中文摘要：

JPEG图像是目前常用的图像格式之一，由于其冗余数据较少，因此实现对JPEG图像的精确认证，需要对认证水印信息进行合适的编码以尽可能地缩短水印长度。为此，结合矩阵编码和多重水印技术，提出了一种用于JPEG图像的块级认证算法。矩阵编码可将长为l的水印信息缩短为log2l数量级，且可准确定位其中1位信息的改变，因此通过矩阵编码可有效缩短水印的长度。同时，为了提高算法的定位准确率，通过嵌入多重水印共同完成对图像的篡改定位。算法分析中对算法的漏检率、虚检率进行了较为详细的分析。理论分析与实验结果表明，在篡改率不大的情况下，算法能够实现对JPEG图像的块级篡改定位，在篡改率小于5%，向每个图像块仅嵌入约2 bit水印信息的情况下，漏检率和虚检率均在10-2数量级。

英文摘要：

JPEG image is one of the commonly used image format. Because of the less redundant data, the length of authentication watermark for JPEG images authentication should be as short as possible. In this paper, combined with matrix encoding and multiple watermarking, a block-level authentication algorithm for JPEG images is proposed. Matrix encoding can shorten the length of the watermark magnitude and accurately locate one information change. And then multi-watermarks are generated for the tampering of the image block authentication. The detailed analysis is given about the missing rate and the false detection rate in this paper. Theoretical analysis and experimental results show that the JPEG images block-level tamper localization can be done under the lower tamper rate. The missing rate and the false detection rate are at the 10-2 level, even if 2 bits watermark are embedded in the rate of tampering is less than 5%.