Classical Cryptographic Protocols in a Quantum World

Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: what classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions (for example, it suffices that the learning with errors problem be hard for quantum polynomial time). Our result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world.Comment: Full version of an old paper in Crypto'11. Invited to IJQI. This is authors' copy with different formattin

Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round

From the minimal assumption of post-quantum semi-honest oblivious transfers, we build the first $\epsilon$-simulatable two-party computation (2PC) against quantum polynomial-time (QPT) adversaries that is both constant-round and black-box (for both the construction and security reduction). A recent work by Chia, Chung, Liu, and Yamakawa (FOCS\u2721) shows that post-quantum 2PC with standard simulation-based security is impossible in constant rounds, unless either $NP \subseteq BQP$ or relying on non-black-box simulation. The $\epsilon$-simulatability we target is a relaxation of the standard simulation-based security that allows for an arbitrarily small noticeable simulation error $\epsilon$. Moreover, when quantum communication is allowed, we can further weaken the assumption to post-quantum secure one-way functions (PQ-OWFs), while maintaining the constant-round and black-box property. Our techniques also yield the following set of constant-round and black-box two-party protocols secure against QPT adversaries, only assuming black-box access to PQ-OWFs: - extractable commitments for which the extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge commit-and-prove whose commit stage is extractable with $\epsilon$-simulation; - $\epsilon$-simulatable coin-flipping; - $\epsilon$-zero-knowledge arguments of knowledge for $NP$ for which the knowledge extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge arguments for $QMA$. At the heart of the above results is a black-box extraction lemma showing how to efficiently extract secrets from QPT adversaries while disturbing their quantum state in a controllable manner, i.e., achieving $\epsilon$-simulatability of the post-extraction state of the adversary

Composability in quantum cryptography

In this article, we review several aspects of composability in the context of quantum cryptography. The first part is devoted to key distribution. We discuss the security criteria that a quantum key distribution protocol must fulfill to allow its safe use within a larger security application (e.g., for secure message transmission). To illustrate the practical use of composability, we show how to generate a continuous key stream by sequentially composing rounds of a quantum key distribution protocol. In a second part, we take a more general point of view, which is necessary for the study of cryptographic situations involving, for example, mutually distrustful parties. We explain the universal composability framework and state the composition theorem which guarantees that secure protocols can securely be composed to larger applicationsComment: 18 pages, 2 figure

Classical cryptographic protocols in a quantum world

Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: what classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions (for example, it suffices that the learning with errors problem be hard for quantum polynomial time). Our result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world

Complete Insecurity of Quantum Protocols for Classical Two-Party Computation

A fundamental task in modern cryptography is the joint computation of a function which has two inputs, one from Alice and one from Bob, such that neither of the two can learn more about the other's input than what is implied by the value of the function. In this Letter, we show that any quantum protocol for the computation of a classical deterministic function that outputs the result to both parties (two-sided computation) and that is secure against a cheating Bob can be completely broken by a cheating Alice. Whereas it is known that quantum protocols for this task cannot be completely secure, our result implies that security for one party implies complete insecurity for the other. Our findings stand in stark contrast to recent protocols for weak coin tossing, and highlight the limits of cryptography within quantum mechanics. We remark that our conclusions remain valid, even if security is only required to be approximate and if the function that is computed for Bob is different from that of Alice.Comment: v2: 6 pages, 1 figure, text identical to PRL-version (but reasonably formatted

Very-efficient simulatable flipping of many coins into a well

Secure two-party parallel coin-flipping is a cryptographic functionality that allows two mutually distrustful parties to agree on a common random bit-string of a certain target length. In coin-flipping into-a-well, one party learns the bit-string and then decides whether to abort or to allow the other party to learn it. It is well known that this functionality can be securely achieved in the ideal/real simulation paradigm, using commitment schemes that are simultaneously extractable (X) and equivocable (Q). This paper presents two new constant-round simulatable coin-flipping protocols, based explicitly on one or a few X-commitments of short seeds and a Q-commitment of a short hash, independently of the large target length. A pseudo-random generator and a collision-resistant hash function are used to combine the separate X and Q properties (associated with short bit-strings) into a unified X&Q property amplified to the target length, thus amortizing the cost of the base commitments. In this way, the new protocols are significantly more efficient than an obvious batching or extension of coin-flippings designed (in the same security setting) for short bit-strings and based on inefficient X&Q commitments. The first protocol, simulatable with rewinding, deviates from the traditional coin-flipping template in order to improve simulatability in case of unknown adversarial probabilities of abort, without having to use a X&Q commitment scheme. The second protocol, one-pass simulatable, derives from a new construction of a universally composable X&Q commitment scheme for large bit-strings, achieving communication-rate asymptotically close to 1. Besides the base X and Q commitments, the new commitment scheme only requires corresponding collision-resistant hashing, pseudo-random generation and application of a threshold erasure code. Alternative constructions found in recent work with comparable communication complexity require explicit use of oblivious transfer and use different encodings of the committed value

Post-quantum Zero Knowledge in Constant Rounds

We construct a constant-round zero-knowledge classical argument for NP secure against quantum attacks. We assume the existence of Quantum Fully-Homomorphic Encryption and other standard primitives, known based on the Learning with Errors Assumption for quantum algorithms. As a corollary, we also obtain a constant-round zero-knowledge quantum argument for QMA. At the heart of our protocol is a new no-cloning non-black-box simulation technique

Deniable Cryptosystems: Simpler Constructions and Achieving Leakage Resilience

Deniable encryption (Canetti et al. CRYPTO ’97) is an intriguing primitive, which provides security guarantee against coercion by allowing a sender to convincingly open the ciphertext into a fake message. Despite the notable result by Sahai and Waters STOC ’14 and other efforts in functionality extension, all the deniable public key encryption (DPKE) schemes suffer from intolerable overhead due to the heavy building blocks, e.g., translucent sets or indistinguishability obfuscation. Besides, none of them considers the possible damage from leakage in the real world, obstructing these protocols from practical use. To fill the gap, in this work we first present a simple and generic approach of sender-DPKE from ciphertext-simulatable encryption, which can be instantiated with nearly all the common PKE schemes. The core of this design is a newly-designed framework for flipping a bit-string that offers inverse polynomial distinguishability. Then we theoretically expound and experimentally show how classic side-channel attacks (timing or simple power attacks), can help the coercer to break deniability, along with feasible countermeasures

Post-Quantum Multi-Party Computation

We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round protocol, but our main result is a construction of constant-round post-quantum multi-party computation. We assume mildly super-polynomial quantum hardness of learning with errors (LWE), and polynomial quantum hardness of an LWE-based circular security assumption. Along the way, we develop the following cryptographic primitives that may be of independent interest: - A spooky encryption scheme for relations computable by quantum circuits, from the quantum hardness of an LWE-based circular security assumption. This yields the first quantum multi-key fully-homomorphic encryption scheme with classical keys. - Constant-round zero-knowledge secure against multiple parallel quantum verifiers from spooky encryption for relations computable by quantum circuits. To enable this, we develop a new straight-line non-black-box simulation technique against parallel verifiers that does not clone the adversary\u27s state. This forms the heart of our technical contribution and may also be relevant to the classical setting. - A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE