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Re: IPG algorithim
Eric Murray wrote:
>
>
>
> I have translated the IPG algorithim's "engine" to C, to generate
> some random values from it for testing purposes. It does not
> look very random in either the xnoisesph program or the DIEHARD
> test battery. However I may well have misinterprested Mr. Wood's
> description (his writing is, as Mr. Chudov points out, difficult to
> understand) or written my code incorrectly. Here it is, play
> with it yourself. To my untrained eye the lack of randomness
> in what's essentially a stream cipher would be disturbing.
> However I am not a cryptoanalysist so I do not know to
> what extent this weakens the cipher.
Thanks for an interestnig approach to testing (see below).
> The IPG description does not say (but implies to me) that
> the various tables that are to be filled in by "random" values must
> be filled in by PRNGs that are seeded with the same seeds by
> each of the party that knows the key. Otherwise the "encryptor
> streams" that are generated will be unrelated and decryption will not
> be possible. To make my test work I have used the simple rand()
> function to fill in the tables.
A good point.
> Corrections are welcome.
see below.
>
> #include <stdio.h>
>
> /* a C translation of the IPG "EUREKA" algorithim's "engine".
> ** This is supposed to produce random numbers for the IPG
> ** "encryptor stream".
> ** See http://www.netprivacy.com/ for the original description.
> ** Eric Murray [email protected] This code placed under GNU copyleft. */
>
> /* machine-dependent stuff, change to suit different platforms: */
> typedef unsigned char byte;
> typedef unsigned short uint16;
>
>
> /* tables: */
> uint16 A[53];
> uint16 B[53];
> uint16 C[53];
>
>
> int init_table(uint16*table, uint16 min, uint16 max)
> {
> /* IPG specifies no algorithim for producing the "random"
> ** initial values in the ABC tables, but it's obvious that
> ** it requires a PRNG that's somehow seeded from the "key".
> ** I've just used rand() here. In UNIX rand() called with no
> ** seed is supposed to seed itself with 0. */
> int i;
> int count, r;
>
> for(i = 0; i < 53; i++) {
> table[i] = min + (rand() % (max - min));
> }
> }
>
> main(int argc, char **argv)
> {
> uint16 jv;
> int argcnt, i, n, count, diehard, nelem;
>
> diehard = 0;
> argcnt = 1;
how about doing randomize()?
> if (argc >= 2) {
> if (strncmp(argv[argcnt],"-d") == 0) {
> diehard++;
> argcnt++;
> }
> }
> if (argc > argcnt - 1 ) {
> n = atoi(argv[argcnt]);
> fprintf(stderr,"Generating %d values\n",n);
> }
> else {
> n = 2000;
> }
>
> /* seed tables: */
> fprintf(stderr,"Seeding: A"); fflush(stderr);
> init_table(A,0,65535);
> fprintf(stderr," B"); fflush(stderr);
> init_table(B,0,12227);
> fprintf(stderr," C"); fflush(stderr);
> init_table(C,16384,20361);
> fprintf(stderr,"\n"); fflush(stderr);
>
> /* generate n values: */
> for(; n > 0; n--) {
> /* jv is "random" (where's it seeded from?) */
> jv = (uint16)(rand() % 53);
>
> /* count limits the number of traverses to 53^2 so we don't get stuck */
> for(count = 0; count < 2809; count++) {
2809 is a too small limit. For example, if ALL B == 1, A == 16385, and
C == 20361, the loop may need (20361-16385) passes to get to the < 16384
value.
Again, if all A = 16385, all B = 0, all C = 16386, the loop will never
end with a correct A (your code reflects that).
> jv++;
> if (jv == 53) jv = 0;
> A[jv] = (A[jv] + B[jv]) % C[jv];
> if (A[jv] < 16384) break;
> }
> if (count == 2809) fprintf(stderr,"Oops.\n");
> else {
> if (!diehard) {
> printf("%d\n",A[jv]);
> }
> else {
> /* print output in DIEHARD required format:
> ** actually since we have 16-bit ints and DIEHARD
> ** wants 32-bit ints, we print 20 per line instead of 10 */
> if (nelem++ > 19) {printf("\n"); nelem = 0;}
> printf("%4.4x",(unsigned int)A[jv]);
> }
> }
> }
> }
>
>
You are also bringing a good point that Chi-squared tests are not
sufficient to make any conclusions about usefulness of this particular
pseudo random number generator.
- Igor.