1. Motivations Algebraic Manipulation Detection Codes
Steps to break any protections based
on single error detecting codes:
Select an input, observe y
Investigating the code, select e=(ey,ef)
so that for the codeword (y, f(y)),
also belongs to the code.
Inject faults manifested as e
Codes that can still provide guaranteed level of protection even if the attacker can control the error as well as the input to the device are called algebraic manipulation codes.
Strongest Attacker Model!
Any protection based on single
error detecting code won’t work!
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2. General Architecture Algebraic Manipulation Detection Codes
Talk about attacker capability
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3. Definitions Algebraic Manipulation Detection Codes
The codewords of the AMD code are in the format of ..
We define the security kernel of the code as …
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4. Worst Case Error Masking Probability
Algebraic Manipulation Detection Codes
Worst Case Error Masking Probability
The error detecting capability of AMD codes can be characterized using Q(y,e)
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5. Algebraic Manipulation Detection Codes Lower Bounds
Can you list more classical bounds that can be used to derive dq(2m,M)?
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6. Algebraic Manipulation Detection Codes
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7. Algebraic Manipulation Detection Codes Example
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8. Algebraic Manipulation Detection Codes Example: r=1
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9. Algebraic Manipulation Detection Codes Special Cases
When b=1 and y is always distorted,
A(x) can be removed
When t=1, the code is optimal!
Encoding can be based on multivariate Horner Scheme!
Close to optimal complexity!
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10. Algebraic Manipulation Detection Codes
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11. Algebraic Manipulation Detection Codes
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12. Algebraic Manipulation Detection Codes
Example. Let t = b = 2 and assume r is large enough. Then the
resulting code is a (7r; 2r; r) AMD code. At most 8 multipliers and 7
adders in GF(2r) are required for the encoding or the decoding.
The critical path of the encoder contains 4 multipliers and 4 adders in
GF(2^r).

13. Encoder Architecture
for the (7r; 2r; r) AMD Code