## DORIAN GOLDFELD

Professor

Mathematics Building, Room 422

Columbia University

New York, NY 10027(212) 854-4304

Telephone:

Fax:(212) 854-8962

e-mail:goldfeld@columbia.edu

Research Interests:Number Theory curriculum vitae

Some Preprints: (pdf files)

An additive prime divisor function of Alladi and Erdős

A standard zero free region for Rankin-Selberg L-functions (with X. Li)

A converse theorem for double Dirichlet series and Shintani zeta functions

(with N. Diamantis)

On the determination of the Plancherel measure for Lebedev-Whittaker transforms on GL(n)

(with A. Kontorovich)

Fourier expansions of GL(2) newforms at various cusps

(with J. Hundley and M. Lee)

Natural boundaries and the correct notion of integral moments of L-functions

(with A. Diaconu and P. Garrett)

Moments for L-functions for GL(r) x GL(r-1) (with A. Diaconu and P. Garrett)

A converse theorem for double Dirichlet series (with N. Diamantis)

Voronoi Formulas on GL(n) (with X. Li)

Second Moments of GL(2) L-Functions (with A. Diaconu)

Counting Congruence Subgroups (with A. Lubotzky and L. Pyber)

Multiple Dirichlet Series and Moments of Zeta and L-Functions

(with A. Diaconu and J. Hoffstein)

Modular Forms, Elliptic Curves, and the ABC Conjecture

The Gauss Class Number problem for Imaginary Quadratic Fields

The Elementary proof of the Prime Number Theorem, An Historical Perspective

BOOKS:

Automorphic Representations and L-Functions for the General Linear Group, Volume 1

Automorphic Representations and L-Functions for the General Linear Group, Volume 2

Automorphic Forms and L-Functions for the Group GL(n,R)

Blog with corrections of Errors in the above books

Links:

(Goldfeld Conference photos)

Joint COLUMBIA-CUNY-NYU Number Theory Seminar

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 2017

Mathematics V3025, MAKING, BREAKING CODES

TR 2:40-3:55 Location: Room 312 Mathematics Building

Textbook: Introduction to Cryptography with Coding Theory (Second Edition)

by Wade Trappe and Lawrence Washington.

TA: James Cornish

e-mail:jsc2219@columbia.eduWed. 12-1, Thurs. 1-3.

Help Room (Math 406) Hours:

UNDERGRAD TA'S:

Jaewan Bahk: jb3621@columbia.edu Help Room Hours: Monday 12-2.

Bharatha Rankothge: bmr2147@columbia.edu Help Room Hours: Tuesday 10-12.

MIDTERM EXAM 1:Tuesday October 3 in class 2:40-3:55pm(20% of total grade for this class).

MIDTERM EXAM 2:Tuesday, November 21 in class 2:40-3:55pm (20% of total grade for this class).

FINAL EXAM:Thursday, December 21 in class 1:10-4pm(35% of total grade for this class).

HOMEWORK(25% of total grade for this course)Please put all homework in the box just opposite Room 415 Math Building.

Deadline is Thursday 11:00pm (Note that Math Building is locked by Facilities at 11:00pm).

All homework is from the Trappe-Washington book.

HW#1due Thursday, September 14:Page 55, Problems 2, 3, 4, 5, 8, 10, 11

HW#2due Thursday, September 21:Page 104, Problems 1, 2, 3, 5, 12, 13, 18, 19, 26

HW#3 due Thursday, September 28:Page 105, Problems 9, 10 Page 192, Problems 1, 3, 7, 9 Page 214, Problems 1, 2, 11

HW#4 due Thursday, October 12:ATTACKS ON RSA AND 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. Notes on Pollard's p-1 Attack

POHLIG-HELLMAN ATTACK: Page 215, Problems 3, 4. Notes on the Pohlig-Hellman Attack

Page 286, Problem 4 (see section 10.1.1 Intruder -in-the-Middle Attacks).

HW#5 due Thursday, October 19:HASH FUNCTIONS AND DIGITAL SIGNATURES

HASH FUNCTIONS: Page 239, Problems 1, 2 see--> SquareRoots(mod pq) ,

Page 239, Problem 4 (see section 8.4 Birthday Attacks) Birthday Attack

EL GAMAL SIGNATURES: Page 252, Problems 1, 2, 4, 5, 8.

HW#6 due Thursday, October 26:ELLIPTIC CURVE CRYPTOGRAPHY

Page 370, Problems 1, 2, 3, 4, 5, 10

HW#7 due Thursday, November 2:

COIN FLIPPING: Page 315, Problems 2, 3

ZERO KNOWLEDGE TECHNIQUES: Page 321, Problems 1, 2, 3, 4, 5, 6

HW#8 due Thursday, November 9:

IRREDUCIBLE POLYNOMIALS Page 110, Problems 33, 34, Page 447, Problem 12(a).

FINITE FIELDS: Construct a finite field of 8 elements.

HW#9 due Thursday, November 16:ERROR CORRECTING CODES

Page 445, Problems 1, 2, 3(a),(b),(c)

MIDTERM EXAM #2 Tuesday, Nov. 21

HW#10 due Thursday, November 30:BINARY CODES

Page 445, Problems 4, 5(a),(b), 6, 8

HW#11 due Thursday, December 7:LINEAR CODES

Page 445, Problems 9, 10, 11, 12, 13