Spring 2021

**Instructor : ** Dhananjay S. Phatak

**Office : ** ITE 327

**Phone :**
410--455--3624

**email :** phatak@umbc.edu

** Class Room and Time : ** Tu Th 1 pm via blackboard course room

**Office Hours : ** TBD and by apt
** course web-site : **
http://www.csee.umbc.edu/`~`phatak/691a

**Textbook : ** None.

Appropriate material (articles from the
literature, web pages....)
will be provided.

Most of the topics will be selected from the following list

(We might deviate and study some other topics (such as
AKS and other most recent primality testing algorithms, etc.)
depending
upon the interests of the students and the instructor).

- Introduction: RSA encryption/decryption, Fermat's Little Theorem, Euler Totient Theorem
- Conventional Residue Number Systems (RNS)
Sets of viewgraphs

- Advanced topics in Residue Number Systems.

Our recent work on (RNS)

Older version of the document (RNS)

- Fast arithmetic for large (cryptographic) wordlengths
- multi-digit multiplication : Karatsubba, Toom-Cook

FFT multiply methods, 3-primes FFT multiplication method

FFT Multiply Viewgraphs JJ 1

FFT Multiply Viewgraphs JJ 2

FFT Multiply Viewgraphs Umass

FFT Multiply Viewgraphs set 4

FFT Multiply Viewgraphs set 5

3 primes FFT Multiply Viewgraphs

- Modular Reducction : Barrett method, Montgomery algorithms

linear, cyclic and negacyclic convolutions,

Further optimization based on Montgomery Methods. - other topics (time permitting) Fully and Partially
Homomorphic Encryption (and Decryption)

- Get familiar with software package Maple

It will be used fairly heavily.

**Evaluation :**

Participation in class discussions about
open problems and/or a Term Project and/or a final exam.

**Goals of the Course :**
Exposure to research in new computing needs and paradigms...

**Prerequisites** : 419/645 or permission of the instructor.