IPCC7: Post-Quantum Encryption Scheme Based on a Perfect Dominating Set in 3-Regular Graph

Post-quantum cryptography (PQC) has been actively explored to meet the requirements arising with the rapid development of quantum computers. The National Institute of Standards and Technology (NIST) conducted a competition to establish the next-generation cryptographic standards. While previous competitions selected a single cryptographic standard, this competition aimed to standardize several algorithms based on various mathematical problems since the security of PQC has not been studied as extensively as that of legacy cryptosystems. The recent exclusion of the isogeny-based key-establishment algorithm, SIKE, from the competition emphasizes the necessity of exploring cryptographic algorithms based on various fundamental problems. In this study, we propose the Improved Perfect Code Cryptosystem 7 (IPCC7), a new post-quantum encryption scheme, as an improved version of the perfect code cryptosystem (PCC) based on combinatorics conceptualized by Koblitz. The security of our cryptosystem relies on the intractability of finding the perfect dominating set in a given graph. A PCC proposed previously by Koblitz did not receive much attention because of its low efficiency for handling higher-order polynomials. To overcome these drawbacks, we used the product of low-degree polynomials and demonstrated the feasibility of a graph-based encryption scheme. IPCC7 has some limitations for use as a general-purpose PQC. However, considering its relatively small key size (768 bytes public-key and 64 bytes secret key), fast decryption speed (2.0 Gbps), and usable encryption speed (8.6Mbps), IPCC7 is particularly suitable for environments with low-memory constraints, such as white-box encryptions.