2,431 research outputs found
Variations of the McEliece Cryptosystem
Two variations of the McEliece cryptosystem are presented. The first one is
based on a relaxation of the column permutation in the classical McEliece
scrambling process. This is done in such a way that the Hamming weight of the
error, added in the encryption process, can be controlled so that efficient
decryption remains possible. The second variation is based on the use of
spatially coupled moderate-density parity-check codes as secret codes. These
codes are known for their excellent error-correction performance and allow for
a relatively low key size in the cryptosystem. For both variants the security
with respect to known attacks is discussed
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes
This work presents a new code-based key encapsulation mechanism (KEM) called
LEDAkem. It is built on the Niederreiter cryptosystem and relies on
quasi-cyclic low-density parity-check codes as secret codes, providing high
decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known
statistical attacks, and takes advantage of a new decoding algorithm that
provides faster decoding than the classical bit-flipping decoder commonly
adopted in this kind of systems. The main attacks against LEDAkem are
investigated, taking into account quantum speedups. Some instances of LEDAkem
are designed to achieve different security levels against classical and quantum
computers. Some performance figures obtained through an efficient C99
implementation of LEDAkem are provided.Comment: 21 pages, 3 table
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
Worst case QC-MDPC decoder for McEliece cryptosystem
McEliece encryption scheme which enjoys relatively small key sizes as well as
a security reduction to hard problems of coding theory. Furthermore, it remains
secure against a quantum adversary and is very well suited to low cost
implementations on embedded devices.
Decoding MDPC codes is achieved with the (iterative) bit flipping algorithm,
as for LDPC codes. Variable time decoders might leak some information on the
code structure (that is on the sparse parity check equations) and must be
avoided. A constant time decoder is easy to emulate, but its running time
depends on the worst case rather than on the average case. So far
implementations were focused on minimizing the average cost. We show that the
tuning of the algorithm is not the same to reduce the maximal number of
iterations as for reducing the average cost. This provides some indications on
how to engineer the QC-MDPC-McEliece scheme to resist a timing side-channel
attack.Comment: 5 pages, conference ISIT 201
A Class of Quantum LDPC Codes Constructed From Finite Geometries
Low-density parity check (LDPC) codes are a significant class of classical
codes with many applications. Several good LDPC codes have been constructed
using random, algebraic, and finite geometries approaches, with containing
cycles of length at least six in their Tanner graphs. However, it is impossible
to design a self-orthogonal parity check matrix of an LDPC code without
introducing cycles of length four.
In this paper, a new class of quantum LDPC codes based on lines and points of
finite geometries is constructed. The parity check matrices of these codes are
adapted to be self-orthogonal with containing only one cycle of length four.
Also, the column and row weights, and bounds on the minimum distance of these
codes are given. As a consequence, the encoding and decoding algorithms of
these codes as well as their performance over various quantum depolarizing
channels will be investigated.Comment: 5pages, 2 figure
Construction of Quasi-Cyclic Product Codes
Linear quasi-cyclic product codes over finite fields are investigated. Given
the generating set in the form of a reduced Gr{\"o}bner basis of a quasi-cyclic
component code and the generator polynomial of a second cyclic component code,
an explicit expression of the basis of the generating set of the quasi-cyclic
product code is given. Furthermore, the reduced Gr{\"o}bner basis of a
one-level quasi-cyclic product code is derived.Comment: 10th International ITG Conference on Systems, Communications and
Coding (SCC), Feb 2015, Hamburg, German
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