Recently, an image encryption algorithm based on scrambling and Vegin`ere cipher has been proposed. However, it was soon cryptanalyzed by Zhang et al. using a combination of chosen-plaintext attack and differential attack. This paper briefly reviews the two attack methods proposed by Zhang et al. and outlines the mathematical interpretations of them. Based on their work, we present an improved chosen-plaintext attack to further reduce the number of chosen-plaintexts required, which is proved to be optimal. Moreover, it is found that an elaborately designed known-plaintex attack can efficiently compromise the image cipher under study. This finding is verified by both mathematical analysis and numerical simulations. The cryptanalyzing techniques described in this paper may provide some insights for designing secure and efficient multimedia ciphers.