Manifest: Wednesday 19 September 2001

Assignments Due
Before 21 September	Email or talk to me about your project topic ideas
Wednesday, 26 September	Problem Set 2
Monday, 1 October	Projects Preliminary Proposal

Readings

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 X_A and sends B: Y_A = α^X_A mod q.
3. B generates random X_B and sends A: Y_B = α^X_B mod q.
4. A calculates secret key: K = (Y_B) ^X_A mod q.
5. B calculates secret key: K = (Y^A) ^X_B mod q.

Transmitted in clear: q, α, Y_A = α^X_A mod q, Y_B = α^X_B mod q.
Only A knows: X_A. Only B knows: X_B.

Primitive Root

α is a primitive root of q if for all 1 ≤ n < q, there is some m, 1 ≤ m < q such that α^m = n mod q

Same Keys are Generated:

K = (Y_B) ^X_A mod q = (Y^A) ^X_B mod q.

(Y_B) ^X_A mod q
= (α^X_B mod q) ^X_A mod q
= α^X_BX_A mod q
= α^X_AX_B mod q

(Y_A) ^X_B mod q
= (α^X_A mod q) ^X_B mod q
= α^X_AX_B mod q

Links

• Prophet of Privacy, Wired Magazine Feature on Whitfield Diffie. November 1994.
• Diffie-Hellman Key Exchange - A Non-Mathematician's Explanation
• Whitfield Diffie and Susan Landau, Privacy on the Line: The Politics of Wiretapping and Encryption, 1998.
• New York Times article on history of public-key cryptography, December 24, 1997.
• Ellis, Cocks and Williamson's original memos on non-secret encryption

Questions

• Why is key distribution important?
• What are some ways to distribute secret keys?
• How does Diffie-Hellman key agreement work?
• What does its security depend on?

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 http://www.ai.sri.com/~luong/research/proof.html.
None of these proof methods are suggested in your CS588 problem sets or exams.

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

David Evans evans@virginia.edu