The BGN (Boneh-Goh-Nissim) cryptosystem is a cryptosystem that permits arbitrary number of additions and one multiplication of ciphertext without growing the size of ciphertext. The scheme of BGV12 is a fully homomorphic encryption from (G)LWE which needs key switching, modulus switching and other technologies for the multiplicative homomorphism. This paper describes a BGN scheme based on BGV12. Although our constructed scheme only permits one multiplication, it does not need other technologies, so it is more efficient. Comparing with the scheme of GVH10, our scheme has better size of parameter. In addition, we extend our scheme to a threshold encryption scheme, which allows parties to cooperatively decrypt a ciphertext without learning anything but the plaintext, and can be protected from related-key attacks.%BGN加密方案是指允许密文任意次加法和一次乘法运算的加密方案,并且在密文的运算中,密文的规模没有增长.BGV12加密方案是基于(G)LWE的全同态加密方案,为了实现乘法同态,需要用到密钥交换、模转换等技术.该文在BGV12基础上构造了一种BGN加密方案.虽然只能支持密文的一次乘法运算,但不需要其他技术的支持,因而更快捷.与GVH10加密方案相比,有更好的参数规模.此外,将BGN加密方案扩展成一种门限加密方案,该门限加密方案同样允许所有参与者共同解密一个密文而没有泄露明文的任何信息,并且能抵抗密钥泄露攻击.
展开▼
