Search Research Symposium Abstracts

Group-based Cryptography in the Quantum Era

In this talk I present an overview of the current state-of-the-art in post-quantum group-based cryptography. I describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic groups and graph groups, dealing in particular with their algorithmic properties and cryptographic applications. I then describe some [Read More...]

Presenter: Delaram Kahrobaei, CUNY Queens College and University of York (UK)
Authors: Delaram Kahrobaei
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 17, 2022; 10:15 am

Root extraction problem in braid group-based cryptography

In the past decades, cryptographers have focused their attention in braid groups to use them as a tool to construct authentication schemes and digital signatures. In this talk we will discuss the application of the root extraction problem for braid group-based cryptography. That is, given a braid $\beta$ and a number $k$, find a braid $\alpha$ such that [Read More...]

Presenter: María Cumplido, Universidad de Sevilla
Authors: María Cumplido, Delaram Kahrobaei, Marialaura Noce
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 17, 2022; 10:40 am

Conjugacy Search in Some Cryptographic Platform Groups

The construction and realization of public-key protocols that resist known quantum attacks comprise a pressing problem in cryptography. Apart from lattice-based, multivariate, and code-based cryptography, nonabelian group-based cryptography has been proposed recently as a viable post-quantum paradigm. Under this, the most prominent algorithmic problem [Read More...]

Presenter: Simran Tinani, University of Zurich
Authors: Simran Tinani
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 17, 2022; 11:05 am

Cryptography with Stabilizer Codes

We consider asymmetric quantum cryptography based on the theory of stabilizer codes. We will consider an algorithm for using qubits to transmit classical bits of information based on stabilizer codes. We first review the notions of stabilizer codes then introduce our [Read More...]

Presenter: Lubjana Beshaj, West Point
Authors: Lubjana Beshaj, Travis Russell.
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 17, 2022; 11:30 am

Cryptographic functions: a selection of some achievements and exploring of new research advances and directions*

Cryptographic functions defined over finite fields play a central role in the security of symmetric crypto-systems. They are one of the cornerstones of our cryptographic landscape today and are used to ensure security for a significant fraction of our daily communication. Notably, for practice use, they are used as the pseudo-random generators of stream [Read More...]

Presenter: Sihem Mesnager, Universities of Paris VIII and Paris XIII-LAGA, and Telecom Paris, Polytechnic Institute
Authors: S. Mesnager
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 18, 2022; 3:20 pm

Code-based cryptography: past, present, future

Public key cryptography protects the privacy and security of our global digital communication infrastructure. All widely-deployed public key cryptographic systems are based on the difficulty in solving variations of the integer factorization and discrete logarithm problems. In 1991, Peter Shor presented quantum algorithms that could solve these problems [Read More...]

Presenter: Angela Robinson, NIST
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 18, 2022; 3:45 pm

Some Applications of Non-Abelian Groups to Hashing

Zemor and Tillich introduced a scheme of Cayley hash functions over $SL_{2}(\mathbb{F}_{2^n})$ in 1994. Other hash functions based on the Zemor and Tillich's design have been proposed since. Cayley hash functions use non-Abelian groups, which a priori can be resistant to quantum attacks. Finding collisions for Cayley hash functions is equivalent to [Read More...]

Presenter: Bianca Sosnovski, Queensborough Community College
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 18, 2022; 4:10 pm

Secure and Efficient Delegation of Pairings with Online Inputs

Delegation of pairings from a computationally weaker client to a computationally stronger server has been advocated to expand the applicability of pairing-based cryptographic protocols to computation paradigms with resource-constrained devices. Important requirements for such delegation protocols include privacy of the client’s inputs and security of the [Read More...]

Presenter: Matluba Khodjaeva, CUNY John Jay College of Criminal Justice
Authors: G. Di Crescenzo, M. Khodjaeva, D. Kahrobaei, V. Shpilrain
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 18, 2022; 4:35 pm

When the whole is more than the sum of parts: interplay of diverse mathematical structures in cryptography*

The security of cryptographic protocols is based on the conjectured intractability of some mathematical problem, typically a single problem. However, in some cases, novel constructions emerge out of the surprising interplay of seemingly disparate mathematical structures and conjectured hard problems on these. Though unusual, this cooperation between [Read More...]

Presenter: Shweta Agrawal, IIT Madras
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 19, 2022; 8:50 am

Cryptographic multilinear maps using pro-p groups*

To any nilpotent group of class $n$, one can associate a non-interactive key exchange protocol between $n+1$ users. The multilinear commutator maps associated to nilpotent groups play a key role in this protocol. We will discuss this key exchange protocol and its security when applied to finite $p$-groups. Moreover, we will explore some alternative [Read More...]

Presenter: Mima Stanojkovski, RWTH Aachen University / MPI MiS Leipzig
Authors: Delaram Kahrobaei, Mima Stanojkovski
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 19, 2022; 9:15 am

Nilpotent groups applied to multilinear cryptography*

I will describe multilinear cryptosystems based on nilpotent group [Read More...]

Presenter: Maria Tota, Università di Salerno, Dipartimento di Matematica, (ITALY)
Authors: Delaram Kahrobaei, Antonio Tortora, and Maria Tota
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 19, 2022; 9:40 am

Group Key Establishment in a Quantum-Future Scenario*

Group key establishment protocols (GAKE) are cryptographic constructions designed for setting up secure sessions. Once a GAKE execution is finalized, the group of involved participants share a high-entropy secret that can be used as common key for different cryptographic tools. However, it is important to understand that the keys stablished today may no [Read More...]

Presenter: Maribel G. Vasco, Universidad Rey Juan Carlos
Authors: Maria Isabel Gonzalez Vasco, Angel L. Perez del Pozo, Rainer Steinwandt
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 19, 2022; 10:05 am

Engel group-based cryptography

Engel groups play an important role in group theory since these groups are closely related to the Burnside problems. In this talk we first introduce Engel groups, and then we present classical and novel protocols built around these groups. Finally, we will present the state of the art of Engel group-based cryptography and propose several open [Read More...]

Presenter: Marialaura Noce, University of Salerno
Authors: Delaram Kahrobaei, Marialaura Noce
Symposium Year: 2022
Session: Mathematical Aspects of Cryptography
Presentation Time: June 19, 2022; 10:30 am