arXiv subjects

Hyeonhak Kim

Publications and source records attributed to Hyeonhak Kim.

3 recordsLinked to original sources

arXiv2026

POKEx: Performance analysis of POKE-key exchange and SIDH-variants

In this paper, we present a comparative performance analysis of the POKE-based key exchange and SIDH variants. SIDH gained attention for its small key size and efficient performance, and has been selected as an alternate candidate in NIST PQC Round 4. However, following the key recovery attack by Castryck and Decru in 2022, SIDH was shown to be vulnerable to polynomial-time attacks on classical computers, undermining its security and removing it from consideration. Given that SIDH was regarded as the leading isogeny-based algorithm, several countermeasures, such as MSIDH, MD-SIDH, and bin/terSIDH have been proposed. However, these approaches still face performance limitations. Meanwhile, POKE, proposed by Basso and Maino at Eurocrypt 2025, is an isogeny-based public key encryption scheme that combines a SIDH-like protocol with higher-dimensional isogenies and has drawn attention for its efficient performance. In this work, we adapt POKE into a key exchange algorithm and benchmark it against M-SIDH, terSIDH, and CSIDH. Targeting NIST security level 1, POKE-based KEM is approximately 21.21 times faster than terSIDH and 64.97 times faster than CSIDH, showing that the POKE-based KEM is currently the most promising isogeny-based key exchange candidate.

cs.CR↗

arXiv2025

Cryptanalysis of Isogeny-Based Quantum Money with Rational Points

Quantum money is the cryptographic application of the quantum no-cloning theorem. It has recently been instantiated by Montgomery and Sharif (Asiacrypt '24) from class group actions on elliptic curves. In this work, we propose a concrete cryptanalysis by leveraging the efficiency of evaluating division polynomials with the coordinates of rational points, offering a speedup of O(log^4p) compared to the brute-force attack. Since our attack still requires exponential time, it remains impractical to forge a quantum banknote. Interestingly, due to the inherent properties of quantum money, our attack method also results in a more efficient verification procedure. Our algorithm leverages the properties of quadratic twists to utilize rational points in verifying the cardinality of the superposition of elliptic curves. We expect this approach to contribute to future research on elliptic-curve-based quantum cryptography.

cs.CR↗

arXiv2023

New Space-Efficient Quantum Algorithm for Binary Elliptic Curves using the Optimized Division Algorithm

In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was the number of the logical qubits. The division algorithm was mainly optimized in [1] since every ancillary qubit is used in the division algorithm. In this paper, we suggest a new quantum division algorithm on the binary field which uses a smaller number of qubits. For elements in a field of $2^n$, we can save $\lceil n/2 \rceil - 1$ qubits instead of using $8n^2+4n-12+(16n-8)\lfloor\log(n)\rfloor$ more Toffoli gates, which leads to a more space-efficient quantum algorithm for binary elliptic curves.

quant-ph↗