Secure and efficient random functions with variable-length output

Many random functions, like Hash, MAC, PRG, have been used in various network applications for different security choices. However, they are either fast but insecure or cryptographic secure but slow. To integrate them together, in this paper we present a new family of square random functions, including SqHash, SqMAC and SqPRG, based on a specially truncated function (MSB or LSB), as well as circular convolution with carry bits. Provable security is provided by the privacy property in hidden number problem and Hard-core unpredication of one-way function. The experiment results show that these schemes have better performance under different input and output lengths. We also perform four types of statistical tests for randomness. The experiments indicate that our construction has good average-case randomness than SHA-2 and original Square algorithm.