arXiv subjects

Subhamoy Maitra

Publications and source records attributed to Subhamoy Maitra.

At least 19 recordsLinked to original sources

arXiv2025

Quantitative Rule-Based Strategy modeling in Classic Indian Rummy: A Metric Optimization Approach

The 13-card variant of Classic Indian Rummy is a sequential game of incomplete information that requires probabilistic reasoning and combinatorial decision-making. This paper proposes a rule-based framework for strategic play, driven by a new hand-evaluation metric termed MinDist. The metric modifies the MinScore metric by quantifying the edit distance between a hand and the nearest valid configuration, thereby capturing structural proximity to completion. We design a computationally efficient algorithm derived from the MinScore algorithm, leveraging dynamic pruning and pattern caching to exactly calculate this metric during play. Opponent hand-modeling is also incorporated within a two-player zero-sum simulation framework, and the resulting strategies are evaluated using statistical hypothesis testing. Empirical results show significant improvement in win rates for MinDist-based agents over traditional heuristics, providing a formal and interpretable step toward algorithmic Rummy strategy design.

cs.AI↗

arXiv2025

Analysing Skill Predominance in Generalized Fantasy Cricket

In fantasy sports, strategic thinking-not mere luck-often defines who wins and who falls short. As fantasy cricket grows in popularity across India, understanding whether success stems from skill or chance has become both an analytical and regulatory question. This study introduces a new limited-selection contest framework in which participants choose from four expert-designed teams and share prizes based on the highest cumulative score. By combining simulation experiments with real performance data from the 2024 Indian Premier League (IPL), we evaluate whether measurable skill emerges within this structure. Results reveal that strategic and informed team selection consistently outperforms random choice, underscoring a clear skill advantage that persists despite stochastic variability. The analysis quantifies how team composition, inter-team correlation, and participant behaviour jointly influence winning probabilities, highlighting configurations where skill becomes statistically dominant. These findings provide actionable insights for players seeking to maximise returns through strategy and for platform designers aiming to develop fair, transparent, and engaging skill-based gaming ecosystems that balance competition with regulatory compliance.

stat.AP↗

arXiv2025

Cryptographic Backdoor for Neural Networks: Boon and Bane

In this paper we show that cryptographic backdoors in a neural network (NN) can be highly effective in two directions, namely mounting the attacks as well as in presenting the defenses as well. On the attack side, a carefully planted cryptographic backdoor enables powerful and invisible attack on the NN. Considering the defense, we present applications: first, a provably robust NN watermarking scheme; second, a protocol for guaranteeing user authentication; and third, a protocol for tracking unauthorized sharing of the NN intellectual property (IP). From a broader theoretical perspective, borrowing the ideas from Goldwasser et. al. [FOCS 2022], our main contribution is to show that all these instantiated practical protocol implementations are provably robust. The protocols for watermarking, authentication and IP tracking resist an adversary with black-box access to the NN, whereas the backdoor-enabled adversarial attack is impossible to prevent under the standard assumptions. While the theoretical tools used for our attack is mostly in line with the Goldwasser et. al. ideas, the proofs related to the defense need further studies. Finally, all these protocols are implemented on state-of-the-art NN architectures with empirical results corroborating the theoretical claims. Further, one can utilize post-quantum primitives for implementing the cryptographic backdoors, laying out foundations for quantum-era applications in machine learning (ML).

cs.CR↗

arXiv2025

On Construction of Approximate Real Mutually Unbiased Bases for an infinite class of dimensions $d \not\equiv 0 \bmod 4$

It is known that real Mutually Unbiased Bases (MUBs) do not exist for any dimension $d > 2$ which is not divisible by 4. Thus, the next combinatorial question is how one can construct Approximate Real MUBs (ARMUBs) in this direction with encouraging parameters. In this paper, for the first time, we show that it is possible to construct $> \lceil \sqrt{d} \rceil$ many ARMUBs for certain odd dimensions $d$ of the form $d = (4n-t)s$, $t = 1, 2, 3$, where $n$ is a natural number and $s$ is an odd prime power. Our method exploits any available $4n \times 4n$ real Hadamard matrix $H_{4n}$ (conjectured to be true) and uses this to construct an orthogonal matrix ${Y}_{4n-t}$ of size $(4n - t) \times (4n - t)$, such that the absolute value of each entry varies a little from $\frac{1}{\sqrt{4n-t}}$. In our construction, the absolute value of the inner product between any pair of basis vectors from two different ARMUBs will be $\leq \frac{1}{\sqrt{d}}(1 + O(d^{-\frac{1}{4}})) < 2$, for proper choices of parameters, the class of dimensions $d$ being infinitely large.

cs.DM↗

arXiv2025

Extending Forrelation: Quantum Algorithms Related to Generalized Fourier-Correlation

In this paper, we study different cryptographically significant spectra of Boolean functions, including the Walsh-Hadamard, cross-correlation, and autocorrelation. The $2^k$-variation by Stanica [IEEE-IT 2016] is considered here with the formulation for any $m \in \mathbb{N}$. Given this, we present the most generalized version of the Deutsch-Jozsa algorithm, which extends the standard and previously extended versions, thereby encompassing them as special cases. Additionally, we generalize the Forrelation formulation by introducing the $m$-Forrelation and propose various quantum algorithms towards its estimation. In this regard, we explore different strategies in sampling these newly defined spectra using the proposed $m$-Forrelation algorithms and present a comparison of their corresponding success probabilities. Finally, we address the problem related to affine transformations of generalized bent functions and discuss quantum algorithms in identifying the shifts between two bent (or negabent) functions with certain modifications, and compare these with existing results.

quant-ph↗

arXiv2025

On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over $\mathbb{R}$

Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain affine algebraic variety. This variety comes from the relations that determine the extendability of a system of MUBs. Finally, we show that some part of this variety gives rise to complete intersection domains. Further, we show that there is a one-to-one correspondence between MUBs and the maximal commuting classes (bases) of orthogonal normal matrices in $\mathcal M_n({\mathbb{C}})$. It means that for $m$ MUBs in $C^n$, there are $m$ commuting classes, each consisting of $n$ commuting orthogonal normal matrices and the existence of maximal commuting basis for $\mathcal M_n({\mathbb{C}})$ ensures the complete set of MUBs in $\mathcal M_n({\mathbb{C}})$.

cs.DM↗

arXiv2025

Optimal T depth quantum circuits for implementing arbitrary Boolean functions

In this paper we present a generic construction to obtain an optimal T depth quantum circuit for any arbitrary $n$-input $m$-output Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}^m$ having algebraic degree $k\leq n$, and it achieves an exact Toffoli (and T) depth of $\lceil \log_2 k \rceil$. This is a broader generalization of the recent result establishing the optimal Toffoli (and consequently T) depth for multi-controlled Toffoli decompositions (Dutta et al., Phys. Rev. A, 2025). We achieve this by inspecting the Algebraic Normal Form (ANF) of a Boolean function. Obtaining a benchmark for the minimum T depth of such circuits are of prime importance for efficient implementation of quantum algorithms by enabling greater parallelism, reducing time complexity, and minimizing circuit latency, making them suitable for near-term quantum devices with limited coherence times. The implications of our results are highlighted explaining the provable lower bounds on S-box and block cipher implementations, for example AES.

quant-ph↗

arXiv2025

Linear Decomposition of the Majority Boolean Function using the Ones on Smaller Variables

A long-investigated problem in circuit complexity theory is to decompose an $n$-input or $n$-variable Majority Boolean function (call it $M_n$) using $k$-input ones ($M_k$), $k < n$, where the objective is to achieve the decomposition using fewest $M_k$'s. An $\mathcal{O}(n)$ decomposition for $M_n$ has been proposed recently with $k=3$. However, for an arbitrary value of $k$, no such construction exists even though there are several works reporting continual improvement of lower bounds, finally achieving an optimal lower bound $\Omega(\frac{n}{k}\log k)$ as provided by Lecomte et. al., in CCC '22. In this direction, here we propose two decomposition procedures for $M_n$, utilizing counter trees and restricted partition functions, respectively. The construction technique based on counter tree requires $\mathcal{O}(n)$ such many $M_k$ functions, hence presenting a construction closest to the optimal lower bound, reported so far. The decomposition technique using restricted partition functions present a novel link between Majority Boolean function construction and elementary number theory. These decomposition techniques close a gap in circuit complexity studies and are also useful for leveraging emerging computing technologies.

cs.LO↗

arXiv2025

On Exact Space-Depth Trade-Offs in Multi-Controlled Toffoli Decomposition

In this paper, we consider the optimized implementation of Multi Controlled Toffoli (MCT) using the Clifford $+$ T gate sets. While there are several recent works in this direction, here we explicitly quantify the trade-off (with concrete formulae) between the Toffoli depth (this means the depth using the classical 2-controlled Toffoli) of the $n$-controlled Toffoli (hereform we will tell $n$-MCT) and the number of clean ancilla qubits. Additionally, we achieve a reduced Toffoli depth (and consequently, T-depth), which is an extension of the technique introduced by Khattar et al. (2024). In terms of a negative result, we first show that using such conditionally clean ancilla techniques, Toffoli depth can never achieve exactly $\ceil{\log_2 n}$, though it remains of the same order. This highlights the limitation of the techniques exploiting conditionally clean ancilla [Nie et al., 2024, Khattar et al., 2024]. Then we prove that, in a more general setup, the T-Depth in the Clifford + T decomposition, via Toffoli gates, is lower bounded by $\ceil{\log_2 n}$, and this bound is achieved following the complete binary tree structure. Since the ($2$-controlled) Toffoli gate can further be decomposed using Clifford $+$ T, various methodologies are explored too in this regard for trade-off related implications.

quant-ph↗

arXiv2024

Skill vs. Chance Quantification for Popular Card & Board Games

This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from four popular games Chess, Rummy, Ludo, and Teen Patti, using empirical win statistics across varying levels of experience. By modeling win rate as a function of experience through a regression framework and employing empirical bootstrap resampling, we estimate the degree to which outcomes improve with repeated play. To summarize these dynamics, we propose a flexible skill score that emphasizes learning over initial performance, aligning with practical and regulatory interpretations of skill. Our results reveal a clear ranking, with Chess showing the highest skill component and Teen Patti the lowest, while Rummy and Ludo fall in between. The proposed framework is transparent, reproducible, and adaptable to other game formats and outcome metrics, offering potential applications in legal classification, game design, and player performance analysis.

cs.GT↗

arXiv2024

SecureVAX: A Blockchain-Enabled Secure Vaccine Passport System

A vaccine passport serves as documentary proof, providing passport holders with greater freedom while roaming around during pandemics. It confirms vaccination against certain infectious diseases like COVID-19, Ebola, and flu. The key challenges faced by the digital vaccine passport system include passport forgery, unauthorized data access, and inaccurate information input by vaccination centers. Privacy concerns also need to be addressed to ensure that the user's personal identification information (PII) is not compromised. Additionally, it is necessary to track vaccine vials or doses to verify their authenticity, prevent misuse and illegal sales, as well as to restrict the illicit distribution of vaccines. To address these challenges, we propose a Blockchain-Enabled Secure Vaccine Passport System, leveraging the power of smart contracts. Our solution integrates off-chain and on-chain cryptographic computations, facilitating secure communication among various entities. We have utilized the InterPlanetary File System (IPFS) to store encrypted vaccine passports of citizens securely. Our prototype is built on the Ethereum platform, with smart contracts deployed on the Sepolia Test network, allowing for performance evaluation and validation of the system's effectiveness. By combining IPFS as a distributed data storage platform and Ethereum as a blockchain platform, our solution paves the way for secure, efficient, and globally interoperable vaccine passport management, supporting comprehensive vaccination initiatives worldwide.

cs.CR↗

arXiv2024

Almost Perfect Mutually Unbiased Bases that are Sparse

In dimension $d$, Mutually Unbiased Bases (MUBs) are a collection of orthonormal bases over $\mathbb{C}^d$ such that for any two vectors $v_1, v_2$ belonging to different bases, the scalar product $|\braket{v_1|v_2}| = \frac{1}{\sqrt{d}}$. The upper bound on the number of such bases is $d+1$. Constructions to achieve this bound are known when $d$ is some power of prime. The situation is more restrictive in other cases and also when we consider the results over real rather than complex. Thus, certain relaxations of this model are considered in literature and consequently Approximate MUBs (AMUB) are studied. This enables one to construct potentially large number of such objects for $\mathbb{C}^d$ as well as in $\mathbb{R}^d$. In this regard, we propose the concept of Almost Perfect MUBs (APMUB), where we restrict the absolute value of inner product $|\braket{v_1|v_2}|$ to be two-valued, one being 0 and the other $ \leq \frac{1+\mathcal{O}(d^{-λ})}{\sqrt{d}}$, such that $λ> 0$ and the numerator $1 + \mathcal{O}(d^{-λ}) \leq 2$. Each such vector constructed, has an important feature that large number of its components are zero and the non-zero components are of equal magnitude. Our techniques are based on combinatorial structures related to RBDs. We show that for several composite dimensions $d$, one can construct $\mathcal{O}(\sqrt{d})$ many APMUBs, in which cases the number of MUBs are significantly small. To be specific, this result works for $d$ of the form $(q-e)(q+f), \ q, e, f \in \mathbb{N}$, with the conditions $0 \leq f \leq e$ for constant $e, f$ and $q$ some power of prime. We also show that such APMUBs provide sets of Bi-angular vectors which are $\mathcal{O}(d^{\frac{3}{2}})$ in numbers, having high angular distances among them. Finally, as the MUBs are equivalent to a set of Hadamard matrices, we show that the APMUBs are so with the set of Weighing matrices.

cs.DM↗

arXiv2024

Further Constructions of AMUBs for Non-prime power Composite Dimensions

Construction of a large class of Mutually Unbiased Bases (MUBs) for non-prime power composite dimensions ($d = k\times s$) is a long standing open problem, which leads to different construction methods for the class Approximate MUBs (AMUBs) by relaxing the criterion that the absolute value of the dot product between two vectors chosen from different bases should be $\leq \fracβ{\sqrt{d}}$. In this chapter, we consider a more general class of AMUBs (ARMUBs, considering the real ones too), compared to our earlier work in [Cryptography and Communications, 14(3): 527--549, 2022]. We note that the quality of AMUBs (ARMUBs) constructed using RBD$(X,A)$ with $|X|= d$, critically depends on the parameters, $|s-k|$, $μ$ (maximum number of elements common between any pair of blocks), and the set of block sizes. We present the construction of $\mathcal{O}(\sqrt{d})$ many $β$-AMUBs for composite $d$ when $|s-k|< \sqrt{d}$, using RBDs having block sizes approximately $\sqrt{d}$, such that $|\braket{ψ^l_i|ψ^m_j}| \leq \fracβ{\sqrt{d}}$ where $β= 1 + \frac{|s-k|}{2\sqrt{d}}+ \mathcal{O}(d^{-1}) \leq 2$. Moreover, if real Hadamard matrix of order $k$ or $s$ exists, then one can construct at least $N(k)+1$ (or $N(s)+1$) many $β$-ARMUBs for dimension $d$, with $β\leq 2 - \frac{|s-k|}{2\sqrt{d}}+ \mathcal{O}(d^{-1})< 2$, where $N(w)$ is the number of MOLS$(w)$. This improves and generalizes some of our previous results for ARMUBs from two points, viz., the real cases are now extended to complex ones too. The earlier efforts use some existing RBDs, whereas here we consider new instances of RBDs that provide better results. Similar to the earlier cases, the AMUBs (ARMUBs) constructed using RBDs are in general very sparse, where the sparsity $(ε)$ is $1 - \mathcal{O}(d^{-\frac{1}{2}})$.

cs.DM↗

arXiv2023

Analysis of Boolean Functions Related to Binary Input Binary Output Two-party Nonlocal Games

The famous CHSH game can be interpreted with Boolean functions while understanding the success probability in the classical scenario. In this paper, we have exhaustively studied all the Boolean functions on four variables to express binary input binary output two-party nonlocal games and explore their performance in both classical and quantum scenarios. Our analysis finds out some other games (other than the CHSH game) which offer a higher success probability in the quantum scenario as compared to the classical one. Naturally, our study also notes that the CHSH game (and the games corresponding to the similar partition) is the most efficient in terms of separation between quantum and classical techniques.

quant-ph↗

arXiv2022

Improved and Formal Proposal for Device Independent Quantum Private Query

In this paper, we propose a novel Quantum Private Query (QPQ) scheme with full Device-Independent certification. To the best of our knowledge, this is the first time we provide such a full DI-QPQ scheme using EPR-pairs. Our proposed scheme exploits self-testing of shared EPR-pairs along with the self-testing of projective measurement operators in a setting where the client and the server do not trust each other. To certify full device independence, we exploit a strategy to self-test a particular class of POVM elements that are used in the protocol. Further, we provide formal security analysis and obtain an upper bound on the maximum cheating probabilities for both the dishonest client as well as the dishonest server.

quant-ph↗

arXiv2021

On Boolean Functions with Low Polynomial Degree and Higher Order Sensitivity

Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial degree and high sensitivity. It is well known that the polynomial degree of of a Boolean function and its resiliency are directly connected. Using this connection we analyze the polynomial degree-sensitivity values through the lens of resiliency, demonstrating existence and non-existence results of functions with low polynomial degree and high sensitivity on small number of variables (upto 10). In this process, borrowing an idea from complexity theory, we show that one can implement resilient Boolean functions on a large number of variables with linear size and logarithmic depth. Finally, we extend the notion of sensitivity to higher order and note that the existing construction idea of Nisan and Szegedy (1994) can provide only constant higher order sensitivity when aiming for polynomial degree of $n-ω(1)$. In this direction, we present a construction with low ($n-ω(1)$) polynomial degree and super-constant $ω(1)$ order sensitivity exploiting Maiorana-McFarland constructions, that we borrow from construction of resilient functions. The questions we raise identify novel combinatorial problems in the domain of Boolean functions.

cs.CC↗

arXiv2021

Exact Quantum Query Algorithms Outperforming Parity -- Beyond The Symmetric functions

In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two bits can be obtained by a single query. Thus, exact quantum query algorithms outperforming parity decision trees are rare. In this paper we first obtain optimal exact quantum query algorithms ($Q_{algo}(f)$) for a direct sum based class of $Ω\left( 2^{\frac{\sqrt{n}}{2}} \right)$ non-symmetric functions. We construct these algorithms by analyzing the algebraic normal form together with a novel untangling strategy. Next we obtain the generalized parity decision tree complexity ($D_{\oplus}(f)$) analysing the Walsh Spectrum. Finally, we show that query complexity of $Q_{algo}$ is $\lceil \frac{3n}{4} \rceil$ whereas $D_{\oplus}(f)$ varies between $n-1$ and $\lceil \frac{3n}{4} \rceil+1$ for different classes, underlining linear separation between the two measures in many cases. To the best of our knowledge, this is the first family of algorithms beyond generalized parity (and thus parity) for a large class of non-symmetric functions. We also implement these techniques for a larger (doubly exponential in $\frac{n}{4}$) class of Maiorana-McFarland type functions, but could only obtain partial results using similar algorithmic techniques.

quant-ph↗

arXiv2021

Following Forrelation -- Quantum Algorithms in Exploring Boolean Functions' Spectra

Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al, 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation spectrum and the autocorrelation spectrum. We introduce the existing 2-fold Forrelation formulation with bent duality based promise problems as desirable instantiations. Next we concentrate on the $3$-fold version through two approaches. First, we judiciously set-up some of the functions in $3$-fold Forrelation, so that given an oracle access, one can sample from the Walsh Spectrum of $f$. Using this, we obtain improved results than what we obtain from the Deutsch-Jozsa algorithm, and in turn it has implications in resiliency checking. Furthermore, we use similar idea to obtain a technique in estimating the cross-correlation (and thus autocorrelation) value at any point, improving upon the existing algorithms. Finally, we tweak the quantum algorithm with superposition of linear functions to obtain a cross-correlation sampling technique. To the best of our knowledge, this is the first cross-correlation sampling algorithm with constant query complexity. This also provides a strategy to check if two functions are uncorrelated of degree $m$. We further modify this using Dicke states so that the time complexity reduces, particularly for constant values of $m$.

quant-ph↗