Title of the talk: Algebraic and Combinatorial Approaches to Secure Authentication, Encryption, and Verifiable Secret Sharing

Date, Time & Venue: 21 May 2026 at 11:00 A.M on Seminar room, Dept. of Mathematics

Abstract: This research seminar outlines technical contributions from my doctoral and postdoctoral tenures. The presentation integrates results on the tight security of existing and new message authentication codes (MACs), established via extensions of Patarin's Mirror Theory. These improvements are achieved through a novel graph-theoretic treatment of affine bivariate equations and non-equations in GF(2^n) providing the framework for deriving tight security bounds. We begin with the design and analysis of the nonce-based Enhanced Hash-then-Mask (nEHtM) MAC, which achieves gracefully degrading security in the presence of faulty nonces, and its application in the CWC+ AE mode. The discussion proceeds to public random permutation-based constructions, including PDMMAC, PEDM, and pDbHtS Plus. We subsequently examine the security of the classical block cipher-based Double-Block Hash-then-Sum (DbHtS) in multi-user environments.

Moving on to Authenticated Encryption (AE), we investigate security concepts regarding the release of unverified plaintext. This work provides refined definitions for plaintext awareness to resolve ambiguities and introduces a formalization for valid configurations. Within this framework, we evaluate two of the three block cipher modes of operation: Encrypt-and-MAC and Encrypt-then-MAC. Beyond classical security, we analyze post-quantum resilience in the Q1 random oracle model, focusing on the Ascon authenticated encryption mode and Key-Alternating Feistel (KAF) ciphers. For the NIST lightweight standard Ascon, I establish a post-quantum security bound of min{2^(c/3), 2^(k/2)} against block-wise adaptive adversaries. Similarly, I prove post-quantum PRP and SPRP security for 3-round and 4-round KAFs, with advantage bounds of at most p√(q/2^n) or q√(p/2^n).

Finally, I present research on ramp-type verifiable secret sharing, where we developed an ε-almost access structure hiding scheme that is simultaneously verifiable and frameproof. My future research focuses on the post-quantum algebraic security of lightweight schemes such as Romulus, GIFT-COFB, and Saturnin. For both symmetric as well as asymmetric cryptographic schemes, I intend to characterize the growth of the algebraic degree in permutations and analyze the Algebraic Normal Form (ANF) under superposition queries. Furthermore, I will investigate Fourier analysis over finite Abelian groups for refining quantum query complexity bounds. I am also interested in evaluating alternative frameworks in combinatorial secret sharing for IoT, integrated with blockchain and threshold encryption. I look forward to collaborating with departmental colleagues specialising in cryptographic Boolean functions and extremal combinatorics. In support of the National Quantum Mission, I intend to apply for various research grants. I conclude with a list of proposed courses for the Department of Mathematics.

About the Speaker: Dr. Suprita Subhash Talnikar is currently a Visiting Scientist at the Applied Statistics Unit of the Indian Statistical Institute, Kolkata. Dr. Talnikar earned her Ph.D. in Computer Science from ISI Kolkata in 2023, during which she worked on provable security in symmetric-key cryptography. This was preceded by an M.Sc. in Mathematics from VNIT Nagpur. Her research expertise lies at the intersection of discrete mathematics and theoretical cryptology, specifically focusing on provable security, extended Mirror Theory, post-quantum security, combinatorial secret sharing and applications to the Internet of Things. She has held a post-doctoral position under Professor Joan Daemen and Professor Bart Mennink at Radboud University in the Netherlands, and under Professor Kouichi Sakurai at Kyushu University in Japan.