Chosen-ciphertext secure code-based threshold public key encryptions with short ciphertext

Threshold public-key encryption (threshold PKE) has various useful applications. A lot of threshold PKE schemes are proposed based on RSA, Diffie–Hellman and lattice, but to the best of our knowledge, code-based threshold PKEs have not been proposed. In this paper, we provide three IND-CCA secure code-based threshold PKE schemes. The first scheme is the concrete instantiation of Dodis–Katz conversion (Dodis and Katz, TCC’05) that converts an IND-CCA secure PKE into an IND-CCA secure threshold PKE using parallel encryption and a signature scheme. This approach provides non-interactive threshold decryption, but ciphertexts are large (about 16 kilobytes for 128-bit security) due to long code-based signatures even in the state-of-the-art one. The second scheme is a new parallel encryption-based construction without signature schemes. Unlike the Dodis–Katz conversion, our parallel encryption converts an OW-CPA secure PKE into an OW-CPA secure threshold PKE. To enhance security, we use Cong et al.’s conversion (Cong et al., ASIACRYPT’21). Thanks to eliminating signatures, its ciphertext is 512 bytes, which is only 3% of the first scheme. The decryption process needs an MPC for computing hash functions, but decryption of OW-CPA secure PKE can be done locally. The third scheme is an MPC-based threshold PKE scheme from code-based assumption. We take the same approach Cong et al. took to construct efficient lattice-based threshold PKEs. We build an MPC for the decryption algorithm of OW-CPA secure Classic McEliece PKE. This scheme has the shortest ciphertext among the three schemes at just 192 bytes. Compared to the regular CCA secure Classic McEliece PKE, the additional ciphertext length is only 100 bytes. The cons are heavy distributed computation in the decryption process.