Related papers: Generic Decoding of Restricted Errors
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
Decoy-state protocols provide a way to defeat photon-number splitting attacks in quantum cryptography implemented with weak coherent pulses. We point out that previous security analyses of such protocols relied on assumptions about…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
Noise causes severe difficulties in implementing quantum computing and quantum cryptography. Several schemes have been suggested to reduce this problem, mainly focusing on quantum computation. Motivated by quantum cryptography, we suggest a…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular…
This paper studies the security of a recently-proposed chaos-based image encryption scheme, and points out the following problems: 1) there exist a number of invalid keys and weak keys, and some keys are partially equivalent for…
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…
Developing secure distributed systems is difficult, and even harder when advanced cryptography must be used to achieve security goals. Following prior work, we advocate using secure program partitioning to synthesize cryptographic…
Providing closed-form estimates of the decoding failure rate of iterative decoders for low- and moderate-density binary parity-check codes has attracted significant interest in the research community. Recently, interest in this topic has…
Fracton topological phases have a large number of materialized symmetries that enforce a rigid structure on their excitations. Remarkably, we find that the symmetries of a quantum error-correcting code based on a fracton phase enable us to…
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate…
A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them…
We consider the problem of slotted asynchronous coded communication, where in each time frame (slot), the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide…
Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…