If you use RandRange you can specify which algorithm to use. Or use rand() with randomize() to seed the random number generator.
RandRange(number1, number2[, algorithm])
ColdFusion MX 7: Added the algorithm parameter.
Integer numbers. If the numbers are not in the range -2,147,483,648 - 2,147,483,647, ColdFusion generates an error.
(Optional) The algorithm to use to generated the random number. ColdFusion installs a cryptography library with the following algorithms:
CFMX_COMPAT: the algorithm used in ColdFusion (default).
SHA1PRNG: generates a number using the Sun Java SHA1PRNG algorithm. This algorithm provides greater randomness than the default algorithm
IBMSecureRandom: for IBM WebSphere (IBM JVM does not support the SHA1PRNG algorithm.)
Presumably the querystring-parameter you are passing to the other page, which is not currently used, can be used as the seed.