A block cipher cryptosystem using wavelet transforms over finite fields

We present a new private key cryptosystem based on the finite-field wavelet. The encryption and decryption are performed by the synthesis and analysis banks of the nonlinear finite-field wavelet transform, whose filter coefficients are determined by the keys of the users. We exploit the polyphase representation of the wavelets to introduce a shared key mechanism for the wavelet cryptosystem. We propose to use wavelets that operate over GF(256) and a nonlinear device that performs a mapping on the field elements to their inverse in the field. The introduced cryptographic system can operate in either stream-cipher or block-cipher modes depending on whether the filterbanks perform linear or circular convolution. The block cipher system has a key length of 16 symbols (128 bits) and an input block size of 30 symbols (240 bits). To evaluate the efficiency of the developed two-round wavelet cryptographic scheme, we compare it with DES and AES. Our results suggest that the wavelet cryptosystem has comparable computational complexity to AES and approximately half the complexity of DES. The security is tied to the length of the wavelet basis function and to the nonlinearity within the wavelet transform. We study the security of the block-cipher wavelet cryptosystem in response to classical attacks and those specific to this algorithm, particularly those which use variations of the divide and conquer, interpolation attack, and discrete Fourier transform techniques. We show that chosen ciphertext attacks of the wavelet encryption system can reduce to the problem of solving a set of nonlinear equations over finite fields. By considering existing classical and structure-specific attacks, we conclude that the lowest complexity of any of these attacks is greater than an exhaustive key search.

I. Introduction

Security technologies are critical for building user confidence and facilitating broad market adoption of next-generation wireless e-business solutions. For example, while future mobile phones will play a pivotal role in electronic-business by delivering a range of services anywhere, and at any time, they are a possible target to attacks. Anyone could intercept virtually any cellular transmission or conversation. Imagine a situation where hackers can steal a phone user's billing data and make fraudulent calls. A more catastrophic threat exists when sensitive or private information (i.e., personal medical insurance applications or credit card, and social security numbers) is being relayed, and consequently eavesdropped, through a cellar phone. If there exists a constant paranoia of insecure communications, users will not be willing to use such technologies.