International Association
for Cryptologic Research

Two most common ways to design non-interactive zero knowledge (NIZK) proofs are based on Sigma ($\Sigma$)-protocols (an efficient way to prove algebraic statements) and zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARK) protocols (an efficient way to prove arithmetic statements). However, in the applications of cryptocurrencies such as privacy-preserving credentials, privacy-preserving audits, and blockchain-based voting systems, the zk-SNARKs for general statements are usually implemented with encryption, commitment, or other algebraic cryptographic schemes. Moreover, zk-SNARKs for many different arithmetic statements may also be required to be implemented together. Clearly, a typical solution is to extend the zk-SNARK circuit to include the code for algebraic part. However, complex cryptographic operations in the algebraic algorithms will significantly increase the circuit size, which leads to impractically large proving time and CRS size. Thus, we need a flexible enough proof system for composite statements including both algebraic and arithmetic statements. Unfortunately, while the conjunction of zk-SNARKs is relatively natural and numerous effective solutions are currently available (e.g. by utilizing the commit-and-prove technique), the disjunction of zk-SNARKs is rarely discussed in detail. In this paper, we mainly focus on the disjunctive statements of Groth16, and we propose a Groth16 variant---CompGroth16, which provides a framework for Groth16 to prove the disjunctive statements that consist of a mix of algebraic and arithmetic components. Specifically, we could directly combine CompGroth16 with $\Sigma$-protocol or even CompGroth16 with CompGroth16 just like the logical composition of $\Sigma$-protocols. From this, we can gain many good properties, such as broader expression, better prover's efficiency and shorter CRS. In addition, for the combination of CompGroth16 and $\Sigma$-protocol, we also present two representative application scenarios to demonstrate the practicality of our construction.

In this paper we propose a constant time lattice reduction algorithm for integral dimension-4 lattices. Motivated by its application in the SQIsign post-quantum signature scheme, we provide for the first time a constant time LLL-like algorithm with guarantees on the length of the shortest output vector. We implemented our algorithm and ensured through various tools that it indeed operates in constant time. Our experiments suggest that in practice our implementation outputs a Minkowski reduced basis and thus can replace a non constant time lattice reduction subroutine in SQIsign.

In this work, we study cryptosystems that can be executed securely without fully trusting all machines, but only trusting the user's brain. This paper focuses on signature scheme. We first introduce a new concept called ``server-aided in-brain signature,'' which is a cryptographic protocol between a human brain and multiple servers to sign a message securely even if the user's device and servers are not completely trusted. Second, we propose a concrete scheme that is secure against mobile hackers in servers and malware infecting user's devices.

Functional Encryption is a powerful cryptographic primitive that allows for fine-grained access control over encrypted data. In the multi-user setting, especially Multi-Client and Multi-Input, a plethora of works have been proposed to study on concrete function classes, improving security, and more. However, the CCA-security for such schemes is still an open problem, where the only known works are on Public-Key Single-Client FE (Benhamouda, Bourse, and Lipmaa, PKC'17). This work provides the first generic construction of CCA-secure Multi-Client FE for Inner Products, and Multi-Input FE for Inner Products, with instantiations from $\mathsf{SXDH}$ and $\mathsf{DLIN}$ for the former, and $\mathsf{DDH}$ or $\mathsf{DCR}$ for the latter. Surprisingly, in the case of secret key MIFE we attain the same efficiency as in the public key single-client setting. In the MCFE setting, a toolkit of CCA-bootstrapping techniques is developed to achieve CCA-security in its $\mathit{secret~key}$ setting.

Secret handshakes, introduced by Balfanz et al. [3], allow users associated with various groups to determine if they share a common affiliation. These protocols ensure crucial properties such as fairness (all participants learn the result simultaneously), affiliation privacy (failed handshakes reveal no affiliation information), and result-hiding (even participants within a shared group cannot infer outcomes of unrelated handshakes). Over time, various secret-handshake schemes have been proposed, with a notable advancement being the modular framework by Tsudik and Xu. Their approach integrates three key components: group signature schemes, centralized secure channels for each group, and decentralized group key-agreement protocols. Building upon this modularity, we propose significant updates. By addressing hidden complexities and revising the security model, we enhance both the efficiency and the privacy guarantees of the protocol. Specifically, we achieve the novel property of Self distinction—the ability to distinguish between two users in a session without revealing their identities—by replacing the group signature primitive with a new construct, the List MAC. This primitive is inherently untraceable, necessitating adjustments to the original syntax to support stronger privacy guarantees. Consequently, we introduce the Traitor Catching paradigm, where the transcript of a handshake reveals only the identity of a traitor, preserving the anonymity of all other participants. To showcase the flexibility and robustness of our updated framework, we present two post-quantum instantiations (a hash-based one and another based on lattices). Our approach not only corrects prior limitations but also establishes a new benchmark for privacy and security in secret handshakes.