@phdthesis {27697,
	title = {Hard Mathematical Problems in Cryptography and Coding Theory},
	year = {2020},
	author = {Varadharajan, Srimathi}
}
@inproceedings {27705,
	title = {Graphs and Self-dual additive codes over GF(4)},
	journal = {The Eleventh International Workshop on Coding and Cryptography},
	year = {2019},
	abstract = {We initiate the study of self-dual codes over GF(4) whose corresponding graphs have fixed rankwidth. We show that by combining the structural properties of rankwidth 1 graphs, the classification of corresponding codes becomes significantly faster.
We give a new algorithm for computing weight enumerators using Binary Decision Diagrams (BDD), which has similar complexity to brute force O(2^k) but has the benefit that we automatically get complexity O(2^min{k,n-k}) (for k > n/2) without needing to consider the dual code.
We show that the minimum distance of a code is at least 3 if and only if the corresponding graph does not contain any pendant vertex or any twin-pairs. We also give an algorithm for computing an approximate minimum distance in codes corresponding to general graphs.},
	keywords = {binary decision diagram, Minimum Distance, Rankwidth, Self-dual, Stabilizer Code},
	author = {Kumar, Mithilesh and Varadharajan, Srimathi and Raddum, H{\r a}vard}
}
@article {27708,
	title = {Reducing Lattice Enumeration Search Trees},
	journal = {Infocommunications Journal},
	volume = {11},
	year = {2019},
	month = {12/2019},
	pages = {8-16},
	publisher = {The scientific association for infocommunications},
	address = {Budapest, Hungary},
	abstract = {We revisit the standard enumeration algorithm for finding the shortest vectors in a lattice, and study how the number of nodes in the associated search tree can be reduced. Two approaches for reducing the number of nodes are suggested. First we show that different permutations of the basis vectors have a big effect on the running time of standard enumeration, and give a class of permutations that give relatively few nodes in the search tree. This leads to an algorithm called hybrid enumeration that has a better running time than standard enumeration when the lattice is large. Next we show that it is possible to estimate the signs of the coefficients yielding a shortest vector, and that a pruning strategy can be based on this fact. Sign-based pruning gives fewer nodes in the search tree, and never missed the shortest vector in the experiments we did.},
	keywords = {enumeration, Lattices, pruning, SVP problem},
	issn = {2061-2079},
	doi = {10.36244/ICJ.2019.4.2},
	author = {Kumar, Mithilesh and Raddum, H{\r a}vard and Varadharajan, Srimathi}
}
@article {26355,
	title = {Factorization using binary decision diagrams},
	journal = {Cryptography and Communications},
	volume = {11},
	year = {2018},
	month = {2018},
	pages = {1-18},
	publisher = { Springer},
	abstract = {We address the factorization problem in this paper: Given an integer\&nbsp;N=pq, find two factors\&nbsp;p\&nbsp;and\&nbsp;q\&nbsp;of\&nbsp;N\&nbsp;such that\&nbsp;p\&nbsp;and\&nbsp;q\&nbsp;are of same bit-size. When we say integer multiplication of\&nbsp;N, we mean expressing\&nbsp;N\&nbsp;as a product of two factors\&nbsp;p\&nbsp;and\&nbsp;q\&nbsp;such that\&nbsp;p\&nbsp;and\&nbsp;q\&nbsp;are of\&nbsp;same bit-size. We work on this problem in the light of Binary Decision Diagrams (BDD). A Binary Decision Diagram is an acyclic graph which can be used to represent Boolean functions. We represent integer multiplication of\&nbsp;N\&nbsp;as product of factors\&nbsp;p\&nbsp;and\&nbsp;q\&nbsp;using a BDD. Using various operations on the BDD we present an algorithm for factoring\&nbsp;N. All calculations are done over\&nbsp;GF(2). We show that the number of nodes in the constructed BDD is\&nbsp;O(n3)\&nbsp;where\&nbsp;n\&nbsp;is the number of bits in\&nbsp;p\&nbsp;or\&nbsp;q. We do factoring experiments for the case when\&nbsp;p\&nbsp;and\&nbsp;q\&nbsp;are primes as in the case of RSA modulus\&nbsp;N, and report on the observed complexity. The multiplication of large RSA numbers (that cannot be factored fast in practice) can still be easily represented as a BDD.},
	keywords = {Binary decision diagrams, Integer factorization, RSA},
	issn = {1936-2447},
	doi = {10.1007/s12095-018-0304-7},
	url = {https://link.springer.com/article/10.1007/s12095-018-0304-7},
	author = {Raddum, H{\r a}vard and Varadharajan, Srimathi}
}
