Notes - Burdens of Proof - page 199

Sons, 1997); and Whitfield Diffie and Susan Landau, Privacy on the Line: The Politics
of Wiretapping and Encryption (Cambridge, MA: MIT Press, 1998).
4. Diffie and Hellman, “New Directions in Cryptography,” 644.
5. Steven Levy, “The Cypherpunks vs. Uncle Sam,” in Building in Big Brother: The
Cryptographic Policy Debate , ed. Lance J. Hoffman (Berlin: Springer, 1995), 270.
6. Steven Levy, “Crypto: The Story of How a Group of Code Rebels Saved Your
Privacy on the Internet,” Newsweek , January 15, 2001, 42-52.
7. Levy, Crypto , 17.
8. See Menezes, van Oorschot, and Vanstone, Handbook of Applied Cryptography ,
12.6.1.
9. Diffie and Hellman, “New Directions in Cryptography,” 650.
10. Ibid., 652. The concept of trapdoors was also related to the recent debate over
the actual security of the DES algorithm. Diffie and Hellman noted, “ Trap doors have
already been seen . . . in the form of trap-door one way functions, but other variations
exist. A trap-door cipher is one which strongly resists cryptanalysis by anyone not in
possession of trap-door information used in the design of the cipher. This allows the
designer to break the system after he has sold it to a client and yet falsely to maintain
his reputation as a builder of secure systems. . . . The situation is precisely analogous
to a combination lock. Anyone who knows the combination can do in seconds what
even a skilled locksmith would require hours to accomplish.” Ibid., 652; emphasis
in original.
11. Ron L. Rivest, Adi Shamir, and Leonard Adleman, “A Method for Obtaining
Digital Signatures and Public-Key Cryptosystems,” Communications of the ACM 21,
no. 2 (1978): 120-126.
12. How does a known unknown become a bona fide mathematical conjecture?
Jack Edmond explains, “The classes of problems which are respectively known and
not known to have good algorithms are of great theoretical interest. . . . I conjecture
that there is no good algorithm for the traveling salesman problem. My reasons are
the same as for any mathematical conjecture: (1) It is a legitimate mathematical
possibility, and (2) I do not know.” Quoted in Christos H. Papadimitriou, Computa-
tional Complexity (Reading, MA: Addison-Wesley, 1994), 137.
13. For an overview, see Menezes, van Oorschot, and Vanstone, Handbook of Applied
Cryptography , chapters 3, 4, and 14. Over time, this interest has waned. Shparlinski
calls for the renewal of the special bonds between number theory and cryptography,
noting that “over the years, the tight links and the mutual interest have somewhat
diminished,” as the cryptographic research community has become increasingly
preoccupied with protocol design, a “not so mathematically rich part of cryptogra-
phy.” Igor E. Shparlinski, “Numbers at Work and Play,” Notices of the American
Mathematical Society 57, no. 3 (March 2010): 335.