous credentials schemes and to achieve an even more comprehensive range of functionalities in the decentralized web. Substantial work has been done to formalize different types of signatures where an allowable set of transformations can be applied to message-signature pairs to obtain new related pairs. Most of the previous work focused on transformations with respect to the message being signed, but little has been done to study what happens when transformations apply to the signing keys. A first attempt to thoroughly formalize such aspects was carried by Derler and Slamanig (ePrint \u2716, Designs, Codes and Cryptography \u2719), followed by the more recent efforts by Backes et. al (ASIACRYPT \u2718) and Eaton et. al (ePrint \u2723). However, the literature on the topic is vast and different terminology is used across contributions, which makes it difficult to compare related works and understand the range of applications covered by a given construction. In this work, we present a unified view of signatures with randomizable keys and revisit their security properties. We focus on state-of-the-art constructions and related applications, identifying existing challenges. Our systematization allows us to highlight gaps, open questions and directions for future research on signatures with randomizable keys

Group Signatures without NIZK: From Lattices in the Standard Model

In a group signature scheme, users can anonymously sign messages on behalf of the group they belong to, yet it is possible to trace the signer when needed. Since the first proposal of lattice-based group signatures in the random oracle model by Gordon, Katz, and Vaikuntanathan (ASIACRYPT 2010), the realization of them in the standard model from lattices has attracted much research interest, however, it has remained unsolved. In this paper, we make progress on this problem by giving the first such construction. Our schemes satisfy CCA-selfless anonymity and full traceability, which are the standard security requirements for group signatures proposed by Bellare, Micciancio, and Warinschi (EUROCRYPT 2003) with a slight relaxation in the anonymity requirement suggested by Camenisch and Groth (SCN 2004). We emphasize that even with this relaxed anonymity requirement, all previous group signature constructions rely on random oracles or NIZKs, where currently NIZKs are not known to be implied from lattice-based assumptions. We propose two constructions that provide tradeoffs regarding the security assumption and efficiency: - Our first construction is proven secure assuming the standard LWE and the SIS assumption. The sizes of the public parameters and the signatures grow linearly in the number of users in the system. - Our second construction is proven secure assuming the standard LWE and the subexponential hardness of the SIS problem. The sizes of the public parameters and the signatures are independent of the number of users in the system. Technically, we obtain the above schemes by combining a secret key encryption scheme with additional properties and a special type of attribute-based signature (ABS) scheme, thus bypassing the utilization of NIZKs. More specifically, we introduce the notion of \emph{indexed} ABS, which is a relaxation of standard ABS. The above two schemes are obtained by instantiating the indexed ABS with different constructions. One is a direct construction we propose and the other is based on previous work

Post Quantum Fuzzy Stealth Signatures and Applications

Private payments in blockchain-based cryptocurrencies have been a topic of research, both academic and industrial, ever since the advent of Bitcoin. Stealth address payments were proposed as a solution to improve payment privacy for users and are, in fact, deployed in several major cryptocurrencies today. The mechanism lets users receive payments so that none of these payments are linkable to each other or the recipient. Currently known stealth address mechanisms either (1) are insecure in certain reasonable adversarial models, (2) are inefficient in practice or (3) are incompatible with many existing currencies. In this work, we formalize the underlying cryptographic abstraction of this mechanism, namely, stealth signatures with formal game-based definitions. We show a surprising application of our notions to passwordless authentication defined in the Fast IDentity Online (FIDO) standard. We then present SPIRIT, the first efficient post-quantum secure stealth signature construction based on the NIST standardized signature and key-encapsulation schemes, Dilithium and Kyber. The basic form of SPIRIT is only secure in a weak security model, but we provide an efficiency-preserving and generic transform, which boosts the security of SPIRIT to guarantee the strongest security notion defined in this work. Compared to state-of-the-art, there is an approximately 800x improvement in the signature size while keeping signing and verification as efficient as 0.2 ms. We extend SPIRIT with a fuzzy tracking functionality where recipients can outsource the tracking of incoming transactions to a tracking server, satisfying an anonymity notion similar to that of fuzzy message detection (FMD) recently introduced in [CCS 2021]. We also extend SPIRIT with a new fuzzy tracking framework called scalable fuzzy tracking that we introduce in this work. This new framework can be considered as a dual of FMD, in that it reduces the tracking server\u27s computational workload to sublinear in the number of users, as opposed to linear in FMD. Experimental results show that, for millions of users, the server only needs 3.4 ms to filter each incoming message which is a significant improvement upon the state-of-the-art

Key-Homomorphic Signatures: Definitions and Applications to Multiparty Signatures and Non-Interactive Zero-Knowledge

Key-homomorphic properties of cryptographic objects, i.e., homomorphisms on their key space, have proven to be useful, both from a theoretical as well as a practical perspective. Important cryptographic objects such as pseudorandom functions or (public key) encryption have been studied previously with respect to key-homomorphisms. Interestingly, however, signature schemes have not been explicitly investigated in this context so far. We close this gap and initiate the study of key-homomorphic signatures, which turns out to be an interesting and versatile concept. In doing so, we firstly propose a definitional framework for key-homomorphic signatures distilling various natural flavours of key-homomorphic properties. Those properties aim to classify existing signature schemes and thus allow to infer general statements about signature schemes from those classes by simply making black-box use of the respective properties. We apply our definitional framework to show elegant and simple compilers from classes of signature schemes admitting different types of key-homomorphisms to a number of other interesting primitives such as ring signature schemes, (universal) designated verifier signature schemes, simulation-sound extractable non-interactive zero-knowledge (NIZK) arguments, and multisignature schemes. Additionally, using the formalisms provided by our framework, we can prove a tight implication from single-user security to key-prefixed multi-user security for a class of schemes admitting a certain key-homomorphism. Finally, we discuss schemes that provide homomorphic properties on the message space of signatures under different keys in context of key-homomorphisms and present some first constructive results from key-homomorphic schemes

Functional Encryption from (Small) Hardware Tokens

Functional encryption (FE) enables fine-grained access control of encrypted data while promising simplified key management. In the past few years substantial progress has been made on functional encryption and a weaker variant called predicate encryption. Unfortunately, fundamental impossibility results have been demonstrated for constructing FE schemes for general functions satisfying a simulation-based definition of security. We show how to use \emph{hardware tokens} to overcome these impossibility results. In our envisioned scenario, an authority gives a hardware token and some cryptographic information to each authorized user; the user combines these to decrypt received ciphertexts. Our schemes rely on \emph{stateless} tokens that are \emph{identical} for all users. (Requiring a different token for each user trivializes the problem, and would be a barrier to practical deployment.) The tokens can implement relatively ``lightweight\u27\u27 computation relative to the functions supported by the scheme. Our token-based approach can be extended to support hierarchal functional encryption, function privacy, and more