RIT Computer Science

Advanced Cryptography
Spring 2020


Stanisław Radziszowski

bldg. 70, room 3657,
(585) 475-5193, spr@cs.rit.edu
Office hours: Tuesday/Thursday 10am-11am, 6:20pm-8:00pm, or send email


Tuesday/Thursday, 5:00pm - 6:15pm, room 70-1455

General Course Documents

Syllabus, outcomes, general course documents, policies, sample schedule: college syllabus, general schedule.
This page gives the current offering's contents and schedule.

Books and Other Reading


CSCI-462 or CSCI-662, or permission of the instructor.



This course investigates advanced topics in cryptography. It begins with an overview of necessary background in algebra and number theory, private- and public-key cryptosystems, and basic signature schemes. The course will cover number theory and basic theory of Galois fields used in cryptography; history of primality algorithms and the polynomial-time test of primality; discrete logarithm based cryptosystems including those based on elliptic curves; interactive protocols including the role of zero-knowledge proofs in authentication; construction of untraceable electronic cash on the net; and quantum cryptography. Other topics may include digital watermarking, fingerprinting, and steganography. Programming will be required.

Students will write a term paper, either theoretical based on literature or reporting student's own implementation or experiments with a chosen cryptographic scheme. Depending on the size of the group, some or all students will give a presentation to the class.

The specific topics will include

Slides used in class so far

Cryptography - A Crash Overview
ElGamal and Shanks
RSA, Pollard p-1
Euler criterion, CDH and DDH
Pohlig-Hellman and index calculus
Galois field GF(27)
elliptic curves basics
elliptic curves in crypto

Switch to the remote mode from March 24

remote mode information, join class on zoom, meeting ID 637 783 735

ECDSA in Bitcoin
more signatures
EC in signal
X3DH, see also pages 478-484 of edition 4 of the textbook
NIST update on EC and PQC
SIKE (5 intro slides): supersingular isogeny key encapsulation PQC competitor
Two more presentations on SIKE: short and long.
Full SIKE document (101 pages).
Montgomery and Edwards curves by Tanay Dusane.

Slides to be used in class

full domain hash signatures security
knapsack cryptosystem, broken but still nice

Other links