751 research outputs found
A Post-Quantum Digital Signature Scheme from QC-LDPC Codes
We propose a novel post-quantum code-based digital signature algorithm whose security is based on the difficulty of decoding Quasi-Cyclic codes in systematic form, and whose trapdoor relies on the knowledge of a hidden Quasi-Cyclic Low-Density-Parity-Check (QC-LDPC) code. The utilization of Quasi-Cyclic (QC) codes allows us to balance between security and key size, while the LDPC property lighten the encoding complexity, thus the signing algorithm complexity, significantly
Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel
In this paper, we show that Quasi-Cyclic LDPC codes can efficiently
accommodate the hybrid iterative/ML decoding over the binary erasure channel.
We demonstrate that the quasi-cyclic structure of the parity-check matrix can
be advantageously used in order to significantly reduce the complexity of the
ML decoding. This is achieved by a simple row/column permutation that
transforms a QC matrix into a pseudo-band form. Based on this approach, we
propose a class of QC-LDPC codes with almost ideal error correction performance
under the ML decoding, while the required number of row/symbol operations
scales as , where is the number of source symbols.Comment: 6 pages, ISITA1
Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes
Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are
promising post-quantum candidates to replace quantum vulnerable classical
alternatives. However, a new type of attacks based on Bob's reactions have
recently been introduced and appear to significantly reduce the length of the
life of any keypair used in these systems. In this paper we estimate the
complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based
variants of the McEliece cryptosystem. We also show how the structure of the
secret key and, in particular, the secret code rate affect the complexity of
these attacks. It follows from our results that QC-LDPC code-based systems can
indeed withstand reaction attacks, on condition that some specific decoding
algorithms are used and the secret code has a sufficiently high rate.Comment: 21 pages, 2 figures, to be presented at CANS 201
Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications
Low decoding latency and complexity are two important requirements of channel
codes used in many applications, like machine-to-machine communications. In
this paper, we show how these requirements can be fulfilled by using some
special quasi-cyclic low-density parity-check block codes and spatially coupled
low-density parity-check convolutional codes that we denote as compact. They
are defined by parity-check matrices designed according to a recent approach
based on sequentially multiplied columns. This method allows obtaining codes
with girth up to 12. Many numerical examples of practical codes are provided.Comment: 5 pages, 1 figure, presented at IEEE PIMRC 201
Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes with Large Girth
We propose a low-complexity method to find quasi-cyclic low-density
parity-check block codes with girth 10 or 12 and shorter length than those
designed through classical approaches. The method is extended to time-invariant
spatially coupled low-density parity-check convolutional codes, permitting to
achieve small syndrome former constraint lengths. Several numerical examples
are given to show its effectiveness.Comment: 4 pages, 3 figures, 1 table, accepted for publication in IEEE
Communications Letter
- …