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Mathematics

Indian Statistical Institute

Theses/Dissertations

2005

Mathematics

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Some Nonparametric And Semiparametric Methods For Discriminant Analysis., Anil Kumar Ghosh Dr. Apr 2005

Some Nonparametric And Semiparametric Methods For Discriminant Analysis., Anil Kumar Ghosh Dr.

Doctoral Theses

Discriminant analysis (see e.g., Devijver and Kittler, 1982; Duda, Hart and Stork, 2000; Hastle, Tibahirani and Friedman, 2001) deals with the separation of different groups of obaervationa and allocation of a new oboervation to one of the previously delined grouga. In a J-class discriminant analysis problem, we usually hae a training sample of the form {(xk, ck) : k = 1,2,...,N}, where xk = (Ik1,Ik2,...J) is a d-dimensional measarement vector, and ca € {1,2,...,J} is its class label. On the basis of thia training sample, one aims to form a decision rule d(x) : Rd + (1,2,...,J} for clasifying the …


Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr. Feb 2005

Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.

Doctoral Theses

In this thesis we study combinatorial aspects of Boolean functions and S-boxes with impor- tant cryptographic properties and construct new functions possesing such properties. These have possible applications in the design of private key (symmetric key) cryptosystems.Symmetric key cryptosystems are broadly divided into two classes.1. Stream Ciphers,2. Block Ciphers.Some recent proposals of stream ciphers are SNOW [37], SCREAM [52], TURING (98], MUGI (117), HBB (102], RABBIT (9), HELIX (38] and some proposals of block ciphers are DES, AES, RC6 [97), MARS (12], SERPENT (6], TWOFISH (104].In stream cipher cryptography a pseudorandom sequence of bits of length cqual to the message …


On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr. Jan 2005

On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr.

Doctoral Theses

In this thesis, we propose two new subband transforms entitled ISITRA and YKSK transforms and their possible applications in image compression and encryption. Both these transforms are developed based on a common model of multiplication known as Bino’s model of multiplication. ISITRA is a convolution based transforms i.e., that both forward and inverse transform of ISITRA is based on convolution as in DWT or 2-channel filter bank. However, it is much more general than the existing DWT or 2-channel filter bank scheme in the sense that it we can get different kinds of filters in addition to the filters specified …