Year: 2026
Type: article
Abstract: This paper proposes a topology-based post-quantum public-key cryptosystem constructed from the Topological Conjugacy Search Problem in Mapping Class Groups (TCSP-MCG).The scheme is formulated as a non-Abelian ElGamal-type construction over mapping class groups, where the public key is generated from a conjugate pseudo-Anosov mapping class and the secret key is the hidden conjugator.Plaintexts, or fixed-length encapsulation seeds in the KEM-compatible mode, are injectively embedded into an abelian subgroup generated by commuting Dehn twists, while the non-Abelian group mask is produced through exponentiation.The security model designed through an explicit game-based IND-CPA analysis under TCSP-MCG search hardness, structured-key indistinguishability, decisional mask indistinguishability, and fixed-length encoding regularity.Classical, quantum, and geometric-group attacks are evaluated through direct search, meet-in-the-middle search, length-based heuristics, homological and traintrack invariant pruning, centralizer attacks, normal-form leakage, and non-Abelian Fourier-type attacks.A concrete serialization model, generator indexing rule, deterministic reduction procedure, capacity-constrained genus rule, bounded public-key normalization rule, bounded ciphertext normalization rule, and executable reproducibility artifact are provided to regenerate all numerical estimates.Representative profiles are labeled by nominal 128-, 192-, and 256bit post-quantum target levels, while their estimated quantum-amplified generic search exponents are intentionally higher, namely 192, 288, and 384 bits, respectively.These conservative profiles yield public-key sizes of 1536, 2304, and 3072 bits, secret-key sizes of 384, 576, and 768 bits, and encapsulation-ciphertext sizes of 1792, 2176, and 2560 bits, respectively.A KEM-oriented comparison with ML-KEM shows that the proposed profiles provide smaller serialized public keys, secret keys, ciphertexts, bandwidth, and persistent key-material storage under the stated representation model.These results indicate that TCSP-MCG offers a compact, mathematically distinct, and reproducible topology-based direction for post-quantum public-key cryptography.
Institution: Mustansiriyah University
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204652052
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