Homomorphic polynomial public key encapsulation over two hidden rings for quantum-safe key encapsulation

Kuang et al. recently introduced a novel quantum-safe public key scheme, called the multivariate Polynomial Public Key or MPPK. MPPK is based upon the mutual inversion relationship of multiplication and division, with the former used for key pair construction, and the latter used for decryption. For key pair construction, two solvable univariate polynomials are each multiplied by a base multivariate polynomial used for the purpose of noise injection. The constant term and highest order term of the produced product polynomials with respect to the message variable are set aside and used to create two noise functions, concealed using a hidden ring. The remaining parts of the product polynomials and two noise functions constitute the public key. The operation used to create noise functions is partially homomorphic. In this paper, we propose to extend the key construction to use this partially homomorphic operator and two hidden rings to hide the public key product polynomials, one for each polynomial. In other words, we propose to encrypt the product polynomials in their entirety with a pair of hidden rings using the partially homomorphic operator. Encrypting the public key this way complicates possible attacks on the public key and forces the adversary to guess the pair of hidden rings. We name this new construction Homomorphic Polynomial Public Key over Two Hidden Rings or HPPK-THR. HPPK-THR demonstrates the IND-CPA property with uninterpretable security in secret recovery attacks, due to the modular Diophantine Equation Problem. In our brief benchmark performance, HPPK-THR outperforms MPPK KEM and NIST Round 3 finalists.