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For Transformer models, cryptographically secure inference ensures that the client learns only the final output, while the server learns nothing about the client's input. However, securely computing nonlinear layers remains a major…

We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\alpha=M/N$ close to the…

Large language models (LLMs) can detect software vulnerabilities, but how do they actually identify vulnerable code? We address this question using mechanistic interpretability; analyzing the internal computations of a neural network to…

In this paper we present an improved version of HF-hash, viz., GB-hash : Hash Functions Using Groebner Basis. In case of HF-hash, the compression function consists of 32 polynomials with 64 variables which were taken from the first 32…

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…

In a world heavily loaded by information, there is a great need for keeping specific information secure from adversaries. The rapid growth in the research field of lightweight cryptography can be seen from the list of the number of…

The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…

In this paper we present an algorithm to compute keyed hash function (message authentication code MAC). Our approach uses a family of expander graphs of large girth denoted $D(n,q)$, where $n$ is a natural number bigger than one and $q$ is…

Perceptual hashing algorithms (PHAs) are widely used for identifying illegal online content and are thus integral to various sensitive applications. However, due to their hasty deployment in real-world scenarios, their adversarial security…

We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and privacy amplification for secret key generation. The security functions are…

This thesis introduces a formal general framework for scaling blockchain protocols by sharding. The framework is modular and it can be adjusted for different needs or sets of assumptions. We prove that sharded protocols obtained by…

Two recent Hill cipher modifications which iteratively use interweaving and interlacing are considered. We show that strength of these ciphers is due to non-linear transformation used in them (bit-level permutations). Impact of number of…

Property-preserving hash functions allow for compressing long inputs $x_0$ and $x_1$ into short hashes $h(x_0)$ and $h(x_1)$ in a manner that allows for computing a predicate $P(x_0, x_1)$ given only the two hash values without having…

Linear hashes are known to possess error-correcting capabilities. However, in most applications, non-linear hashes with pseudorandom outputs are utilized instead. It has also been established that classical non-systematic random codes, both…

We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…

One of the major open problems in symmetric cryptanalysis is to discover new specif i c types of invariant properties which can hold for a larger number of rounds of a block cipher. We have Generalised Linear Cryptanalysis (GLC) and…

Bipartite graph hashing (BGH) is extensively used for Top-K search in Hamming space at low storage and inference costs. Recent research adopts graph convolutional hashing for BGH and has achieved the state-of-the-art performance. However,…

Proving that a cryptographic protocol is correct for secrecy is a hard task. One of the strongest strategies to reach this goal is to show that it is increasing, which means that the security level of every single atomic message exchanged…

Reliability has emerged as a key topic of interest for researchers around the world to detect and/or mitigate the side effects of decreasing transistor sizes, such as soft errors. Traditional solutions, like DMR and TMR, incur significant…

A cornerstone theorem in the Graph Minors series of Robertson and Seymour is the result that every graph $G$ with no minor isomorphic to a fixed graph $H$ has a certain structure. The structure can then be exploited to deduce far-reaching…