Cryptology ePrint Archive: Report 2021/1431

Secure and Efficient Multi-Key FHE Scheme Supporting Multi-bit Messages from LWE Preserving Non-Interactive Decryption

Chinmoy Biswas and Ratna Dutta

Abstract: We consider multi-key fully homomorphic encryption (multi-key FHE) which is the richest variant of fully homomorphic encryption (FHE) that allows complex computation on encrypted data under different keys. Since its introduction by Lopez-Alt, Tromer and Vaikuntanathan in 2012, numerous proposals have been presented yielding various improvements in security and efficiency. However, most of these multi-key FHE schemes encrypt a single-bit message. Constructing a multi-key FHE scheme encrypting multi-bit messages have been notoriously difficult without loosing efficiency for homomorphic evaluation and ciphertext extension under additional keys. In this work, we study multi-key FHE that can encrypt multi-bit messages. Motivated by the goals of improving the efficiency, we propose a new construction with non-interactive decryption and security against chosen-plaintext attack (IND-CPA) from the standard learning with errors (LWE) assumption. We consider a binary matrix as plaintext instead of a single-bit. Our approach supports efficient homomorphic matrix addition and multiplication. Another interesting feature is that our technique of extending a ciphertext under additional keys yields significant reduction in the computational overhead. More interestingly, when contrasted with the previous multi-key FHE schemes for multi-bit messages, our candidates exhibits favorable results in the length of the secret key, public key and ciphertext preserving non-interactive decryption.

Keywords: lattice based cryptosystem, multi-key fully homomorphic encryption, learning with errors, multi-bit messages

Category / Keywords: public-key cryptography / lattice techniques, public-key cryptography

Date: received 25 Oct 2021

Contact author: chinmoy88biswas at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20211026:065720 (All versions of this report)

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