IPG algorithim

[Igor Chudov @ home]

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  ericm at lne.com  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.