*Topics in Mathematics and Computer Science related to Cryptography and Information Security *

*March 16, 2020 - Cancelled*

**Speaker:** Tovohery Hajatiana Randrianarisoa, Florida Atlantic University

**Title**
**:** A geometric approach to rank metric codes

**Abstract**
**:** Generalized weights are important parameters of rank metric codes. The 1st generalized rank weight which is nothing else than the minimum rank distance of the code is important when the codes are used in code-based public-key cryptosystems. The more general r-the generalized rank weights describe the security drop when a rank metric code is used in wiretap network coding. In this talk, I present a different approach to study the generalized weights of rank metric codes and show that the approach helps to easily describe the property of constant rank weight codes.

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March 2, 2020, SE-43, Room 215; 4:00 p.m.
**

**Speaker**
**:** Roger Wiegand, University of Nebraska

**Title**
**:** Iterated blowups of two-dimensional regular local rings

**Abstract**
**:** A major component of the resolution of surface singularities is the blowing up of singular points on the surface. It turns out that blowing up yields interesting results even when the surface is smooth. In this talk we will discuss two types of blowups, say, A and B. In either case, we start with a field F and two algebraically independent elements a and b. We write F[a,b]__ for the local ring obtained by inverting the elements of F[a,b] that are not in the maximal ideal (a,b). Type A replaces the ring F[a,b]__ by the ring F[a,b/a]__ , and type B replaces the ring F[a,b]__ by F[a/b,b]__ . Suppose we have a sequence of positive integers [a_0,a_1,a_2,…]. We start with the localized polynomial ring F[x,y]__ and do A a_0 times, then B a_1 times, then A a_2 times, then B a_3 times, and so on. This gives an infinite strictly increasing chain of rings, all with the same quotient field F(x,y). It is known that the union V of these rings is a valuation ring. I will show that the value group of this ring is Z + Zg, where Z is the additive group of integers and g is the irrational number obtained as the value of the continued fraction represented by the given sequence. This is joint work with Sylvia Wiegand and was inspired by discussions we had with Karen Smith back in 1996. This work has considerable overlap with Mark Spivakovsky’s Ph.D. thesis and with more recent work by Karen’s Ph.D. students David Bruce, Molly Logue, and Robert Walker.

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February 24, 2020, SE-43, Room 215; 4:00 p.m.
**

**Speaker:** Floyd Johnson, Florida Atlantic University

**Title**: An Introduction to Quantum Key Distribution

**Abstract:** Quantum mechanics was one of the greatest scientific breakthroughs of the last century with applications still being found. Since the 1970’s mathematicians and physicists have been exploring how quantum mechanics can be used in cryptography to achieve previously thought impossible results. In this talk, we will give an overview of the problem of key establishment and how quantum phenomena can be used to achieve a secure key establishment.

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February 10, 2020, SE-43, Room 215; 4:00 p.m.
**

**Speaker**
**:** Ryann Cartor, Clemson University

**Title**
**:** All in the C* Family

**Abstract**
**:** The cryptosystem C*, first proposed and studied by Matsumoto and Imai and introduced in EUROCRYPT '88, is the predecessor of all of the so-called "big field'' schemes of multivariate cryptography. This scheme has since been broken, which has led to the introduction of modifiers. The introduction of the numerous modifiers of multivariate schemes has produced several variants that stay faithful to the central structure of the original. From the tumultuous history of C* derivatives, we now see only a very few survivors in the cryptonomy. In this work, we revisit the roots of multivariate cryptography, investigating the viability of C* schemes, in general, under the entire multidimensional array of the principal modifiers. We reveal that there is a nontrivial space of combinations of modifiers that produce viable schemes resistant to all known attacks. This solution space of seemingly secure C* variants offers trade-offs in multiple dimensions of performance, revealing a family that can be optimized for disparate applications.

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January 27, 2020, SE-43, Room 215; 4:00 p.m.
**

**Speaker**
**:** Shaun Miller, Florida Atlantic University

**Title**
**:** Behavior of a Lattice Basis During Reduction

**Abstract**
**:** Lattice reduction algorithms aim to produce short, almost orthogonal basis vectors. Theoretical estimates are given for the expected behavior of a basis vector's length during reduction. These estimates will be compared to the lengths obtained experimentally after a brief introduction to the motivation behind lattice-based cryptanalysis.

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December 2, 2019, SE-43, Room 215; 4:00 p.m.
**

Speaker: Paolo Santini, Università Politecnica delle Marche

Title: Reaction attacks on cryptosystems based on codes with sparse parity-checks

Abstract: The concept of sparsity is central in code-based cryptography: hard problems from coding theory are based on the difficulty of finding vectors with a small weight, satisfying some given relations. Furthermore, codes with a sparse representation admit efficient decoding algorithms and seem to be natural candidates for cryptographic schemes. However, currently known decoding techniques are characterized by some failure probability, which can be exploited by an adversary to mount so-called reaction attacks. In this talk, I will speak about Low-Density Parity-Check (LDPC) codes and Low-Rank Parity-Check (LRPC) codes, two families of codes that, despite being defined over different metrics, share many similarities. I will briefly describe how such codes can be decoded, how they can be used to instantiate cryptosystems and how such schemes can be attacked through reaction attacks.

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November 18, 2019, SE-43, Room 215; 4:00 p.m.
**

**Speaker**
: Tran Ngo, Florida Atlantic University

**Title**
**:** Mersenne Cryptography system

**Abstract**
**:** In this talk, I will present a cryptosystem based on Mersenne Numbers by Divesh Aggarwal, Antoine Joux, Anupam Prakash, and Miklos Santha in May 2017. The scheme was attacked by [BCGN17] and [dBDJdW17] several months later, and it was reintroduced in November 2017.

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November 4, 2019, SE-43, Room 215; 4:00 p.m.
*

**Speaker:** Abhraneel Dutta, Florida Atlantic University

**Title:** A New Elliptic Curve Scalar Multiplication Algorithm

**Abstract:** Cryptographic applications of elliptic curve scalar multiplication can be widely seen in the Diffie-Hellman key exchange and elliptic curve digital signature algorithms. I will first review some basic algorithms for scalar multiplication and explain how some of the irregularities in these algorithms can be exploited by side-channel attacks. Second, I will introduce the signed digit representation of scalars and signed aligned column (SAC) encoding algorithms. These algorithms provide some protection against simple power analysis attacks but are limited in the sense that they are based on the binary representation of scalars. In the last part of my talk, I will present our work on the full generalization of signed digit representations and SAC encodings. I will discuss some theoretical results and evaluate them in a cryptographic setting.

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October 21, 2019, SE-43, Room 215; 4:00 p.m.
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October 7, 2019, SE-43, Room 215; 4:00 p.m.
*

**Speaker**: Shaun Miller, Florida Atlantic University

**Title:** A brief introduction to quantum circuits

**Abstract:** To implement quantum algorithms like Shor's and Grover's, we need to be able to translate classical loops to quantum circuits. I will give an introduction to bra-ket notation as well as quantum circuits. We will use this knowledge to translate a classical while loop into a conditioned quantum loop.

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September 23, 2019, SE-43, Room 215; 4:00 p.m.
*

**Speaker**
**:** Edoardo Persichetti, Florida Atlantic University

**Title**
: Research Challenges in Code-Based Cryptography

**Abstract**
**:** In this talk, I will present the area of code-based cryptography, one of the most active and exciting areas of research within post-quantum cryptography. After a brief introduction, I will discuss some research avenues and open problems. Everyone welcome!

*
September 9, 2019, SE-43, Room 215; 4:00 p.m.
*

**Speaker**: Shi Bai, Florida Atlantic University

**Title:** Lattice attacks for variants of LWE

**Abstract:** The learning with errors (LWE) problem introduced by Regev (STOC'05) is one of the fundamental problems in lattice-based cryptography. It has been used extensively as a security foundation, for public-key encryption, signatures, fully homomorphic encryption (FHE), pseudorandom functions (PRF) and many others. One standard strategy to solve the LWE problem is to reduce it to a unique SVP (uSVP) problem via Kannan's embedding and then apply a lattice reduction to solve the uSVP problem. In this talk, we will discuss and compare various lattice algorithms for solving LWE, and then give some concrete estimates for breaking various variants of LWE (e.g. generic, small secrets, restricted samples). In the end, we will discuss some recent developments on algorithms for solving LWE.