Math 477 Midtern Exam Review Note
Throughout the exam, m denotes a positive integer, and a; b; x; y denote elements of
Z.
Review Key word
1.Define the following terms.
a. x = y mod m means
b. W
Class Notes: The RSA scheme
RSA scheme
Question:
How can it be that DA isnt easily computable from EA? How can there be such
functions?
The RSA is based on the following empirically observed fact (her
Class Notes: Protocols
Protocols
Zero-
knowledge proofs. Alice can unequivocally convince Bob that she has a
certain piece of information, without revealing the exact piece of information to Bob.
Secret sha
Class Notes: Cryptology
Cryptography is the process of writing using various methods (ciphers) to keep
messages secret.
Cryptanalysis is the science of attacking ciphers, nding weaknesses, or even
proving that
UMASS AMHERST MATH 471, F. HAJIR
HOMEWORK 7: CONGRUENCES II
1. True or False: (You dont have to justify)
(a) 2x 5 mod m has a solution x Z if and only if m is odd.
(b) For odd integers k , 2x k mod m has a solution x Z if and only if m is odd.
(c) For int
UMASS AMHERST MATH 471, F. HAJIR
EXAM 1 SAMPLE
Exam 1 will take place Thursday October 11 in class. Dont be late! The format of the
exam will be pretty close to what you get here (approximately the same number of questions,
etc.)
For the true/false and sh
UMASS AMHERST MATH 471, F. HAJIR
HOMEWORK 6: IDEALS AND CONGRUENCES I
PART UN: Ideals in G
Denition. A suset I G is called an ideal of G if it satises the following properties:
1a) 0 I
1b) If I , then I
1c) If , I , then + I .
2) If I and G, then I .
Loos
UMASS AMHERST MATH 471, F. HAJIR
HOMEWORK 4: GAUSSIAN INTEGERS IV
This homework is due at the start of class on Thursday October 4. The exam has been
moved to Thursday Oct. 11 in class.
Reminder: Oce hours are Tue and Th 11-12 and Wed 2-3, in 1623C.
1. De
UMASS AMHERST MATH 471, F. HAJIR
HOMEWORK 3: GAUSSIAN INTEGERS III
This homework is due on Thursday September 27.
Reminder: Oce hours are Tue Th 11-12 in 1623C LGRT. I will usually be around 2-3
Wed also. You can also email me for an appointment.
0. Read,
UMASS AMHERST MATH 471, F. HAJIR
HOMEWORK 1: GAUSSIAN INTEGERS I
The rst thing you should note is that there are very few problems. Nonetheless, get
started right away, because it will take you a long time to come up with the solutions and
write them up c