University of Virginia, Department of Computer Science
CS588: Cryptology - Principles and Applications, Fall 2001

Manifest: Wednesday 19 September 2001
Assignments Due
Before 21 SeptemberEmail or talk to me about your project topic ideas
Wednesday, 26 SeptemberProblem Set 2
Monday, 1 OctoberProjects Preliminary Proposal


R.L. Rivest, A. Shamir, L. Adleman. A Method for Obtaining Digital Signatures and Public-Key Cryptosystems , 1978. - This is the original RSA paper, perhaps the most important paper in any field in the last 30 years. You should read it in the Rotunda or a lawn garden.

Code Book, Chapter 6

[optional] Whitfield Diffie and Martin Hellman. New Directions in Cryptography, 1976. (This is a PDF conversion of an optical scan, hence all the language problems.)

Diffie-Hellman Key Agreement
  1. Choose public numbers: q (large prime number), α (primitive root of q)
  2. A generates random XA and sends B: YA = αXA mod q.
  3. B generates random XB and sends A: YB = αXB mod q.
  4. A calculates secret key: K = (YB) XA mod q.
  5. B calculates secret key: K = (YA) XB mod q.

Transmitted in clear: q, α, YA = αXA mod q, YB = αXB mod q.
Only A knows: XA. Only B knows: XB.

Primitive Root

α is a primitive root of q if for all 1 ≤ n < q, there is some m, 1 ≤ m < q such that αm = n mod q
Same Keys are Generated:
K = (YB) XA mod q = (YA) XB mod q.

(YB) XA mod q
= (αXB mod q) XA mod q
= αXBXA mod q
= αXAXB mod q

(YA) XB mod q
= (αXA mod q) XB mod q
= αXAXB mod q

Useful Proof Methods

Proof by intimidation: "Trivial" or "obvious."
Proof by exhaustion: An issue or two of a journal devoted to your proof is useful.
Proof by omission: ``The reader may easily supply the details'', ``The other 253 cases are analogous''
Proof by obfuscation: A long plotless sequence of true and/or meaningless syntactically related statements.
Proof by funding: How could three different government agencies be wrong?
Proof by lack of funding: How could anything funded by those bozos be correct?
Proof by democracy: A lot of people believe it's true: how could they all be wrong?
Proof by reference to inaccessible literature: The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Icelandic Philological Society, 1883. This works even better if the paper has never been translated from the original Icelandic.
Proof by forward reference: Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
Proof by flashy graphics: A moving sequence of shaded, 3D color models will convince anyone that your object recognition algorithm works. An SGI workstation is helpful here.
Proof by vehement assertion: It is useful to have some kind of authority relation to the audience, so this is particularly useful in classroom settings.
Proof by vigorous handwaving: Works well in a classroom, seminar, or workshop setting.
Proof by cumbersome notation: Best done with access to at least four alphabets, special symbols, and the newest release of LaTeX.
Proof by lack of space: "The proof is not detailled due to lack of space in this proceedings..." works well in conjunction with proof by forward reference.

Selected from
None of these proof methods are suggested in your CS588 problem sets or exams.

CS 655 University of Virginia
Department of Computer Science
CS 588: Cryptology - Principles and Applications
David Evans