Difference between revisions of "83Plus:BCALLs:80A5"
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| − | [[Category:83Plus:BCALLs:By_Name|TransformHash]] | + | [[Category:83Plus:BCALLs:By_Name:Cryptography|TransformHash]] [[Category:83Plus:BCALLs:By Name:Math:Big Integer|TransformHash]] [[Category:83Plus:BCALLs:By_Name:Math|TransformHash]] [[Category:83Plus:BCALLs:By_Name|TransformHash]] [[Category:83Plus:BCALLs:By_Address|80A5 - TransformHash]] |
| − | [[Category:83Plus:BCALLs:By_Name:Math|TransformHash]] | + | |
| − | [[Category:83Plus:BCALLs:By_Address|80A5 - TransformHash]] | + | |
== Synopsis == | == Synopsis == | ||
'''Official Name:''' TransformHash | '''Official Name:''' TransformHash | ||
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=== Inputs === | === Inputs === | ||
| − | * [[83Plus:RAM:8291|8291]]: The MD5 hash as a big integer | + | * [[83Plus:RAM:8291|8291]]: The MD5 hash as a [[83Plus:OS:Big Integers|big integer]] |
* [[83Plus:RAM:83E6|83E6]]: The parameter ''f'' as a big integer | * [[83Plus:RAM:83E6|83E6]]: The parameter ''f'' as a big integer | ||
* [[83Plus:RAM:8000|8000]]: The modulus | * [[83Plus:RAM:8000|8000]]: The modulus | ||
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== Comments == | == Comments == | ||
| − | Given ''p'', ''q'' prime, ''p'' | + | 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''-2''m'' | * ''pq''-2''m'' | ||
* ''pq''-''m'' | * ''pq''-''m'' | ||
Latest revision as of 07:26, 11 April 2005
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.
