We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. Thi...We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.展开更多
利用中国剩余定理研究了环Z_k上循环码及其对偶码,其中k=（multiply from （p_i） i=1 to s）~m,p_i表示不同的素数,m是一个正整数,并且p_i不能整除码长n,给出了一个非平凡循环自对偶码存在的充要条件,得到了中国积循环码最小距离的上界...利用中国剩余定理研究了环Z_k上循环码及其对偶码,其中k=（multiply from （p_i） i=1 to s）~m,p_i表示不同的素数,m是一个正整数,并且p_i不能整除码长n,给出了一个非平凡循环自对偶码存在的充要条件,得到了中国积循环码最小距离的上界,并且确定了中国积循环码的秩和最小生成集.展开更多
文摘We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or knowing the decryption keys. This is a rational solution to an old problem proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to evaluate its own decryption function. To date, it remains the only known way of obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded homomorphic computation on any refreshed ciphertexts without bootstrapping transformation technique.
文摘利用中国剩余定理研究了环Z_k上循环码及其对偶码,其中k=（multiply from （p_i） i=1 to s）~m,p_i表示不同的素数,m是一个正整数,并且p_i不能整除码长n,给出了一个非平凡循环自对偶码存在的充要条件,得到了中国积循环码最小距离的上界,并且确定了中国积循环码的秩和最小生成集.
