Algebraic attacks constitute an effective class of cryptanalytic attacks which have come up recently. In algebraic attacks, the relations between the input, output and the key are expressed as a system of equations and ...

In this thesis, we investigate in detail, certain important problems in cryptography and coding theory. In the first part of this thesis, we discuss the number field sieve and compare the two ways in which the sieving ...

This thesis introduces a new mathematical object: collection of arithmetic progressions with elements satisfying the inverse property, \j-th terms of i-th and (i+1)-th progressions are multiplicative inverses of each other ...

Secure multiparty computation (MPC) allows n distrustful parties to jointly compute a function on their inputs while keeping their inputs private. The distrust is modelled as an adversary that controls up to t parties and ...

As an alternative to performing analytics in the clear, there is an increasing demand for developing privacy-preserving solutions that aim to protect sensitive data while still allowing for its efficient analysis. Among ...

In the era of digitalization, data privacy and integrity are of utmost importance. Secure multiparty computation (MPC) and zero-knowledge (ZK) facilitate data privacy and integrity. MPC enables privacy-preserving collaborative ...

Non-malleable secret sharing (NMSS) schemes, introduced by Goyal and Kumar (STOC 2018), ensure that a secret m can be distributed into shares m1,...,mn (for some n), such that any t (a parameter <= n) shares can be ...

Cryptographic techniques are essential for the security of communication in modern society. Today, nearly all public key cryptographic schemes used in practice are based on the two problems of factoring large integers and ...

In secure multi-party computation (MPC), n parties wish to jointly perform a computation on their private inputs in a secure way, so that no adversary corrupting a subset of the parties can learn more information than their ...

Zero-Knowledge Proofs (ZKPs) are fundamental cryptographic tools enabling a prover to convince a verifier about the knowledge of a secret witness related to a public statement, without revealing any information beyond the ...