The aim of this paper is to adapt automatic jigsaw puzzle solvers, which are methods of assembling jigsaw puzzles, to the field of information security. Encryption-then-Compression (ETC) systems have been considered for the user-controllable privacy protection of digital images in social network services. Block scrambling-based encryption schemes, which have been proposed to construct ETC systems, have enough key spaces for protecting brute-force attacks. However, each block in encrypted images has almost the same correlation as that of original images. Therefore, it is required to consider the security from different viewpoints from number theory-based encryption methods with provable security such as RSA and DES. In this paper, existing jigsaw puzzle solvers are first reviewed in terms of attacking strategies on encrypted images. Then, an extended jigsaw puzzle solver is considered to improve some limitations of the conventional ones. In the experiments, the jigsaw puzzle solvers are applied to encrypted images to consider the security conditions of the encryption schemes.