Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

World University root node

Department of Computer Science and Engineering

Almost full rank matrices arising from transitive tournaments

It is known, from the work of Dai et al. (in CRYPTO’17), that the PRF advantage of XORP (bitwise-xor of two outputs of n-bit random permutations with domain separated inputs), against an adversary making q queries, is about q/ 2n for q≤ 2n - 5. The same bound can be easily shown to hold for XORP[ k] (bitwise-xor of k outputs n-bit pseudorandom random permutations with domain separated inputs), for k≥ 3. In this work, we first consider multi-user security of XORP[ 3 ]. We show that the multi-user PRF advantage of XORP[ 3 ] is about uqmax/2n for all qmax≤ 2n/ 12, where u is the number of users and qmax is the maximum number of queries the adversary can make to each user. In the multi-user setup, this implies that XORP[ 3 ] gives security for O(2n) users even allowing almost O(2n) queries to each user. This also indicates significant improvement in the single-user setup (i.e., when u= 1 ), where the distinguishing advantage of the adversary even after making O(2n) queries is O(12n), i.e., negligible. Subsequently, we consider a simple efficient variant of XORP[ 3 ] in which we use five calls to produce 2n bit output (instead of six calls in the case of XORP[ 3 ] ). This variant also achieves similar level of security. As an immediate application, we can construct a variant of block cipher based counter mode which provides much higher security (both in the single-user and the multi-user setup) compared to the security of the encryption part of GCM at the cost of efficiency. © 2021, International Association for Cryptologic Research.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Luby-Rackoff Backwards with More Users and More Security

arXiv preprint arXiv:2108.

An ensemble of high rank matrices arising from tournaments

Intelligent Electrical Systems: A Step towards Smarter Earth

Natural Ground-Water Recharge Scenario in Kolkata and a Review of Artificial Recharging

Let σ be some positive integer and (formula presented). The theory behind finding a lower bound on the number of distinct blocks P 1 , …, P σ ∈ {0, 1} n satisfying a set of linear equations {P i ⊕ P j = c i,j : (i, j) ∈ C} for some c i,j ∈ {0, 1} n , is called mirror theory. Patarin introduced the mirror theory and provided a proof for this. However, the proof, even for a special class of equations, is complex and contains several non-trivial gaps. As an application of mirror theory, XORP[w] (known as XOR construction) returning (w − 1) block output, is a pseudorandom function (PRF) for some parameter w, called width. The XOR construction can be seen as a basic structure of some encryption algorithms, e.g., the CENC encryption and the CHM authenticated encryption, proposed by Iwata in 2006. Due to potential application of XORP[w] and the nontrivial gaps in the proof of mirror theory, an alternative simpler analysis of PRF-security of XORP[w] would be much desired. Recently (in Crypto 2017) Dai et al. introduced a tool, called the χ 2 method, for analyzing PRF-security. Using this tool, the authors have provided a proof of PRF-security of XORP[2] without relying on the mirror theory. In this paper, we resolve the general case; we apply the χ 2 method to obtain a simpler security proof of XORP[w] for any w ≥ 2. For w = 2, we obtain a tighter bound for a wider range of parameters than that of Dai et al.. Moreover, we consider variable width construction XORP[∗] (in which the widths are chosen by adversaries adaptively), and also provide variable output length pseudorandom function (VOLPRF) security analysis for it. As an application of VOLPRF, we propose an authenticated encryption which is a simple variant of CHM or AES-GCM and provides much higher security than those at the cost of one extra blockcipher call for every message. © 2018, Ruhr-Universitat Bochum. All rights reserved.

IACR Transactions on Symmetric Cryptology

Revisiting variable output length XOR pseudorandom function

Very recently (in CRYPTO 2017) Dai, Hoang, and Tessaro have introduced the Chi-square method (χ2 method) which can be applied to obtain an upper bound on the statistical distance between two joint probability distributions. The authors have applied this method to prove the pseudorandom function security (PRF-security) of sum of two random permutations. In this work, we revisit their proof and find a non-trivial gap in the proof. We plug this gap for two specific cases and state the general case as an assumption whose proof is essential for the completeness of the proof by Dai et al. A complete, correct, and transparent proof of the full security of the sum of two random permutations construction is much desirable, especially due to its importance and two decades old legacy. The proposed χ2 method seems to have potential for application to similar problems, where a similar gap may creep into a proof. These considerations motivate us to communicate our observation in a formal way. On the positive side, we provide a very simple proof of the PRF-security of the truncated random permutation construction (a method to construct PRF from a random permutation) using the χ2 method. We note that a proof of the PRF-security due to Stam is already known for this construction in a purely statistical context. However, the use of the χ2 method makes the proof much simpler. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Cryptography and Communications

A note on the chi-square method: A tool for proving cryptographic security

The construction XORP (bitwise-xor of outputs of two independent n-bit random permutations) has gained broad attention over the last two decades due to its high security. Very recently, Dai et al. (CRYPTO’17), by using a method which they term the Chi-squared method (X2 method), have shown n-bit security of XORP when the underlying random permutations are kept secret to the adversary. In this work, we consider the case where the underlying random permutations are publicly available to the adversary. The best known security of XORP in this security game (also known as indifferentiable security) is 2n/3-bit, due to Mennink et al. (ACNS’15). Later, Lee (IEEE-IT’17) proved a better (k-1)n/k -bit security for the general construction XORP[k] which returns the xor of k (≥2) independent random permutations. However, the security was shown only for the cases where k is an even integer. In this paper, we improve all these known bounds and prove full, i.e., n-bit (indifferentiable) security of XORP as well as XORP[k] for any k. Our main result is n-bit security of XORP, and we use the X2 method to prove it. © International Association for Cryptologic Research 2018.

Full indifferentiable security of the Xor of two or more random permutations using the X2 method

In this work, we completely characterize (1) permutation binomials of the form x2n-12t-1+1+ax∈F2n[x],n=2st,a∈F22t∗, and (2) permutation trinomials of the form x2s+1+x2s-1+1+αx∈F2t[x], where s, t are positive integers. The first result, which was our primary motivation, is a consequence of the second result. The second result may be of independent interest. © 2016, Springer Science+Business Media New York.

Designs, Codes, and Cryptography

On some permutation binomials and trinomials over F2n

Indian Statistical Institute, Kolkata

Some Results on Combinatorial Batch Codes and Permutation Binomials over Finite Fields

Combinatorial Batch Codes (CBCs), replication-based variant of Batch Codes introduced by Ishai et al. in [IKOS04], abstracts the following data distribution problem: n data items are to be replicated among m servers in such a way that any k of the n data items can be retrieved by reading at most one item from each server with the total amount of storage over m servers restricted to N. Given parameters m, c, and k, where c and k are constants, one of the challenging problems is to construct c-uniform CBCs (CBCs where each data item is replicated among exactly c servers) which maximizes the value of n. In this work, we present explicit construction of c-uniform CBCs with Ω(mc − 1+ 1/ k) data items. The construction has the property that the servers are almost regular, i. e., number of data items stored in each server is in the range [nc/m −√n/2 ln(4m), nc/m +√n/2 ln(4m)]. The construction is obtained through better analysis and derandomization of the randomized construction presented in [IKOS04]. Analysis reveals almost regularity of the servers, an aspect that so far has not been addressed in the literature. The derandomization leads to explicit construction for a wide range of values of c (for given m and k) where no other explicit construction with similar parameters, i. e., with n = Ω(mc − 1+ 1/ k), is known. Finally, we discuss possibility of parallel derandomization of the construction. © Springer International Publishing Switzerland 2015.

Derandomized construction of combinatorial batch codes

Let n,r,k be positive integers such that 3≤k&lt;n and 2≤r≤k-1. Let m(n,r,k) denote the maximum number of edges an r-uniform hypergraph on n vertices can have under the condition that any collection of i edges spans at least i vertices for all 1≤i≤k. We are interested in the asymptotic nature of m(n,r,k) for fixed r and k as n→∞. This problem is related to the forbidden hypergraph problem introduced by Brown, Erdos, and Sós and very recently discussed in the context of combinatorial batch codes (CBCs). In this short paper we obtain the following results. Using a result due to Erdos we are able to show m(n,r,k)=o(nr) for 7≤k, and 3≤r≤k-1- ⌈logk⌉. This result is best possible with respect to the upper bound on r as we subsequently show through explicit construction that for 6≤k, and k-⌈logk⌉≤r≤k-1,m(n,r,k)=Θ(nr).This explicit construction improves on the non-constructive general lower bound obtained by Brown, Erdos, and Sós for the considered parameter values.For 2-uniform CBCs we obtain the following results. We provide exact value of m(n,2,5) for n≥5.Using a result of Lazebnik et al. regarding maximum size of graphs with large girth, we improve the existing lower bound on m(n,2,k) (Ω(n k+1/k-1)) for all k≥8 and infinitely many values of n.We show m(n,2,k)=O(n1 + 1/⌊k/4⌋) by using a result due to Bondy and Simonovits, and also show m(n,2,k)=Θ(n3/2) for k=6,7,8 by using a result of Kovári, Sós, and Turán. © 2013 Elsevier B.V. All rights reserved.

Discrete Applied Mathematics

On an extremal hypergraph problem related to combinatorial batch codes

Batch codes, introduced by Ishai et al. in [11], are methods for solving the following data storage problem: n data items are to be stored in m servers in such a way that any k of the n items can be retrieved by reading at most t items from each server, and that the total number of items stored in m servers is N. A combinatorial batch code (CBC) is a batch code where each data item is stored without change, i.e., each stored data item is a copy of one of the n data items. One of the basic yet challenging problems is to find optimal CBCs, i.e., CBCs for which total storage (N) is minimal for given values of n, m, k, and t. In [13], Paterson et al. exclusively studied CBCs and gave constructions of some optimal CBCs. In this article, we give a lower bound on the total storage (N) for CBCs. We give explicit construction of optimal CBCs for a range of values of n. For a different range of values of n, we give explicit construction of optimal and almost optimal CBCs. Our results partly settle an open problem of [13]. © 2012 AIMS.

Advances in Mathematics of Communications

Combinatorial batch codes: A lower bound and optimal constructions

Based on a criterion of permutation polynomials of the form x rf(x q-1/m) by Wan and Lidl (1991) and some very elementary techniques we show existence of permutation binomials of the following forms (i) x(x 2n-1/3 + a) ∈ double-struck F 2n[x], for n &gt; 4 (ii) x 22n-1/2n-1+1 + ax = x 2n+2 + ax ∈ double-struck F 22n[x], for n ≥ 3. In (i), we extend a result of Carlitz (1962) for even characteristic. Moreover we present the count of such permutation binomials when a is in a certain subfield of double-struck F 2n. In (ii), we reprove, using much simpler technique, a recent result of Charpin and Kyureghyan (2008) and give the number of permutation binomials of this form. Finally, we discuss some cryptographic relevance of these results. © 2012 Springer-Verlag.