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Fine-Grained Verifier NIZK and Its Applications
Get PDFIn this paper, we propose a new type of non-interactive zero-knowledge (NIZK), called Fine-grained Verifier NIZK (FV-NIZK), which provides more flexible and more fine-grained verifiability of proofs than standard NIZK that supports public verifiability and designated-verifier NIZK (DV-NIZK) that supports private verifiability. FV-NIZK has two statistically (or computationally) equivalent verification approaches:
--- a master verification using the master secret key ;
--- a fine-grained verification using a derived secret key , which is derived from w.r.t. (which may stand for user identity, email address, vector, etc.).
We require unbounded simulation soundness (USS) of FV-NIZK to hold, even if an adversary obtains derived secret keys with of its choices, and define proof pseudorandomness which stipulates the pseudorandomness of proofs for adversaries that are not given any secret key.
We present two instantiations of FV-NIZK for linear subspace languages, based on the matrix decisional Diffie-Hellman (MDDH) assumption.
One of the FV-NIZK instantiations is pairing-free and achieves almost tight USS and proof pseudorandomness. We also adapt the two instantiations to support unbounded fine-grained secret key delegations.
We illustrate the usefulness of FV-NIZK by showing two applications and obtain the following pairing-free schemes:
--- the first almost tightly multi-challenge CCA (mCCA)-secure inner-product functional encryption (IPFE) scheme without pairings;
--- the first public-key encryption (PKE) scheme that reconciles the inherent contradictions between public verifiability and anonymity.
We formalize such PKE as Fine-grained Verifiable PKE (FV-PKE), which derives a special key from the decryption secret key, such that for those who obtain the derived key, they can check the validity of ciphertexts but the anonymity is lost from their views (CCA-security still holds for them), while for others who do not get the derived key, they cannot do the validity check but the anonymity holds for them.
Our FV-PKE scheme achieves almost tight mCCA-security for adversaries who obtain the derived keys, and achieves almost tight ciphertext pseudorandomness (thus anonymity) for others who do not get any derived key
ProofFrog: A Tool For Verifying Game-Hopping Proofs
Get PDFCryptographic proofs allow researchers to provide theoretical guarantees on the security that their constructions provide. A proof of security can completely eliminate a class of attacks by potential adversaries. Human fallibility, however, means that even a proof reviewed by experts may still hide flaws or outright errors. Proof assistants are software tools built for the purpose of formally verifying each step in a proof, and as such have the potential to prevent erroneous proofs from being published and insecure constructions from being implemented.
Unfortunately, existing tooling for verifying cryptographic proofs has found limited adoption in the cryptographic community, in part due to concerns with ease of use. We present ProofFrog: a new tool for verifying cryptographic game-hopping proofs. ProofFrog is designed with the average cryptographer in mind, using an imperative syntax similar to C for specifying games and a syntax for proofs that closely models pen-and-paper arguments. As opposed to other proof assistant tools which largely operate by manipulating logical formulae, ProofFrog manipulates abstract syntax trees (ASTs) into a canonical form to establish indistinguishable or equivalent behaviour for pairs of games in a user-provided sequence. We also detail the domain-specific language developed for use with the ProofFrog proof engine, the exact transformations it applies to canonicalize ASTs, and case studies of verified proofs. A tool like ProofFrog that prioritizes ease of use can lower the barrier of entry to using computer-verified proofs and aid in catching insecure constructions before they are made public
On the Soundness of Algebraic Attacks against Code-based Assumptions
Get PDFWe study recent algebraic attacks (Briaud-Øygarden EC\u2723) on the Regular Syndrome Decoding (RSD) problem and the assumptions underlying the correctness of their attacks\u27 complexity estimates. By relating these assumptions to interesting algebraic-combinatorial problems, we prove that they do not hold in full generality. However, we show that they are (asymptotically) true for most parameter sets, supporting the soundness of algebraic attacks on RSD. Further, we prove—without any heuristics or assumptions—that RSD can be broken in polynomial time whenever the number of error blocks times the square of the size of error blocks is larger than 2 times the square of the dimension of the code.
Additionally, we use our methodology to attack a variant of the Learning With Errors problem where each error term lies in a fixed set of constant size. We prove that this problem can be broken in polynomial time, given a sufficient number of samples. This result improves on the seminal work by Arora and Ge (ICALP\u2711), as the attack\u27s time complexity is independent of the LWE modulus
Deimos Cipher: A High-Entropy, Secure Encryption Algorithm with Strong Diffusion and Key Sensitivity
Get PDFDeimos Cipher is a symmetric encryption algorithm designed to achieve high entropy, strong diffusion, and computational efficiency. It integrates HKDF with BLAKE2b for key expansion, ensuring secure key derivation from user-supplied passwords. The encryption process employs XChaCha20, a high-speed stream cipher, to provide strong security and resistance against nonce reuse attacks. To guarantee data integrity and authentication, HMAC-SHA256 is used, preventing unauthorized modifications.
Security evaluations demonstrate that Deimos Cipher exhibits superior randomness, achieving 6.24 bits per byte entropy for short plaintexts and 7.9998 bits per byte for long plaintexts, surpassing industry standards like AES and ChaCha20. Avalanche Effect analysis confirms optimal diffusion, with 50.18% average bit change, ensuring high resistance to differential cryptanalysis. Additionally, key sensitivity tests reveal 50.54% ciphertext change for minimal key variations, making brute-force and key-recovery attacks impractical.
With its combination of a robust key expansion mechanism, stream cipher encryption, and cryptographic authentication, Deimos Cipher offers a secure and efficient encryption scheme suitable for secure messaging, cloud data protection, and high-security environments. This paper presents the algorithm’s design, security analysis, and benchmarking against established cryptographic standards
Provably Secure Approximate Computation Protocols from CKKS
Get PDFSecure multi-party computation (MPC) enables collaborative, privacy-preserving computation over private inputs. Advances in homomorphic encryption (HE), particularly the CKKS scheme, have made secure computation practical, making it well-suited for real-world applications involving approximate computations. However, the inherent approximation errors in CKKS present significant challenges in developing MPC protocols.
This paper investigates the problem of secure approximate MPC from CKKS. We first analyze CKKS-based protocols in two-party setting. When only one party holds a private input and the other party acts as an evaluator, a simple protocol with the noise smudging technique on the encryptor\u27s side achieves security in the standard manner. When both parties have private inputs, we demonstrate that the protocol incorporating independent errors from each party achieves a relaxed standard security notion, referred to as a liberal security. Nevertheless, such a protocol fails to satisfy the standard security definition. To address this limitation, we propose a novel protocol that employs a distributed sampling approach to generate smudging noise in a secure manner, which satisfies the standard security definition.
Finally, we extend the two-party protocols to the multi-party setting. Since the existing threshold CKKS-based MPC protocol only satisfies the liberal security, we present a novel multi-party protocol achieving the standard security by applying multi-party distributed sampling of a smudging error.
For all the proposed protocols, we formally define the functionalities and provide rigorous security analysis within the simulation-based security framework. To the best of our knowledge, this is the first work to explicitly define the functionality of CKKS-based approximate MPC and achieve formal security guarantees
Blockchain-based Secure D2D localisation with adaptive precision
Get PDFIn this paper we propose a secure best effort methodology for providing localisation information to devices in a heterogenous network where devices do not have access to GPS-like technology or heavy cryptographic infrastructure. Each device will compute its localisation with the highest possible accuracy based solely on the data provided by its neighboring anchors. The security of the localisation is guarantied by registering the localisation information on a distributed ledger via smart contracts. We prove the security of our solution under the adaptive chosen message attacks model. We furthermore evaluate the effectiveness of our solution by measuring the average register location time, failed requests, and total execution time using as DLT case study Hyperledger Besu with QBFT consensus
Split Prover Zero-Knowledge SNARKs
Get PDFWe initiate the study of {\em split prover zkSNARKs}, which allow Alice to offload part of the zkSNARK computation to her assistant, Bob. In scenarios like online transactions (e.g., zCash), a significant portion of the witness (e.g., membership proofs of input coins) is often available to the prover (Alice) before the transaction begins. This setup offers an opportunity to Alice to initiate the proof computation early, even before the entire witness is available. The remaining computation can then be delegated to Bob, who can complete it once the final witness (e.g., the transaction amount) is known.
To prevent Bob from generating proofs independently (e.g., initiating unauthorized transactions), it is essential that the data provided to him for the second phase of computation does not reveal the witness used in the first phase. Additionally, the verifier of the zkSNARK should be unable to determine whether the proof was generated solely by Alice or through this two-step process. To achieve this efficiently, we require this two-phase proof generation to only use cryptography in a black-box manner.
We propose a split prover zkSNARK based on the Groth16 zkSNARKs [Groth, EUROCRYPT 2016], meeting all these requirements. Our solution is also \emph{asymptotically tight}, meaning it achieves the optimal second phase proof generation time for Groth16. Importantly, our split prover zkSNARK preserves the verification algorithm of the original Groth16 zkSNARK, enabling seamless integration into existing deployments of Groth16
Simple Public Key Anamorphic Encryption and Signature using Multi-Message Extensions
Get PDFAnamorphic encryption (AE) considers secure communication in the presence of a powerful surveillant (typically called a ``dictator\u27\u27) who only allows certain cryptographic primitives and knows all the secret keys in a system. The basic idea is that there is a second (anamorphic) mode of encryption that allows for transmitting an anamorphic message using a double key to a receiver who can decrypt this message using the same double key. From the point of view of the dictator, the encryption keys as well as the ciphertexts in the regular and anamorphic modes are indistinguishable. The most recent works in this field consider public key anamorphic encryption (PKAE), i.e., the sender of an anamorphic message requires an encryption double key (or no key at all), and the receiver requires an associated decryption double key. Known constructions, however, either work only for schemes that are mostly of theoretical interest or come with conceptual limitations, assuming additional unnecessary properties (e.g., randomness recoverability and CCA security).
In this paper, we ask whether we can design PKAE schemes without such limitations and be closer to practically used PKE schemes. In fact, such schemes are more likely to be allowed by a cognizant dictator. Moreover, we initiate the study of identity-based anamorphic encryption (IBAE), as the IBE setting seems to be a natural choice for a dictator. For both PKAE and IBAE, we show how well-known IND-CPA and IND-CCA secure primitives can be extended by an anamorphic encryption channel. In contrast to previous work, we additionally consider CCA (rather than just CPA) security notions for the anamorphic channel and also build upon CPA (rather than only CCA) secure PKE.
Finally, we ask whether it is possible to port the recent concept of anamorphic signatures, which considers constructing symmetric anamorphic channels in case only signature schemes are allowed by the dictator, to the asymmetric setting, which we denote by public-key anamorphic signatures (PKAS). Moreover, we consider IND-CCA security for the anamorphic channel of our PKAS
Polynomial Secret Sharing Schemes and Algebraic Matroids
Get PDFPolynomial secret sharing schemes generalize the linear ones by adding more expressivity and giving room for efficiency improvements. In these schemes, the secret is an element of a finite field, and the shares are obtained by evaluating polynomials on the secret and some random field elements, i.e., for every party there is a set of polynomials that computes the share of the party. Notably, for general access structures, the best known polynomial schemes have better share size than the best known linear ones. This work investigates the properties of the polynomials and the fields that allow these efficiency gains and aims to characterize the access structures that benefit from them.
We focus first on ideal schemes, which are optimal in the sense that the size of each share is the size of the secret. We prove that, under some restrictions, if the degrees of the sharing polynomials are not too big compared to the size of the field, then its access structure is a port of an algebraic matroid. This result establishes a new connection between ideal schemes and matroids, extending the known connection between ideal linear schemes and linearly representable matroids.
For general polynomial schemes, we extend these results and analyze their privacy and correctness. Additionally, we show that given a set of polynomials over a field of large characteristic, one can construct linear schemes that realize the access structure determined by these polynomials; as a consequence, polynomial secret sharing schemes over these fields are not stronger than linear schemes.
While there exist ports of algebraic matroids that do not admit ideal schemes, we demonstrate that they always admit schemes with statistical security and information ratio tending to one. This is achieved by considering schemes where the sharings are points in algebraic varieties
Lattice-Based Updatable Public-Key Encryption for Group Messaging
Get PDFUpdatable Public-Key Encryption (UPKE) augments the security of PKE with Forward Secrecy properties. While requiring more coordination between parties, UPKE enables much more efficient constructions than full-fledged Forward-Secret PKE. Alwen, Fuchsbauer and Mularczyk (AFM, Eurocrypt’24) presented the strongest security notion to date. It is the first to meet the needs of UPKE’s most important applications: Secure Group Messaging and Continuous Group Key Agreement. The authors provide a very efficient construction meeting their notion with classic security based on the Computational Diffie-Hellman (CDH) assumption in the Random Oracle Model (ROM).
In this work we present the first post-quantum secure UPKE construction meeting (a slight relaxation of) the AFM security notion. Based on the Module LWE assumption, our construction is practically efficient. Moreover, public key sizes are about and ciphertext sizes around of those of the state-of-the-art lattice-based UPKE scheme in the ROM by Abou Haidar, Passelègue and Stehlé – despite only being shown to satisfy a significantly weaker security notion. As the AFM proofs relies on random self-reducibility of CDH, which has no analogue for lattices, we develop a new proof technique for strong UPKE, identifying the core properties required from the underlying (lattice-based) encryption scheme