Links:
(Goldfeld
Conference photos)
Joint
COLUMBIA-CUNY-NYU Number Theory Seminar
First
JNT Biennial Conference (2019)
Bretton
Woods
Workshop on Multiple Dirichlet Series (2005)
(Conference
photos)
AAG
key exchange
Edinburgh
Workshop
on Multiple Dirichlet Series(2008)
Decision
Regarding World Record Musky Challenge
My Daughter's art work
(including my portrait above)
Some
Interesting
Chemistry
Very accurate clock
TEACHING,
FALL 2019
Mathematics UN30251,
MAKING
BREAKING CODES
TR 1:10 - 2:25pm Location: Room
312 Mathematics Building
TEXTBOOK:
Introduction
to
Cryptography
with Coding
Theory,
2nd edition
by Wade Trappe
& Lawrence
C Washington
EXAMS:
Exam 1: Thursday, October 3 in class 1:10-2:25pm
(
20% of course grade),
Exam 2: Thursday, November 7 in class 1:10-2:25pm (
20%
of course grade),
Final Exam: (35% of course grade).
TA's:
Shalin Parekh
<sp3577@columbia.edu>
Matthew Lawhon
<mwl2131@columbia.edu>
For TA Help
Room Hours
see:
HOMEWORK:
(
25%
of course grade)
HW#1 due Tuesday, September 10:
EARLY CRYPTOGRAPHY:
Page 55, Problems 2, 3, 4, 5, 8, 10, 11
HW#2 due Tuesday, September 17:
EUCLIDEAN ALGORITHM & FERMAT'S LITTLE THEOREM:
Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26
HW#3 due Tuesday, September 24:
CHINESE REMAINDER THEOREM:
Notes on the Chinese
Remainder theorem
Page 105, Problems 9, 10
RSA CRYPTOSYSTEM:
Page 192, Problems 1, 3, 7, 9
DISCRETE LOG'S & DIFFIE HELLMAN CRYPTOSYSTEM :
Page 214, Problems 1, 2, 11
HW#4 due Tuesday, October 1:
ATTACKS ON RSA & DIFFIE-HELLMAN
Problem 1: Using the fact that 1024 =
(2^6)x(2^3)x(2)
compute 3^1024 (mod 7). (See section 3.5, Modular
Exponentiation).
Problem 2: Factor 497 using the Pollard p-1
Factoring Algorithm
with B! = 3! and a=3. (See Page 182).
Notes on the Pollard Attack
POHLIG-HELLMAN ATTACK:
Notes
on the Pohlig-Hellman Attack
Page 215, Problems 3, 4.
Page 286, Problem 4 (see section 10.1.1 Intruder
-in-the-Middle Attacks).
EXAM 1: Thursday, October 3 in
class 1:10-2:25pm.
HW#5 due Tuesday, October 15:
HASH FUNCTIONS & DIGITAL SIGNATURES
Page 239, Problem 1, 2, 4
Notes on Computing square
roots (mod pq) is hard
and see section 8.4 Birthday Attacks)
Notes on the Birthday attack
EL GAMAL SIGNATURES:
Page 252, Problems 1, 2, 4, 5, 8.
HW#6 due Tuesday, October 22:
ELLIPTIC CURVE CRYPTOGRAPHY
Notes
on Elliptic Curve Cryptography
Page 370, Problems 1, 2, 3, 4, 5, 10
HW#7 due Tuesday, October 29:
COIN FLIPPING: Page 315, Problems 2, 3
Notes on Square Roots (mod p)
ZERO KNOWLEDGE TECHNIQUES: Page 321, Problems 1, 2, 3, 4, 5, 6
Notes on Zero-Knowledge Proofs
How
to Explain Zero-Knowledge Protocols to Your Children
HW#8 due Thursday, Nov. 7:
IRREDUCIBLE POLYNOMIALS:
Page 110, Problems 33, 34, Page 447, Problem
12(a).
FINITE FIELDS:
Construct a finite field of 8 elements.
EXAM 2: Thursday, Nov. 7 in
class 1:10-2:25pm.
HW#9 due Tuesday, November 19:
ERROR CORRECTING CODES
Page 445, Problems 1, 2, 3(a),(b),(c)
HW#10 due Thursday, November 26:
BINARY CODES
Page 445, Problems 4, 5(a),(b), 6, 8
HW#11 due Thursday, December 3:
LINEAR CODES
Page 445, Problems 9, 10, 11, 12, 13
