Related papers: Worst case QC-MDPC decoder for McEliece cryptosyst…

Quantum computers can break the RSA and El Gamal public-key cryptosystems, since they can factor integers and extract discrete logarithms. If we believe that quantum computers will someday become a reality, we would like to have…

This paper propose a decoder architecture for low-density parity-check convolutional code (LDPCCC). Specifically, the LDPCCC is derived from a quasi-cyclic (QC) LDPC block code. By making use of the quasi-cyclic structure, the proposed…

Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…

Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes offer excellent decoding performance and can be elegantly decoded with a Windowed Decoder (WD). We determine an efficient WD configuration with low control overhead. For fair…

Bit-Flipping (BF) decoders are a family of decoders widely employed in post-quantum cryptographic schemes based on Quasi-Cyclic Moderate-Density Parity-Check (QC-MDPC) codes, such as BIKE. BF decoders suffer from trapping sets,…

LDPC (Low Density Parity Check) codes are among the most powerful and widely adopted modern error correcting codes. The iterative decoding algorithms required for these codes involve high computational complexity and high processing…

This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying…

Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel…

In order to protect intellectual property against untrusted foundry, many logic-locking schemes have been developed. The main idea of logic locking is to insert a key-controlled block into a circuit to make the circuit function incorrectly…

In this paper, we study the behavior of the true dimension of the subfield subcodes of Hermitian codes. Our motivation is to use these classes of linear codes to improve the parameters of the McEliece cryptosystem, such that key size and…

Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…

Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…

In this work, we analyze efficient window shift schemes for windowed decoding of spatially coupled low-density parity-check (SC-LDPC) codes, which is known to yield close-tooptimal decoding results when compared to full belief propagation…

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…

Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to…

Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires…

This paper considers the performance of $(j,k)$-regular low-density parity-check (LDPC) codes with message-passing (MP) decoding algorithms in the high-rate regime. In particular, we derive the high-rate scaling law for MP decoding of LDPC…

This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring…

We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an Error…

Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…