Related papers: A proof of P != NP (New symmetric encryption algor…
We prove that any algorithm for learning parities requires either a memory of quadratic size or an exponential number of samples. This proves a recent conjecture of Steinhardt, Valiant and Wager and shows that for some learning problems a…
We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
The no-cloning principle of quantum mechanics enables us to achieve amazing unclonable cryptographic primitives, which is impossible in classical cryptography. However, the security definitions for unclonable cryptography are tricky.…
In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^\star$, and the goal is to find a certificate of size $\le \text{poly}(k)$ for $f$'s value at $x^\star$. This problem is in…
In modern cryptography, block encryption is a fundamental cryptographic primitive. However, it is impossible for block encryption to achieve the same security as one-time pad. Quantum mechanics has changed the modern cryptography, and lots…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
Generating secure random numbers is a central problem in cryptography that needs a reliable source of enough computing entropy. Without enough entropy available - meaning no good source of secure random numbers - a device is susceptible to…
We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
There is a large amount of work dedicated to the formal verification of security protocols. In this paper, we revisit and extend the NP-complete decision procedure for a bounded number of sessions. We use a, now standard, deducibility…
The problem of Syndrome Decoding was proven to be NP-complete in 1978 and, since then, quite a few cryptographic applications have had their security rely on the (provable) difficulty of solving some instances of it. However, in most cases,…
In this paper, we study a generalization of the classical minimum cut prob- lem, called Connectivity Preserving Minimum Cut (CPMC) problem, which seeks a minimum cut to separate a pair (or pairs) of source and destination nodes and…
We introduce an explicit construction for a key distribution protocol in the Quantum Computational Timelock (QCT) security model, where one assumes that computationally secure encryption may only be broken after a time much longer than the…
The Plug-and-Play (PnP) algorithm is popular for inverse image problem-solving. However, this algorithm lacks theoretical analysis of its convergence with more advanced plug-in denoisers. We demonstrate that discrete PnP iteration can be…
According to recent studies, the vulnerability of state-of-the-art Neural Networks to adversarial input samples has increased drastically. A neural network is an intermediate path or technique by which a computer learns to perform tasks…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…