Abstract
AbstractCryptographic primitives from coding theory are some of the most promising candidates for NIST’s Post-Quantum Cryptography Standardization process. In this paper, we introduce a variety of techniques to improve operations on dyadic matrices, a particular type of symmetric matrices that appear in the automorphism group of certain linear codes. Besides the independent interest, these techniques find an immediate application in practice. In fact, one of the candidates for the Key Exchange functionality, called DAGS, makes use of quasi-dyadic matrices to provide compact keys for the scheme.
Highlights
Cryptographic primitives from coding theory are some of the most promising candidates for NIST’s Post-Quantum Cryptography Standardization process
We introduce a variety of techniques to improve operations on dyadic matrices, a particular type of symmetric matrices that appear in the automorphism group of certain linear codes
Post-Quantum Cryptography is the area of research that investigates cryptographic primitives that are deemed secure against attackers equipped with quantum technology
Summary
Post-Quantum Cryptography is the area of research that investigates cryptographic primitives that are deemed secure against attackers equipped with quantum technology These include schemes based on a variety of mathematical problems, such as finding short vectors in a lattice, or decoding random linear codes. Among the code-based candidates for NIST’s call, DAGS [3] is a Key Encapsulation Mechanism (KEM) that uses Quasi-Dyadic (QD) matrices to considerably reduce the size of the public key, following a McEliecelike approach. The method effectively factors every quasi-dyadic matrix into a product of two triangular matrices and a permutation matrix This leads to the possibility of a very efficient algorithm for computing the inverse of a matrix, which is useful in code-based cryptography, for instance for computing the systematic form of a parity-check (or generator) matrix.
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