Denition: Let V be a nite dimensional vector space and let T :
V V be linear. If is a basis for V such that T
is a Jordan
form, then we say that is a Jordan (canonical) basis.
Assume that J is a Jordan form for a n n matrix A. We have previously seen that

ASSIGNMENT 4
MATC16
due: November 6, 2015
(1) (a) List the points on the elliptic curve E : y 2 x3 2
(mod 7).
(b) Find the sum (3, 2) + (5, 5) on E.
(c) Find the sum (3, 2) + (3, 2) on E.
(2) (a) Show that P = (0, 1) on y 2 = x3 + 1 satisfies 6P = . Do
th

ASSIGNMENT 3
MATC16
due: October 19, 2015
(1) (a) Suppose that the primes used in the RSA cryptosystem are
consecutive primes. How would you factor n?
(b) The ciphertext 10787770728 was encrypted using e = 113
and n = 10993522499. The factors p and q were

ASSIGNMENT 1
MATC16
due: September 25, 2015
(1) The ciphertext 5859 was obtained from the RSA algorithm using n = 11413 and e = 7467. Using the factorization 11413 =
101 113 , nd the plaintext.
(2) Naive Nelson uses RSA to receive a single ciphertext c, c

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATC16H
Coding Theory and Cryptography
Examiner: E. Mendelsohn
Date: February 13, 2004
Room: BV 516
Duration: 100 minutes
1. Dene
(a) [2 points] A private key cryptosystem

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
Midterm Test
MATC16 - Coding Theory and Cryptography
Examiner: T. Pham
Date: October 28, 2006
Duration: 120 minutes
FAMILY NAME:
GIVEN NAMES:
STUDENT NUMBER:
NOTES:
There

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
Term Test
MATC16H
Coding Theory and Cryptography
Examiner: E. Mendelsohn
Date: Friday, March 4, 2005
Time: 10:1012:00 PM
1. [each part worths 5 points]
(a) Find gcd (217 3

MATC16 Cryptography and Coding Theory
Gbor Pete
a
University of Toronto Scarborough
gpete at utsc dot utoronto dot ca
Solutions for Assignment 1
The solutions below are sometimes sketchy, skipping computational details.
Problem 1. What is 491 (mod 50)? An

University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
Midterm Test
MATC16H Coding Theory and Cryptography
Examiner: P. Selick
Date: October 21, 2005
Duration: 120 minutes
1. [13 points] Find an integer x such that x 4(mod 9),

Let and be ordered bases for a nite dimensional vector space V
and let I : V V be the identity map. Then for v V ,
v
The matrix I
= I(v)
= I
v
.
is called the change of coordinate matrix
from to .
This matrix is unique.
Two n n matrices are similar if and

MATC16
CODING THEORY AND CRYPTOGRAPHY
Administrivia
Instructor: Professor John Scherk
Oce: IC496
Email: scherk@utsc.utoronto.ca
(emails will be answered within 24 hours, but may not be answered immediately)
Oce Hour: Monday, 1:30-2:30
Description
The stud