Indistinguishability Obfuscation of Null Quantum Circuits and Applications

We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of "dual-mode" classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP

Publicly-Verifiable Deletion via Target-Collapsing Functions

We build quantum cryptosystems that support publicly-verifiable deletion from standard cryptographic assumptions. We introduce target-collapsing as a weakening of collapsing for hash functions, analogous to how second preimage resistance weakens collision resistance; that is, target-collapsing requires indistinguishability between superpositions and mixtures of preimages of an honestly sampled image. We show that target-collapsing hashes enable publicly-verifiable deletion (PVD), proving conjectures from [Poremba, ITCS'23] and demonstrating that the Dual-Regev encryption (and corresponding fully homomorphic encryption) schemes support PVD under the LWE assumption. We further build on this framework to obtain a variety of primitives supporting publicly-verifiable deletion from weak cryptographic assumptions, including: - Commitments with PVD assuming the existence of injective one-way functions, or more generally, almost-regular one-way functions. Along the way, we demonstrate that (variants of) target-collapsing hashes can be built from almost-regular one-way functions. - Public-key encryption with PVD assuming trapdoored variants of injective (or almost-regular) one-way functions. We also demonstrate that the encryption scheme of [Hhan, Morimae, and Yamakawa, Eurocrypt'23] based on pseudorandom group actions has PVD. - $X$ with PVD for $X \in \{$attribute-based encryption, quantum fully-homomorphic encryption, witness encryption, time-revocable encryption$\}$, assuming $X$ and trapdoored variants of injective (or almost-regular) one-way functions.Comment: 52 page

Weakening Assumptions for Publicly-Verifiable Deletion

We develop a simple compiler that generically adds publicly-verifiable deletion to a variety of cryptosystems. Our compiler only makes use of one-way functions (or one-way state generators, if we allow the public verification key to be quantum). Previously, similar compilers either relied on the use of indistinguishability obfuscation (Bartusek et. al., ePrint:2023/265) or almost-regular one-way functions (Bartusek, Khurana and Poremba, arXiv:2303.08676).Comment: 13 pages. arXiv admin note: text overlap with arXiv:2303.0867

Delegatable homomorphic encryption with applications to secure outsourcing of computation

In this work we propose a new cryptographic primitive called Delegatable Homomorphic Encryption (DHE). This allows a Trusted Authority to control/delegate the capability to evaluate circuits over encrypted data to untrusted workers/evaluators by issuing tokens. This primitive can be both seen as a public-key counterpart to Verifiable Computation, where input generation and output verification are performed by different entities, or as a generalisation of Fully Homomorphic Encryption enabling control over computations on encrypted data. Our primitive comes with a series of extra features as follows: 1) there is a one-time setup procedure for all circuits; 2) senders do not need to be aware of the functions which will be evaluated on the encrypted data, nor do they need to register keys; 3) tokens are independent of senders and receiver; and 4) receivers are able to verify the correctness of computation given short auxiliary information on the input data and the function, independently of the complexity of the computed circuit. We give a modular construction of such a DHE scheme from three components: Fully Homomorphic Encryption (FHE), Functional Encryption (FE), and a (customised) MAC. As a stepping stone, we first define Verifiable Functional Encryption (VFE), and then show how one can build a secure DHE scheme from a VFE and an FHE scheme. We also show how to build the required VFE from a standard FE together with a MAC scheme. All our results hold in the standard model.Finally, we show how one can build a verifiable computation (VC) scheme generically from a DHE. As a corollary, we get the first VC scheme which remains verifiable even if the attacker can observe verification result

Constructing CCA-secure predicate encapsulation schemes from CPA-secure schemes and universal one-way hash functions

We present a new transformation of chosen-plaintext secure predicate encryption schemes with public index into chosen-ciphertext secure schemes. Our construction requires only a universal one-way hash function and is selectively secure in the standard model. The transformation is not generic but can be applied to various existing schemes constructed from bilinear groups. Using common structural properties of these schemes we provide an efficient and simple transformation without overhead in form of one-time signatures or message authentication codes as required in the known generic transformations

Delegated Time-Lock Puzzle

Time-Lock Puzzles (TLPs) are cryptographic protocols that enable a client to lock a message in such a way that a server can only unlock it after a specific time period. However, existing TLPs have certain limitations: (i) they assume that both the client and server always possess sufficient computational resources and (ii) they solely focus on the lower time bound for finding a solution, disregarding the upper bound that guarantees a regular server can find a solution within a certain time frame. Additionally, existing TLPs designed to handle multiple puzzles either (a) entail high verification costs or (b) lack generality, requiring identical time intervals between consecutive solutions. To address these limitations, this paper introduces, for the first time, the concept of a "Delegated Time-Lock Puzzle" and presents a protocol called "Efficient Delegated Time-Lock Puzzle" (ED-TLP) that realises this concept. ED-TLP allows the client and server to delegate their resource-demanding tasks to third-party helpers. It facilitates real-time verification of solution correctness and efficiently handles multiple puzzles with varying time intervals. ED-TLP ensures the delivery of solutions within predefined time limits by incorporating both an upper bound and a fair payment algorithm. We have implemented ED-TLP and conducted a comprehensive analysis of its overheads, demonstrating the efficiency of the construction

YOLO YOSO: Fast and Simple Encryption and Secret Sharing in the YOSO Model

Achieving adaptive (or proactive) security in cryptographic protocols is notoriously difficult due to the adversary\u27s power to dynamically corrupt parties as the execution progresses. Inspired by the work of Benhamouda et al. in TCC 2020, Gentry et al. in CRYPTO 2021 introduced the YOSO (You Only Speak Once) model for constructing adaptively (or proactively) secure protocols in massively distributed settings (e.g. blockchains). In this model, instead of having all parties execute an entire protocol, smaller anonymous committees are randomly chosen to execute each individual round of the protocol. After playing their role, parties encrypt protocol messages towards the the next anonymous committee and erase their internal state before publishing their ciphertexts. However, a big challenge remains in realizing YOSO protocols: efficiently encrypting messages towards anonymous parties selected at random without learning their identities, while proving the encrypted messages are valid w.r.t. the protocol. In particular, the protocols of Benhamouda et al. and of Gentry et al. require showing ciphertexts contain valid shares of secret states. We propose concretely efficient methods for encrypting a protocol\u27s secret state towards a random anonymous committee. We start by proposing a very simple and efficient scheme for encrypting messages towards randomly and anonymously selected parties. We then show constructions of publicly verifiable secret (re-)sharing (PVSS) schemes with concretely efficient proofs of (re-)share validity that can be generically instantiated from encryption schemes with certain linear homomorphic properties. Finally, we show that our PVSS schemes can be efficiently realized from our encyption scheme

On Improving Communication Complexity in Cryptography

Cryptography grew to be much more than "the study of secret writing". Modern cryptography is concerned with establishing properties such as privacy, integrity and authenticity in protocols for secure communication and computation. This comes at a price: Cryptographic tools usually introduce an overhead, both in terms of communication complexity (that is, number and size of messages transmitted) and computational efficiency (that is, time and memory required). As in many settings communication between the parties involved is the bottleneck, this thesis is concerned with improving communication complexity in cryptographic protocols. One direction towards this goal is scalable cryptography: In many cryptographic schemes currently deployed, the security degrades linearly with the number of instances (e.g. encrypted messages) in the system. As this number can be huge in contexts like cloud computing, the parameters of the scheme have to be chosen considerably larger - and in particular depending on the expected number of instances in the system - to maintain security guarantees. We advance the state-of-the-art regarding scalable cryptography by constructing schemes where the security guarantees are independent of the number of instances. This allows to choose smaller parameters, even when the expected number of instances is immense. - We construct the first scalable encryption scheme with security against active adversaries which has both compact public keys and ciphertexts. In particular, we significantly reduce the size of the public key to only about 3% of the key-size of the previously most efficient scalable encryption scheme. (Gay,Hofheinz, and Kohl, CRYPTO, 2017) - We present a scalable structure-preserving signature scheme which improves both in terms of public-key and signature size compared to the previously best construction to about 40% and 56% of the sizes, respectively. (Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018) Another important area of cryptography is secure multi-party computation, where the goal is to jointly evaluate some function while keeping each party’s input private. In traditional approaches towards secure multi-party computation either the communication complexity scales linearly in the size of the function, or the computational efficiency is poor. To overcome this issue, Boyle, Gilboa, and Ishai (CRYPTO, 2016) introduced the notion of homomorphic secret sharing. Here, inputs are shared between parties such that each party does not learn anything about the input, and such that the parties can locally evaluate functions on the shares. Homomorphic secret sharing implies secure computation where the communication complexity only depends on the size of the inputs, which is typically much smaller than the size of the function. A different approach towards efficient secure computation is to split the protocol into an input-independent preprocessing phase, where long correlated strings are generated, and a very efficient online phase. One example for a useful correlation are authenticated Beaver triples, which allow to perform efficient multiplications in the online phase such that privacy of the inputs is preserved and parties deviating the protocol can be detected. The currently most efficient protocols implementing the preprocessing phase require communication linear in the number of triples to be generated. This results typically in high communication costs, as the online phase requires at least one authenticated Beaver triple per multiplication. We advance the state-of-the art regarding efficient protocols for secure computation with low communication complexity as follows. - We construct the first homomorphic secret sharing scheme for computing arbitrary functions in NC 1 (that is, functions that are computably by circuits with logarithmic depth) which supports message spaces of arbitrary size, has only negligible correctness error, and does not require expensive multiplication on ciphertexts. (Boyle, Kohl, and Scholl, EUROCRYPT, 2019) - We introduce the notion of a pseudorandom correlation generator for general correlations. Pseudorandom correlation generators allow to locally extend short correlated seeds into long pseudorandom correlated strings. We show that pseudorandom correlation generators can replace the preprocessing phase in many protocols, leading to a preprocessing phase with sublinear communication complexity. We show connections to homomorphic secret sharing schemes and give the first instantiation of pseudorandom correlation generators for authenticated Beaver triples at reasonable computational efficiency. (Boyle, Couteau, Gilboa, Ishai, Kohl, and Scholl, CRYPTO, 2019