This paper discusses DNA watermarking for copyright protection and authentication of a DNA sequence. We then propose a DNA watermarking method that confers mutation resistance, amino acid residue conservation, and watermark security. Our method allocates codons to random circular angles using a random mapping table and selects a number of codons for embedding targets using the Lipschitz regularity that is measured from the evolution across scales of local modulus maxima of codon circular angles. We then embed the watermark into random circular angles of codons without changing the amino acid residue. The length and location of target codons depend on the random mapping table and the singularity of detection of Lipschitz regularity. This table is used as the watermark key and can be applied to any codon sequence regardless of sequence length. Without knowledge of this table, it is very difficult to detect the length and location of sequences for extracting the watermark. From experimental results on the suitability of similar watermark capacities, we verified that our method has a lower bit-rate error for point mutations compared with previous methods. Further, we established that the entropies of the random mapping table and the location of target codons are high, indicating that the watermark is secure. 
DNA sequence watermarking based on random circular angle