Numerous cryptographic techniques have been developed to be used on mobile devices for various security and privacy protections. However, these cryptographic primitives, working under different mathematical assumptions, tend to become more and more complex and intricate, which makes it increasingly more difficult for proper implementation and management. Thus, it is desired to simplify management and improve efficiency by means of designing a general function family to meet a variety of security requirements. In this paper, we present such a family of square functions, including SqHash, SqMAC and SqPRF, based on a specially truncated function (MSB or LSB). We further improve the efficiency of these algorithms by using 'circular convolution with carry bits' which makes parallel processing possible. We prove the security of these functions based on the privacy in hidden number problem and hard-core predicate of one-way function. We also show that the proposed schemes achieve better performance with a complexity reduction from O(n2) to O(kn/w) for n-bit message, k-bit output and w-bit word size.