cryptocafe

Department of Mathematical Sciences
Florida Atlantic University

Crypto Café

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

 

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), pseudo-random 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. 

Video Recording

 

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

SpeakerEdoardo 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!

Video Recording

 

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.

Video Recording

 

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

Speaker: Emrah Karagoz, Florida Atlantic University

Title: Knapsack Problem: Is it Post-Quantum Secure?

Abstract: The Knapsack Problem has been popular in cryptography since the Merkle–Hellman knapsack cryptosystem was announced in 1978, which was one of the first public-key cryptosystems, but had a very short life and was broken in 1982. Although it was discouraged with this failure and beside of the rising popularity of RSA, there are many other proposed algorithms such as the Chor-Rivest Cryptosystem, which are still secure.

Even though the Knapsack Problem is an NP-hard problem, and therefore believed to be a good candidate for Post Quantum secure algorithms, there was no submission based on Knapsack Problem in the NIST competition. We are still waiting (or maybe studying)!

In this talk, we will discuss the cryptographic aspects of the Knapsack Problem towards the Post-Quantum Secure World.  

Video Recording

 

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

SpeakerAbhraneel 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.

Video Recording

 

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.

 

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 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.