In 2013, Tang, Carlet and Tang presented two classes of functions.The functions in the first class are unbalanced and the functions in the second one are balanced.Both of these two classes of functions have high nonlinearity, high algebraic degree, optimal algebraic immunity, and high fast algebraic immunity.However, they are not 1-resilient which represents a drawback for their use as filter functions in stream ciphers.In this paper, we first propose a large family of 1-resilient functions of 2k ≥ 6 variables having high nonlinearity, optimal algebraic immunity, optimal algebraic degree, that is, meet the Siegenthaler bound.Specifically, we can mathematically prove that every functions in this family has fast algebraic immunity no less than n-6, which is the first time that an infinite family of 1-resilient functions with provably high fast algebraic immunity has been invented.For every n =2k ≥ 4, this family include (2k-1)· (2k-12k-2)1-resilient Boolean functions.Further, we exhibit a subclass of the family which has nonlinearity at least 22k-1-(1+k ln2/π+π+16/32) 2k-1, which is much better than the lower bounds on nonlinearity of known 1-resilient functions with potentially high fast algebraic immunity.