Blind signature schemes enable a user to obtain a digital signature on a message from a signer without revealing the message itself. Among the most fundamental examples of such a scheme is blind Schnorr, but recent results show that it does not satisfy the standard notion of security against malicious users, One-More Unforgeability (OMUF), as it is vulnerable to the ROS attack. However, blind Schnorr does satisfy the weaker notion of sequential OMUF, in which only one signing session is open at a time, in the Algebraic Group Model (AGM) + Random Oracle Model (ROM), assuming the hardness of the Discrete Logarithm (DL) problem.

This paper serves as a first step towards characterizing the security of blind Schnorr in the limited concurrency setting. Specifically, we show that blind Schnorr satisfies OMUF when at most two signing sessions can be concurrently open (in the AGM+ROM, assuming DL). Our argument suggests that it is plausible that blind Schnorr satisfies OMUF for up to polylogarithmically many concurrent signing sessions. Our security proof involves interesting techniques from linear algebra and combinatorics.

The generic-group model (GGM) and the algebraic-group model (AGM) have been exceptionally successful in proving the security of many classical and modern cryptosystems. These models, however, come with standard-model uninstantiability results, raising the question of whether the schemes analyzed under them can be based on firmer standard-model footing.

We formulate the uber-knowledge (UK) assumption, a standard-model assumption that naturally extends the uber-assumption family to knowledge-type problems. We justify the soundness of UK in both the bilinear GGM and the bilinear AGM. Along the way we extend these models to account for hashing into groups, an adversarial capability that is available in many concrete groups—In contrast to standard assumptions, hashing may affect the validity of knowledge assumptions. These results, in turn, enable a modular approach to security in the GGM and the AGM.

As example applications, we use the UK assumption to prove knowledge soundness of Groth's zero-knowledge SNARK (EUROCRYPT 2016) and of KZG polynomial commitments (ASIACRYPT 2010) in the standard model, where for the former we reuse the existing proof in the AGM without hashing.

In this work, we introduce two post-quantum Verifiable Random Function (VRF) constructions based on abelian group actions and isogeny group actions with a twist. The former relies on the standard group action Decisional Diffie-Hellman (GA-DDH) assumption. VRFs serve as cryptographic tools allowing users to generate pseudorandom outputs along with publicly verifiable proofs. Moreover, the residual pseudorandomness of VRFs ensures the pseudorandomness of unrevealed inputs, even when multiple outputs and proofs are disclosed. Our work aims at addressing the growing demand for post-quantum VRFs, as existing constructions based on elliptic curve cryptography (ECC) or classical DDH-type assumptions are vulnerable to quantum threats.

In our contributions, our two VRF constructions, rooted in number-theoretic pseudorandom functions, are both simple and secure over the random oracle model. We introduce a new proof system for the factorization of group actions and set elements, serving as the proofs for our VRFs. The first proposal is based on the standard GA-DDH problem, and for its security proof, we introduce the (group action) master Decisional Diffie-Hellman problem over group actions, proving its equivalence to the standard GA-DDH problem. In the second construction, we leverage quadratic twists to enhance efficiency, reducing the key size and the proof sizes, expanding input size. The scheme is based on the square GA-DDH problem.

Moreover, we employ advanced techniques from the isogeny literature to optimize the proof size to 39KB and 34KB using CSIDH-512 without compromising VRF notions. The schemes feature fast evaluations but exhibit slower proof generation. To the best of our knowledge, these constructions represent the first two provably secure VRFs based on isogenies.

Watermarking pseudorandom functions (PRF) allow an authority to embed an unforgeable and unremovable watermark into a PRF while preserving its functionality. In this work, we extend the work of Kim and Wu [Crypto'19] who gave a simple two-step construction of watermarking PRFs from a class of extractable PRFs satisfying several other properties – first construct a mark-embedding scheme, and then upgrade it to a message-embedding scheme.

While the message-embedding scheme of Kim and Wu is based on complex homomorphic evaluation techniques, we observe that much simpler constructions can be obtained and from a wider range of assumptions, if we forego the strong requirement of security against the watermarking authority. Concretely, we introduce a new notion called extractable PRGs (xPRGs), from which extractable PRFs (without security against authorities) suitable for the Kim-Wu transformations can be simply obtained via the Goldreich-Goldwasser-Micali (GGM) construction. We provide simple constructions of xPRGs from a wide range of assumptions such as hardness of computational Diffie-Hellman (CDH) in the random oracle model, as well as LWE and RSA in the standard model.

Public-key searchable encryption allows keyword-associated tokens to be used to test if a ciphertext contains specific keywords. Due to the low entropies of keywords, the token holder can create ciphertexts from candidate keywords and test them using the token in hand to recover the keywords, known as inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search is a searchable encryption proposed to defend against such attacks. It ensures the sender's private key protects the ciphertexts from the IKGA. PAEKS schemes with reasonable security and practical efficiency remain elusive despite many proposals. This work provides a simple generic PAEKS scheme from non-interactive key exchange (NIKE) and symmetric-key equality-predicate encryption with three new constructions for the latter, respectively from pseudorandom functions (PRFs), the decision bilinear Diffie-Hellman assumption, and the learning-with-errors assumption. Instantiating our generic scheme, we derive several PAEKS schemes from the most well-known assumptions, with some of them achieving full cipher-keyword indistinguishability and full token indistinguishability in the standard model, for the first time. Our instantiated schemes allow practical implementations and outperform the existing PAEKS schemes under the same assumptions.

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized model. The key difference between our lemma and previous ones is that instead of focusing on the tradeoff between the worst-case or expected running time of the resulting forking algorithm and its success probability, we focus on the tradeoff between higher moments of its running time and its success probability.

Equipped with our lemma, we then establish concrete security bounds for the BN and BLS multi-signature schemes that are significantly tighter than the concrete security bounds established by Bellare and Neven (CCS '06) and Boneh, Drijvers and Neven (ASIACRYPT '18), respectively. Our analysis does not limit adversaries to any idealized algebraic model, such as the algebraic group model in which all algorithms are assumed to provide an algebraic justification for each group element they produce. Our bounds are derived in the random-oracle model based on the standard-model second-moment hardness of the discrete logarithm problem (for the BN scheme) and the computational co-Diffie-Hellman problem (for the BLS scheme). Such second-moment assumptions, asking that the success probability of any algorithm in solving the underlying computational problems is dominated by the second moment of the algorithm's running time, are particularly plausible in any group where no better-than-generic algorithms are currently known.

X-Wing is a hybrid key-encapsulation mechanism based on X25519 and ML-KEM-768. It is designed to be the sensible choice for most applications. The concrete choice of X25519 and ML-KEM-768 allows X-Wing to achieve improved efficiency compared to using a generic KEM combiner. In this paper, we introduce the X-Wing hybrid KEM construction and provide a proof of security. We show (1) that X-Wing is a classically IND-CCA secure KEM if the strong Diffie-Hellman assumption holds in the X25519 nominal group, and (2) that X-Wing is a post-quantum IND-CCA secure KEM if ML-KEM-768 is itself an IND-CCA secure KEM and SHA3-256 is secure when used as a pseudorandom function. The first result is proved in the ROM, whereas the second one holds in the standard model. Loosely speaking, this means X-Wing is secure if either X25519 or ML-KEM-768 is secure. We stress that these security guarantees and optimizations are only possible due to the concrete choices that were made, and it may not apply in the general case.

In a multiparty signing protocol, also known as a threshold signature scheme, the private signing key is shared amongst a set of parties and only a quorum of those parties can generate a signature. Research on multiparty signing has been growing in popularity recently due to its application to cryptocurrencies. Most work has focused on reducing the number of rounds to two, and as a result: (a) are not fully simulatable in the sense of MPC real/ideal security definitions, and/or (b) are not secure under concurrent composition, and/or (c) utilize non-standard assumptions of different types in their proofs of security. In this paper, we describe a simple three-round multiparty protocol for Schnorr signatures that is secure for any number of corrupted parties; i.e., in the setting of a dishonest majority. The protocol is fully simulatable, secure under concurrent composition, and proven secure in the standard model or random-oracle model (depending on the instantiations of the commitment and zero-knowledge primitives). The protocol realizes an ideal Schnorr signing functionality with perfect security in the ideal commitment and zero-knowledge hybrid model (and thus the only assumptions needed are for realizing these functionalities).

In our presentation, we do not assume that all parties begin with the message to be signed, the identities of the participating parties and a unique common session identifier, since this is often not the case in practice. Rather, the parties achieve consensus on these parameters as the protocol progresses.

Proving whether it is possible to build IND-CCA public-key encryption (PKE) from IND-CPA PKE in a black-box manner is a major open problem in theoretical cryptography. In a significant breakthrough, Gertner, Malkin and Myers showed in 2007 that shielding black-box reductions from IND-CCA to IND-CPA do not exist in the standard model. Shielding means that the decryption algorithm of the IND-CCA scheme does not call the encryption algorithm of the underlying IND-CPA scheme. In other words, it implies that every tentative construction of IND-CCA from IND-CPA must have a re-encryption step when decrypting.

This result was only proven with respect to classical algorithms. In this work we show that it stands in a post-quantum setting. That is, we prove that there is no post-quantum shielding black-box construction of IND-CCA PKE from IND-CPA PKE. In the type of reductions we consider, i.e. post-quantum ones, the constructions are still classical in the sense that the schemes must be computable on classical computers, but the adversaries and the reduction algorithm can be quantum. This suggests that considering quantum notions, which are stronger than their classical counterparts, and allowing for quantum reductions does not make building IND-CCA public-key encryption easier.

In this work we study algebraic and generic models for group actions, and extend them to the universal composability (UC) framework of Canetti (FOCS 2001). We revisit the constructions of Duman et al. (PKC 2023) integrating the type-safe model by Zhandry (Crypto 2022), adapted to the group action setting, and formally define an algebraic action model (AAM). This model restricts the power of the adversary in a similar fashion to the algebraic group model (AGM). By imposing algebraic behaviour to the adversary and environment of the UC framework, we construct the UC-AAM. Finally, we instantiate UC-AAM with isogeny-based assumptions, in particular the CSIDH action with twists, obtaining the explicit isogeny model, UC-EI; we observe that, under certain assumptions, this model is "closer" to standard UC than the UC-AGM, even though there still exists an important separation. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure oblivious transfer protocol described by Lai et al. (Eurocrypt 2021), hence providing the first concretely efficient two-message isogeny-based OT protocol in the random oracle model against malicious adversaries.

We use theta groups to study $2$-isogenies between Kummer lines, with a particular focus on the Montgomery model. This allows us to recover known formulas, along with more efficient forms for translated isogenies, which require only $2S+2m_0$ for evaluation. We leverage these translated isogenies to build a hybrid ladder for scalar multiplication on Montgomery curves with rational $2$-torsion, which cost $3M+6S+2m_0$ per bit, compared to $5M+4S+1m_0$ for the standard Montgomery ladder.