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Overview of Encryption of Compressed Sensed Images

Signals and images compressed using compressed sensing (CS) are multiplied by a sampling matrix in order to both sample and compress the signal. To reconstruct the signal at the receiver, the original sampling matrix must be known. This paper investigates the concept of using this sampling matrix as an inherent encryption key.

For this work, we make the following assumptions. First, the sampling matrix Φ is an M × N normalized binary matrix where M is the length of the compressed signal, N is the length of the original signal and M &lt N.kΦ is a K bit key which is used to generate Φ using the standard AES key expansion techniques.Finally, we assume that the attacker knows the nature of the encryption and the size of the encrypted image, and only needs to determine Φ to discover the encrypted signal.

There are two cases to consider. If two nodes are setting up permanent or semi- permanent communication between each other, such as two nodes within a wireless multimedia sensor network,kΦ can be expanded to the entire Φmatrix making Φ the entire key. Assuming that the eavesdropping node does not have any knowledge of the pseudo-random process used to generate Φ, this gives 2M× N possible bit combinations. For a 512 X 512 pixel image, N is more than 260,000 and M would typically be around 60,000. This results in an infeasible number of possible combinations for an attacker to determine.

In most systems, however, is is infeasible to transmit or even store the entire Φ matrix. For example, the 512 X 512 image above requires more than 2 GB in storage. This can be reduced through parallel processing techniques to around 32 MB while still maintaining very good protection of the image, but even this is still infeasible if a new key is to be transmitted with each image. In this case,kΦ can be used to generate Φ. By using the AES key expansion techniques, a 128, 192 or 256 bit key can be expanded to the 32 MB Φ matrix needed to decode the image.

The main advantage of this system is that the length of the key is essentially restricted by the physical capabilities of the system (storage and transmission) and not by the encryption protocol. This would allow a user to increase the encryption of ultra-secure images to the point where it would be infeasible to break the encryption using brute force methods.

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