Related papers: Generic Decoding of Restricted Errors
The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable proofs of soundness/completeness, can be used both to identify…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
This paper considers a new secure gradient coding problem with uncoded groupwise keys, formalized as a (K, N, N_r, M, S) secure gradient coding model, where a user aims to compute the sum of the gradients from K datasets with the assistance…
Despite the linearity of its encoding, compressed sensing may be used to provide a limited form of data protection when random encoding matrices are used to produce sets of low-dimensional measurements (ciphertexts). In this paper we…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
In a recent paper, Kim and Kopparty (Theory of Computing, 2017) gave a deterministic algorithm for the unique decoding problem for polynomials of bounded total degree over a general grid. We show that their algorithm can be adapted to solve…
The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple…
A novel decoding algorithm is developed for general quantum convolutional codes. Exploiting useful ideas from classical coding theory, the new decoder introduces two innovations that drastically reduce the decoding complexity compared to…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We construct a public-key encryption scheme from the hardness of the (planted) MinRank problem over uniformly random instances. This corresponds to the hardness of decoding random linear rank-metric codes. Existing constructions of…
Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…
In this work we consider a generalization of the well-studied problem of coding for ``stuck-at'' errors, which we refer to as ``strong stuck-at'' codes. In the traditional framework of stuck-at codes, the task involves encoding a message…