LEE TIEN, ESQ.; SBN 148216
1452 Curtis Street
Berkeley, CA 94702
Tel: (510) 525-0817

Attorneys for Plaintiff
Daniel J. Bernstein

DANIEL J. BERNSTEIN )
) C 95-00582 MHP
Plaintiff, )
) DECLARATION OF
v. ) BRUCE SCHNEIER
) )
UNITED STATES DEPARTMENT OF )
STATE et al., ) )
Defendants. )
)
)

I, BRUCE SCHNEIER declare as follows:
1. I am president of Counterpane Systems, a consulting firm specializing in cryptography and computer security. I am the author of Applied Cryptography: Protocols, Algorithms, and Source Code in C, the second edition of which was published in 1996 by John Wiley & Sons, and of E-Mail Security, published in 1995 by John Wiley & Sons. I am a contributing editor to the computer programming magazine Dr. Dobb's Journal where I have edited the "Algorithm Alley" column. I am a member of the board of directors of the International Association for Cryptologic Research. I have personal knowledge of the facts set forth herein, unless otherwise indicated, and if called as a witness could and would so testify. I executed this Declaration at Stanford, California.

The final 0 means the algorithm terminates, and the solution is the third number in the last row: 2. This is Euclid's algorithm written in the C programming language.
int gcd (int x, int y) { int g; if (x < 0) x = -x; if (y < 0) y = -y;
if (x + y == 0) ERROR; g = y;
while (x > 0) {g = x; x = y % x; y = g;} return g; }

Running the above program with the inputs 6 and 22 yields the same answer: 2:
17. A more complex algorithm is the IDEA encryption algorithm. It takes a 64 bit block of plaintext and turns it into a 64-bit block of ciphertext, with the help of a 128-bit key. Remember, computers represent everything using bits, so anything in a computer can be encrypted in this manner. IDEA encrypts these bits in groups of 64 bits; this is called a block. By using basic mathematical operations like the exclusive-OR logical operation, addition, and modular multiplication, the computer combines the key and the plaintext message to produce ciphertext. It is somewhat like shuffling cards over and over again, but the cards change because you're shuffling them. A full explanation of how IDEA works is provided in my book, APPLIED CRYPTOGRAPHY (Second Edition), on pages 319-325. It's too involved to discuss here. It is possible to implement IDEA by hand, but it is enormously easier to do it on computer. Remember, computers already represent data in terms of bits, and they naturally do the mathematical operations required by the IDEA algorithm. In my book APPLIED CRYPTOGRAPHY, available in foreign countries such as the U.K. Singapore, Japan, Iran, South Africa, Germany, Russia, Korea, and Australia, I published source code for IDEA written in the C programming language. The State Department has declared that my book is in the public domain and thus freely exportable without a license. Both the description and the C code describe the same thing. They convey the same information. One is easier to read, and the other is easier to embed in a computer program. Any competent programmer can translate one into the other; no cryptographic skills are required. C code for the IDEA algorithm is also freely available on the Internet at archive sites in the U.K., Finland, Germany, New Zealand, and Italy. Internet users from all over the world can download C source code from these sites.

25. In the C programming language, RSA encryption might look like:
number RSA_ENCRYPT (number *P, *E, *N) {return modulo (power (P,E), N) }
26. All of these three representations can be read by programmers and mathematicians, and all convey the same information. Cryptographers use different representations in different contexts. In my book, APPLIED CRYPTOGRAPHY, I used both. Some algorithms I explained using mathematical notation; others I explained using C programming notation. Both notations were intended to be read by humans, and I made my choice based on which notation could best explain the algorithm to my readers.