Research Background -
Homomorphic encryption allows specific operations to be performed directly on ciphertext, facilitating privacy protection and data usability without decryption. Since its inception in 1978 and subsequent advancements by Gentry in 2009, the field has evolved into three main categories: partially homomorphic, limited homomorphic, and fully homomorphic encryption. While fully homomorphic encryption offers powerful capabilities, it comes with high computational and storage costs, limiting its practical use. In contrast, partially and limited homomorphic schemes are more applicable and are used in scenarios like confidential queries and secure multi-party computation.
Recent research aims to combine the high performance of elliptic curve cryptography (ECC) with homomorphic encryption's privacy features to enable efficient ciphertext operations, but current solutions face challenges such as supporting only partial operations, limited plaintext space, and low decryption efficiency, hindering their applicability in complex scenarios.
Overview of Core Achievements -
In this context, Beijing Infosec has designed a novel homomorphic encryption scheme called RECHE (homomorphic encryption scheme based on elliptic curves over rings). This scheme supports arbitrary numbers of homomorphic addition and scalar multiplication operations while enabling encryption of plaintext over a larger space with minimal ciphertext expansion (for example, using SM2 parameters, the plaintext space is Zp , where p is the elliptic curve parameter, and the ciphertext length increases by only 512 bits relative to the plaintext). Building on this, the RECHE scheme has been extended to form the E-RECHE (extended RECHE) scheme.
The E-RECHE scheme supports any polynomial ciphertext operations with a degree not exceeding 2 while maintaining low ciphertext expansion and high operational efficiency. Based on the design of the E-RECHE scheme, it is possible to further construct polynomial ciphertext operations with degrees of 4 or even higher.