83Plus:BCALLs:80A5

Synopsis

Official Name: TransformHash

BCALL Address: 80A5

Applies one of the four f-transformations as appropriate for the application to be validated.

Inputs

• 8291: The MD5 hash as a big integer
• 83E6: The parameter f as a big integer
• 8000: The modulus

Outputs

• MD5Buffer: The MD5 hash appropriately transformed.

Destroys

• 8100: 130-byte area which the multiplication routine uses to store its result
• 8182: 65-byte area used as the first argument to the multiplication routine
• 81C3: 65-byte area used as the second argument to the multiplication routine

Comments

Given p, q prime, p = 3 mod 8, q = 7 mod 8, and m relatively prime to both, exactly one of the following is a quadratic residue modulo pq:

• pq-2m
• pq-m
• m
• 2m

Which of the transformations is used is specified by the parameter f. In order to ensure that the message is nonzero, or perhaps just to make life difficult, m is defined to be the MD5 of the application, multiplied by 256, plus 1. Therefore:

• If f=0, the result is n-2*(MD5*256+1)
• If f=1, the result is n-(MD5*256+1)
• If f=2, the result is MD5*256+1
• If f=3, the result is 2*(MD5*256+1)

If the signature is valid, that number is a quadratic residue mod n, and more to the point, it is the square of the Rabin signature. That square is computed by the Rabin B_CALL, and only if the two numbers match is the application considered valid.