Coding theory

In this paper, a brief introduction to coding theory is
presented. Linear (block) codes arc briefly discussed along
with some of their error (multiple error, burst error)
correction and detection properties. Recurrent sequences
are discussed in the major portion of the paper, and it is
shown that the study of general recurrent sequences is
equivalent to the study of sequences associated with
irreducible polynomials. The paper concludes with a brief
mention of autocorrelation functions and a way of finding
the minimal recursion of a recurrent sequence given some
terms of the sequence. The paper is an exposition of
previously known results. Some modification in notation
and proofs has been done to present the material in a
unified and more readable manner.

Visual cryptography concerns the problem of "hiding" a monochrome image among sets of transparencies, known as shares. These are created in such a fashion that certain sets of shares when superimposed, will reveal the image; while other subsets yield no information. A standard model is the (k, n) scheme, where any k shares will reveal the image, but any k - 1 or fewer shares reveal no information. In this thesis, we explain the basic mechanism for creating shares. We survey the literature and show how to create (k, k) schemes which exist for all k > 2. Then we introduce perfect hash functions, which can be used to construct (k, n) schemes from (k, k) schemes for all 2 < k < n. We introduce generalizations of (k, n) schemes that we call covert cryptographic schemes, and extend this notion to multilevel visual cryptographic schemes. We give conditions for the existence of such schemes, and we conclude with a survey of generalizations.

XYZ Video Compression denotes a video compression algorithm that operates in three dimensions, without the overhead of motion estimation. The smaller overhead of this algorithm as compared to MPEG and other "standards-based" compression algorithms using motion estimation suggests the suitability of this algorithm to real-time applications. The demonstrated results of compression of standard motion video benchmarks suggest that XYZ Video Compression is not only a faster algorithm, but develops superior compression ratios as well. The algorithm is based upon the three-dimensional Discrete Cosine Transform (DCT). Pixels are organized as 8 x 8 x 8 cubes by taking 8 x 8 squares out of 8 consecutive frames. A fast three-dimensional transform is applied to each cube, generating 512 DCT coefficients. The energy-packing property of the DCT concentrates the energy in the cube into few coefficients. The DCT coefficients are quantized to maximize the energy concentration at the expense of introduction of a user-determined level of error. A method of adaptive quantization that generates optimal quantizers based upon statistics gathered for the 8 consecutive frames is described. The sensitivity of the human eye to various DCT coefficients is used to modify the quantizers to create a "visually equivalent" cube with still greater energy concentration. Experiments are described that justify choice of Human Visual System factors to be folded into the quantization step. The quantized coefficients are then encoded into a data stream using a method of entropy coding based upon the statistics of the quantized coefficients. The bitstream generated by entropy coding represents the compressed data of the 8 motion video frames, and typically will be compressed at 50:1 at 5% error. The decoding process is the reverse of the encoding process: the bitstream is decoded to generate blocks of quantized DCT coefficients, the DCT coefficients are dequantized, and the Inverse Discrete Cosine Transform is performed on the cube to recover pixel data suitable for display. The elegance of this technique lies in its simplicity, which lends itself to inexpensive implementation of both encoder and decoder. Finally, real-time implementation of the XYZ Compressor/Decompressor is discussed. Experiments are run to determine the effectiveness of the implementation.

In this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the first-order Reed- Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the error-correcting capability and the practical speed of the Golay code and the first-order Reed-Muller code to meet our goal.

Perceptual video coding has been a promising area during the last years. Increases in compression ratios have been reported by applying foveated video coding techniques where the region of interest (ROI) is selected by using a computational attention model. However, most of the approaches for perceptual video coding only use visual features ignoring the auditory component. In recent physiological studies, it has been demonstrated that auditory stimuli affects our visual perception. In this work, we validate some of those physiological tests using complex video sequence. We designed and developed a web-based tool for video quality measurement. After conducting different experiments, we observed that in the general reaction time to detect video artifacts was higher when video was presented with the audio information. We observed that emotional information in audio guide human attention to particular ROI. We also observed that sound frequency change spatial frequency perception in still images.

The aim of this work is to investigate an algebraic attack on block ciphers called Multiple Right Hand Sides (MRHS). MRHS models a block cipher as a system of n matrix equations Si := Aix = [Li], where each Li can be expressed as a set of its columns bi1, . . . , bisi . The set of solutions Ti of Si is dened as the union of the solutions of Aix = bij , and the set of solutions of the system S1, . . . , Sn is dened as the intersection of T1, . . . , Tn. Our main contribution is a hardware platform which implements a particular algorithm that solves MRHS systems (and hence block ciphers). The case is made that the platform performs several thousand orders of magnitude faster than software, it costs less than US$1,000,000, and that actual times of block cipher breakage can be calculated once it is known how the corresponding software behaves. Options in MRHS are also explored with a view to increase its efficiency.

The Intermediate Frequency Acoustic Modem (IFAM), developed by Dr. Beaujean, is designed to transmit the command-and-control messages from the top-side to the wet-side unit in ports and very shallow waters. This research presents the design of the turbo coding scheme and its implementation in the IFAM modem with the purpose of meeting a strict requirement for the IFAM error rate performance. To simulate the coded IFAM, a channel simulator is developed. It is basically a multi-tap filter whose parameters are set depending on the channel geometry and system specifics. The simulation results show that the turbo code is able to correct 89% of the messages received with errors in the hostile channel conditions. The Bose-Chadhuri-Hocquenghem (BCH) coding scheme corrects less that 15% of these messages. The other simulation results obtained for the system operation in different shallow water settings are presented.

In the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and q are primes we use Lehmann's primality test on the commitments. The chapter is based on the paper, "RSA signature schemes with subliminal-free public key" (Tatra Mountains Mathematical Publications 41 (2008)). In chapter 7 a one-time signature scheme using run-length encoding is presented, which in the random oracle model offers security against chosen-message attacks. For parameters of interest, the proposed scheme enables about 33% faster verification with a comparable signature size than a construction of Merkle and Winternitz. The public key size remains unchanged (1 hash value). The main cost for the faster verification is an increase in the time required for signing messages and for key generation. The chapter is based on the paper "A one-time signature using run-length encoding" (Information Processing Letters Vol. 108, Issue 4, (2008)).

The field of Video Transcoding has been evolving throughout the past ten years. The need for transcoding of video files has greatly increased because of the new upcoming standards which are incompatible with old ones. This thesis takes the method of using machine learning for video transcoding mode decisions and discusses ways to improve the process of generating the algorithm for implementation in different video transcoders. The transcoding methods used decrease the complexity in the mode decision inside the video encoder. Also methods which automate and improve results are discussed and implemented in two different sets of transcoders: H.263 to VP6 , and MPEG-2 to H.264. Both of these transcoders have shown a complexity loss of almost 50%. Video transcoding is important because the quantity of video standards have been increasing while devices usually can only decode one specific codec.

H.264/AVC encoder complexity is mainly due to variable size in Intra and Inter frames. This makes H.264/AVC very difficult to implement, especially for real time applications and mobile devices. The current technological challenge is to conserve the compression capacity and quality that H.264 offers but reduce the encoding time and, therefore, the processing complexity. This thesis applies machine learning technique for video encoding mode decisions and investigates ways to improve the process of generating more general low complexity H.264/AVC video encoders. The proposed H.264 encoding method decreases the complexity in the mode decision inside the Inter frames. Results show, at least, a 150% average reduction of complexity and, at most, 0.6 average increases in PSNR for different kinds of videos and formats.