October 27, 2006 20:27 WSPC - Proceedings (ICAPR 2007) Trim Size: 11in x 8.5in 068 1 DCT properties as handle for Image Compression and Cryptanalysis Anil Kr. Yekkala Philips Electronics India Ltd., No 1, Murphy Road, Bangalore 560008, INDIA E-mail: anil.yekkala@philips.com C.E. Veni Madhavan Indian Institute of Science, Bangalore 560012, INDIA E-mail: cevm@csa.iisc.ernet.in Narendranath Udupa Philips Electronics India Ltd., No 1, Murphy Road, Bangalore 560008, INDIA E-mail: narendranath.udupa@philips.com DCT transformation has been traditionally used to exploit spatial redundancy within an image and video for purpose of compression. JPEG standard commonly used for image compression is based on DCT transformation. In this paper we analyze the linear and orthogonal properties of DCT transformation for achieving an improvement over compression provided by JPEG, and we also use the DCT properties to demonstrate vulnerability of lightweight encryption schemes based on encrypting the DC values. Keywords : DCT transformation; JPEG; DC prediction; DC encryption 1. Introduction Both lossy and lossless compression schemes are based on exploiting the spatial redundancy within an image. In case of lossy compression schemes the spatial redundancy is exploited by representing the image in its frequency domain using a transform cod- ing technique, and then doing the further process- ing in the frequency domain. DCT transformation is one of the most popularly used transformation tech- niques for image compression. For instance, in case of JPEG compression 1 the entire image is divided into blocks of size 8x8, and each block is represented in its frequency domain by applying 2-dimensional DCT transformation. In the frequency domain the component corresponding to zero frequency is known as DC value and the non-zero frequency components are known as the AC values. It has been generally observed 7 that most of the energy of an image is con- tained in the DC values. Hence, in order to reduce the number of bits to represent the DC values, the spa- tial redundancy is further exploited by encoding the DC values using Differential DC encoding. It is to be noted that even after differential DC encoding, the DC values generally occupy about 8% of the image space. Using the properties of DCT we propose a re- placement to Differential DC encoding, hence show- ing further improvement in compression achieved by JPEG. Again owing to the fact that most of the en- ergy is present in DC values, several lightweight en- cryption schemes 3 are based on encrypting the DC values to reduce the intelligibility of the image. Even though techniques 4, , 6 , 5 for reconstructing images are available in the case when few of the DC values are corrupted, currently we do not see many methods in literature, which focus on reconstructing an image in the event of corruption of all DC values. Again us- ing the properties of DCT transformation we show a method to reduce the amount of noise introduced in the image due to encryption of DC values, hence showing the vulnerability of Lightweight encryption schemes based on encrypting only the DC values. 1.1. Properties of DCT Transformation In this paper we use the Linear Property and Orthog- onal Property of DCT Transformation, to achieve better compression compared to JPEG, and also to reduce the amount of noise introduced due to en- cryption of DC values. 1.1.1. Linear Property If X is a square matrix of dimension n x n, and if A is a constant square matrix of same dimension with