1. Building the Big Message Authentication Code
Dale R. Thompson, Ph.D., P.E.
Brad Maxwell
July 20, 2004
University of Arkansas

2. Long-term Message Authentication
Mean time to find collision with a custom
$14 million machine
Financial
Bank transactions
Credit card
House purchase
Legal documents
Patents
Contracts
Evidence
Digital photographs
Digital video
# bits
Year 2003
Year 2024
128
6 hours
1 second
160
46 hours
1 day
192
3.0x106 years
180 years
256
1.3x1016 years
7.9x1011 years
320
5.5x1025 years
3.4x1021 years
University of Arkansas

3. Background Definitions
Hash or message digest
A function that maps an arbitrary string to a smaller fixed length string
MAC
A one way function or message digest that is seeded with a shared secret value between two parties. Authenticity can only be verified between the two parties.
Collision
When two different strings map to the same hash or MAC
University of Arkansas

4. University of Arkansas
BigMAC Ideas
Composite hash
Consists of 2 or more hashes concatenated together
If you break one hash, you get caught by another
Use hashes to cover each others weaknesses
The BigMAC implementation uses
Uncompressed data stream
Compression data stream
Blocks
Process data stream in blocks with a hash function and then process the hashes of the blocks with a second hash function
Primary of primary, primary of secondary
University of Arkansas

5. University of Arkansas
BigMAC structure
University of Arkansas

6. Distributions of Collisions on the BigMAC
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7. University of Arkansas
BigMAC Tests
Adler32 does not perform well compared to CRC
Researched Universal Hashing
Uses a family of CRC functions
Picks 2 functions and uses them to create a composite hash
Tested BigMAC using two CRC functions
With different initial vector and same polynomial
With same initial vector and different polynomial
University of Arkansas

8. Distributions of collisions replacing Adler with CRC
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9. Distribution of Collision Results
Compression reduces the data set, thus the CRC functions perform slightly worse on compressed
Blocking is a hash of hashes, which is a hash of a more uniform distribution of data.
University of Arkansas

10. Applied CRC Attack Previously Published
Replaced one byte and changed 4 additional bytes to maintain same CRC.
See for details.
Same polynomial with different initial vectors
Created collision for both CRC functions.
Since the CRCs are cyclic, changing the initial vector just changes the starting point of the cycle.
Reversing CRC attack does not require the initial vector to be known, only the polynomial.
Different polynomials with same initial vectors
Created collision for only one CRC function, but not the other.
University of Arkansas

11. University of Arkansas
Conclusions
The BigMAC
Designed to thwart common attacks over an extend period of time
Composed of multiple hashes concatenated together
Size can easily be increased without redesigning the algorithm
CRC
Must add k zeros to prevent simple forgery
If multiple CRC functions are used, they should have different generating polynomials.
University of Arkansas

12. University of Arkansas
Contact Information
Dale R. Thompson, Ph.D., P.E.
311 Engineering Hall
Fayetteville, Arkansas 72701
WWW:
J. Brad Maxwell
1515 Red Tip Dr. #8
Fayetteville, Arkansas 72704
University of Arkansas