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Cryptography & Computer Security

Instructor:  Professor Delaram Kahrobaei

Dr. Delaram Kahrobaei is an Associate Professor at the City University of New York. She has a joint appointment at CUNY Graduate Center in the PhD program in Computer science and at New York City College of Technology (CUNY) in the Mathematics Department. Her main research area is Information Security, Cryptography, Computational and Combinatorial Group Theory.
She was previously an Assistant Professor in Pure Mathematics at the Mathematical Institute, at Scotland’s prestigious University of St Andrews (2004-2006).
She has done substantial research in Mathematics and computer science both as individual and as a team member and publishes her work in peer reviewed journals and proceedings. Her work is attracting strong international interest and many invited talks (105). She has been awarded substantial prestigious research grants, including Office of Naval Research Office ($448K), American Association for Advances in Sciences, the National Science Foundation, PSC-CUNY Research Foundation, Faculty Fellowship Publication award, London Mathematical Society and Edinburgh Mathematical Society Grants and intends to apply for more grants from government agencies.

She has published in the areas of combinatorial group theory, geometric group theory, computational group theory, combinatorics, logic as well as algebraic cryptography and computational complexity and representation theory.
Delaram is the director of C-LAC, Center for Logic, Algebra and Computation. She enjoys involving students in her research and in the past years she has been a research supervisor to PhD (4), MSc (2) and undergraduate (30) students. Indeed two of her Ph.D. students graduated in 2012 from CUNY Graduate Center in Mathematics. Maggie Habeeb is now a tenure track assistant professor at California University in Pennsylvania and Bobby Koupparis is a vice president and quant at the Royal Bank of Canada in New York.
She is also keen to teach mathematics and computer science at both undergraduate and graduate levels and for the past fourteen years she has done so, at CUNY Graduate Center, City Tech, University of St Andrews and Hunter College, New York University Polytechnic Institute.
Kahrobaei has been co-organizing several conferences, including the ones for American Mathematical Society special sessions (in Newark, New Orleans, Las Vegas, Cornell U., San Diego, Boston, Israel). She is a co-founder of the annual Manhattan Algebra Day (December 6, 2013).
She co-founded the New York Applied Algebra Colloquium with Andrew Douglas. Kahrobaei is also running the Mathematical Aspects of Cryptography Student seminars at CUNY Graduate Center.
She is also co-organizing Algebra Cryptography Seminar at the CUNY Graduate Center.
She is a member of the Algebraic Cryptography Center.
She is the member of the editorial board of the International Journal of Open Problems in Computer Science and Mathematics.

In the Fall 2014, Professor Kahrobaei is teaching, Cryptography & Computer Security, in the PhD programs in Mathematics and Computer Science at CUNY Graduate Center.
Delaram will be traveling in 2013-2014 for conferences and research activity to Barcelona, South Korea, Scotland, Louisville, Paris, Tel Aviv, New Castle, Buenos Aires, Moscow, Baltimore.


The Cryptography and Computer Security is an important area that aligns with the mission of the Ph.D. program in Computer Science; i.e., Computer Science professions need to include security by design in the development of cutting edge technologies.

The Center for Strategic and International Studies in Washington estimates the cost to the United States economy due to security breach at about $100 billion a year, let alone the impact of security breach on the national security. It is paramount for our Ph.D. program in Computer Science to train our students to incorporate security and privacy by design into the research and development of cutting edge technologies. This course is an introductory course for the Cryptography and Computer Security new curriculum, and to fill the need of training our students in this area. More importantly, this new course intends to expose our students early on to anticipate and think out of a box, as opposed to being reactionary, in the design of security solutions.

In this course, we cover various aspects of modern cryptography and computer security. The topics include number theory, group theory, factoring, public-key encryption and digital signature schemes.

Course Topics

  • Introduction

    • Cryptography and Modern Cryptography

    • The Setting of Private-Key Encryption

    • Historical Ciphers and Their Cryptanalysis

    • The Basic Principles of Modern Cryptography

  • Perfectly-Secret Encryption

    • Definitions and Basic Properties

    • The One-Time Pad

    • Limitations of Perfect Secrecy

  • Number Theory and Cryptographic Hardness Assumptions

    • Preliminaries and Basic Group Theory

    • Primes, Factoring, and RSA

    • Assumptions in Cyclic Groups

    • Cryptographic Applications of Number-Theoric Assumptions

  • Factoring and Computing Hardness Logarithms

    • Algorithms for Factoring

    • Algorithms for Computing Discrete Logarithms

  • Public-Key Encryption

    • Public-Key Encryption - An Overview

    • Definitions

    • Hybrid Encryption

    • RSA Encryption

    • The El Gamal Encryption Scheme

    • Security Against Chosen-Ciphertext Attacks

    • Trapdoor Permutations

  • Additional Public-Key Encryption Schemes

    • The Goldwasser-Micali Encryption Scheme

    • The Rabin Encryption Scheme

    • Paillier Encryption Scheme

  • Digital Signature Schemes

    • Digital Signatures - An Overview

    • Definitions

    • RSA Signatures

    • The "Hash-and-sign" Paradigm

    • Lamport's One-Time Signature Scheme

    • Signature from Collision-Resistant Hashing

    • The Digital Signature Standard

    • Certificates and Public-Key Infrastructures


Introduction to Modern Cryptography

  • Authors: Jonathan Katz, Yehuda Lindell

  • Series: Chapman & Hall/CRC Cryptography and Network Security Series

  • Publisher: Chapman and Hall/CRC; 1 edition

  • ISBN-10: 1584885513

  • ISBN-13: 978-1584885511


  • Homework / Project / Attenedance & participation 30%

  • Midterm 30%

  • Final 40%