Papers by Subhrangsu Maitra
Lecture Notes in Computer Science, 2000
This paper addresses the problem of obtaining new construction methods for cryptographically sign... more This paper addresses the problem of obtaining new construction methods for cryptographically significant Boolean functions. We show that for each positive integer m, there are infinitely many integers n (both odd and even), such that it is possible to construct n-variable, m-resilient functions having nonlinearity greater than 2 n−1 − 2 n 2. Also we obtain better results than all published works on the construction of n-variable, m-resilient functions, including cases where the constructed functions have the maximum possible algebraic degree n − m − 1. Next we modify the Patterson-Wiedemann functions to construct balanced Boolean functions on n-variables having nonlinearity strictly greater than 2 n−1 − 2 n−1 2 for all odd n ≥ 15. In addition, we consider the properties strict avalanche criteria and propagation characteristics which are important for design of S-boxes in block ciphers and construct such functions with very high nonlinearity and algebraic degree.
Smoking can be good for you
Journal of Cosmetic Dermatology, 2004
Smoking is without doubt one of the greatest causes of avoidable illness and death in the modern ... more Smoking is without doubt one of the greatest causes of avoidable illness and death in the modern world. Most well known is the relationship between smoking and numerous cancers, cerebrovascular and cardiovascular disease. Smoking and most especially nicotine, are, however, sometimes beneficial in certain diseases, including Parkinson's, Alzheimer's, allergic alveolitis, nausea and vomiting of pregnancy, pre-eclampsia, fibroids, carcinoma of body of uterus, ulcerative colitis, pyoderma gangrenosum, aphthous stomatitis and ulceration, pemphigus, herpes simplex and acne. In the immensely justifiable enthusiasm to discredit this dangerous activity, the mechanisms behind these beneficial effects tend to have been un-discussed or ignored. It is the aim of this paper to spur interest in the reasons for these effects. If the mechanisms are elucidated, therapeutic advances may be possible.
In this paper we discuss the problem of finding nontrivial solutions to the Cubic Sieve Congruenc... more In this paper we discuss the problem of finding nontrivial solutions to the Cubic Sieve Congruence problem, that is, solutions of x 3 ≡ y 2 z (mod p), where x, y, z < p 1 2 and x 3 = y 2 z. The solutions to this problem are useful in solving the Discrete Log Problem or factorization by index calculus method. Apart from the cryptographic interest, this problem is motivating by itself from a number theoretic point of view. Though we could not solve the problem completely, we could identify certain sub classes of primes where the problem can be solved in time polynomial in log p. Further we could extend the idea of Reyneri's sieve and identify some cases in it where the problem can even be solved in constant time. Designers of cryptosystems should avoid all primes contained in our detected cases.
IEEE Transactions on Information Theory, 2006
Recently, algebraic attacks have received a lot of attention in the cryptographic literature. It ... more Recently, algebraic attacks have received a lot of attention in the cryptographic literature. It has been observed that a Boolean function used as a cryptographic primitive, and interpreted as a multivariate polynomial over 2 , should not have low degree multiples obtained by multiplication with low degree nonzero functions. In this paper, we show that a Boolean function having low nonlinearity is (also) weak against algebraic attacks, and we extend this result to higher order nonlinearities. Next, we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity. We identify that functions having low-degree subfunctions are weak in terms of algebraic immunity, and we analyze some existing constructions from this viewpoint. Further, we present a construction method to generate Boolean functions on variables with highest possible algebraic immunity 2 (this construction, first presented at the 2005 Workshop on Fast Software Encryption (FSE 2005), has been the first one producing such functions). These functions are obtained through a doubly indexed recursive relation. We calculate their Hamming weights and deduce their nonlinearities; we show that they have very high algebraic degrees. We express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables. We deduce a very fast way of computing the output to these functions, given their input.
Chaotic Variation of Dissolved Oxygen Concentration During an Antibiotic Fermentation
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Papers by Subhrangsu Maitra