New Paradigm to Construct Public Key Cryptographic Schemes for Lightweight Devices with Provable Security against Quantum Attackers

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In FY 2022, we successfully completed our proposed construction of the post-quantum interactive public-key identification (ID) scheme whose security is based on the hardness of MinRank problem. Since MinRank problem is a computational problem based on binary field, our ID scheme is directly representable in binary field. This makes our scheme to be easily implementable in today's real-world hardwares as most of them are constructed based on electronic circuits which execute binary field operation.We also successfully invented a new computational problem based on multivariate quadratic (MQ) polynomials which is proven to be NP-hard. Based on the new computational problem, we constructed a new post-quantum public-key ID scheme which is proven to be secure as long as the new computational problem is hard. Moreover, since the computational problem can be represented directly in binary field, the new ID scheme is also fully representable directly in binary field.In the other line of research, we successfully derived the capacity region for secure symmetric-key encryption under real-time side-channel attacks where the adversary obtains side-channel information on the secret key used during the encryption process.Finally, as a preparation for constructing post-quantum multi-signatures for blockchains, we also proposed a new framework to construct a tightly secure two-round multi-signature scheme. Based on the framework, we built a multi-signature scheme which is easy to implement securely using the standard elliptic curves.