In this paper, watermarking authentication schemes for binary images are investigated. Dual-Pair Blocks (DPBs), 2 × 2 blocks with two black and two white pixels, are employed as the basic units of information embedding. With 6 distinctive patterns obtained by pixel patterns, a DPB can be represented by a senary value as the embedding information. Variable length coding is adopted to enhance the information embedding capacity of the DPB. The secret key of the watermarking is a pseudo random function with a seed value, which selects DPBs for information embedding. Based on the aforementioned framework, two novel watermarking schemes are presented. The first one, named dual-pair block authentication (DPBA), is an irreversible one featuring high information embedding capacity, and well visual quality. The second scheme, named senary Huffman compression authentication (SHCA) scheme, supports reversible watermarking unique in the literature. Matching-pair technique is further employed both schemes to reduce the number of altered bits after watermarking for better visual quality. Experimental results show that, the DPBA scheme has the highest information embedding capacity on all comparing schemes. The average compression ratio of the reversible SHCA scheme is up to 38.96%. The average distortion rates per accessed DPB for the proposed DPBA and SHCA schemes are 0.485 and 0.46, respectively.