We propose the HBS (Hash Block Stealing) mode of operation. This is the first single-key mode that provably achieves the goal of providing deterministic authenticated encryption. The authentication part of HBS utilizes a newly-developed, vector-input polynomial hash function. The encryption part uses a blockcipher-based, counter-like mode. These two parts are combined in such a way as the numbers of finite-field multiplications and blockcipher calls are minimized. Specifically, for a header of h blocks and a message of m blocks, the HBS algorithm requires just h + m + 2 multiplications in the finite field and m + 2 calls to the blockcipher. Although the HBS algorithm is fairly simple, its security proof is rather complicated.