Giulio Malavolta

Damiano Abram, Giulio Malavolta, Lawrence Roy

We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors $\mathbf{x} \otimes \mathbf{y}$, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of $\mathbf{x}$. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a host of cryptographic primitives, all with security reducible to LWE, such as: * Adaptively secure laconic function evaluation for depth-$D$ functions $f:\{0, 1\}^m\rightarrow\{0, 1\}^\ell$ with communication $m+\ell+D\cdot \mathrm{poly}(λ)$. * A trapdoor hash function for all functions. * An (optimally) succinct homomorphic secret sharing for all functions. * A rate-$1/2$ laconic oblivious transfer for batch messages, which is best possible. In particular, we obtain the first laconic function evaluation scheme that is adaptively secure from the standard LWE assumption, improving upon Quach, Wee, and Wichs (FOCS 2018). As a key technical ingredient, we introduce a new notion of \emph{adaptive lattice encodings}, which may be of independent interest.

Rohit Chatterjee, Kai-Min Chung, Xiao Liang et al.

This work revisits the security of classical signatures and ring signatures in a quantum world. For (ordinary) signatures, we focus on the arguably preferable security notion of blind-unforgeability recently proposed by Alagic et al. (Eurocrypt'20). We present two short signature schemes achieving this notion: one is in the quantum random oracle model, assuming quantum hardness of SIS; and the other is in the plain model, assuming quantum hardness of LWE with super-polynomial modulus. Prior to this work, the only known blind-unforgeable schemes are Lamport's one-time signature and the Winternitz one-time signature, and both of them are in the quantum random oracle model. For ring signatures, the recent work by Chatterjee et al. (Crypto'21) proposes a definition trying to capture adversaries with quantum access to the signer. However, it is unclear if their definition, when restricted to the classical world, is as strong as the standard security notion for ring signatures. They also present a construction that only partially achieves (even) this seeming weak definition, in the sense that the adversary can only conduct superposition attacks over the messages, but not the rings. We propose a new definition that does not suffer from the above issue. Our definition is an analog to the blind-unforgeability in the ring signature setting. Moreover, assuming the quantum hardness of LWE, we construct a compiler converting any blind-unforgeable (ordinary) signatures to a ring signature satisfying our definition.

James Bartusek, Giulio Malavolta

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.

Amit Agarwal, James Bartusek, Vipul Goyal et al.

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: 1. 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. 2. 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's state. This forms the heart of our technical contribution and may also be relevant to the classical setting. 3. A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE.

Giulio Malavolta, Pedro Moreno-Sanchez, Aniket Kate et al.

Permissionless blockchains protocols such as Bitcoin are inherently limited in transaction throughput and latency. Current efforts to address this key issue focus on off-chain payment channels that can be combined in a Payment-Channel Network (PCN) to enable an unlimited number of payments without requiring to access the blockchain other than to register the initial and final capacity of each channel. While this approach paves the way for low latency and high throughput of payments, its deployment in practice raises several privacy concerns as well as technical challenges related to the inherently concurrent nature of payments, such as race conditions and deadlocks, that have been understudied so far. In this work, we lay the foundations for privacy and concurrency in PCNs, presenting a formal definition in the Universal Composability framework as well as practical and provably secure solutions. In particular, we present Fulgor and Rayo. Fulgor is the first payment protocol for PCNs that provides provable privacy guarantees for PCNs and is fully compatible with the Bitcoin scripting system. However, Fulgor is a blocking protocol and therefore prone to deadlocks of concurrent payments as in currently available PCNs. Instead, Rayo is the first protocol for PCNs that enforces non-blocking progress (i.e., at least one of the concurrent payments terminates). We show through a new impossibility result that non-blocking progress necessarily comes at the cost of weaker privacy. At the core of Fulgor and Rayo is Multi-Hop HTLC, a new smart contract, compatible with the Bitcoin scripting system, that provides conditional payments while reducing running time and communication overhead with respect to previous approaches.