Developments in Quantum Cryptography and Coding Theory

The field of quantum cryptography and coding theory is witnessing significant advancements, with a focus on enhancing the security and efficiency of cryptographic protocols and codes. Researchers are exploring new approaches to quantum money, leveraging the properties of elliptic curves and rational points to improve verification procedures. Additionally, there is a growing interest in subspace codes, particularly constant dimension subspace codes, which have applications in random network coding. The sum-rank metric is also being investigated, with studies on one-weight codes and their geometric properties. Furthermore, explicit bases for Riemann-Roch spaces associated with elliptic curve divisors are being developed, enabling efficient code construction and revealing structural properties of the codes. Noteworthy papers include: On the Classical Hardness of the Semidirect Discrete Logarithm Problem in Finite Groups, which investigates the classical hardness of the semidirect discrete logarithm problem and its implications for post-quantum cryptographic protocols. Cryptanalysis of Isogeny-Based Quantum Money with Rational Points, which proposes a concrete cryptanalysis of isogeny-based quantum money and offers a speedup in verification procedures. One-weight codes in the sum-rank metric, which explores the geometry of one-weight sum-rank metric codes and presents new examples and partial structural results.

Sources

Cryptanalysis of Isogeny-Based Quantum Money with Rational Points

Multilevel inserting constructions for constant dimension subspace codes

One-weight codes in the sum-rank metric

Bases of Riemann-Roch spaces associated with arbitrary elliptic curve divisors and their application in constructing various elliptic Codes families

On the Classical Hardness of the Semidirect Discrete Logarithm Problem in Finite Groups

$\mathbb{F}_{2}\mathbb{F}_{4}$-Additive Complementary Dual Codes

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