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What is the difference between Strict Avalanche Criterion(SAC) and Avalanche criterion?

Sangeetha
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2 Answers2

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The definition of avalanche effect is given in the paper of Webster, A. F. "On the design of S-boxes". Advances in Cryptology - Crypto '85 as :

For a given transformation to exhibit the avalanche effect, an average of one half of the output bits should change whenever a single input bit is complemented.

It is also seen as each bit should have 50% chances to change if you change 1 bit of the input. (strict avalanche)

In the avalanche criterion you look at the output as a whole (average 50% of the bits changes).

In the strict avalanche criterion, you look at each bit one by one and you verify that what ever the other bits will change, it will have a 50% probability to switch.

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Community
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Biv
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  • Unless you specifically code an algorithm to do something extremely weird, does not avalanche = strict avalanche in all practical regards for a grown up candidate hash function? – Paul Uszak Dec 21 '16 at 23:01
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    No. For example you can have a look at the aes s box. The strict criterion is not here. And to check it on hash candidates you would need too much time. – Biv Dec 21 '16 at 23:03
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Avalanche criterion, or Avalanche effect is informal. Small changes in inputs should always lead to large changes in outputs.

Consider a vector Boolean function $$f:F_2^n \rightarrow F_2^m$$ with $n$ bit input and $m$ bit output.

Strict Avalanche Criterion (SAC) says that if any input bit is flipped then exactly half of output bits should change. There are higher order versions as well where $k$ input bits are flipped and the same property is required of the output bits.

kodlu
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    The strict avalanche criterion (SAC) is a formalization of the avalanche effect. It is satisfied if, whenever a single input bit is complemented, each of the output bits changes with a 50% probability.

    it does not say that exactly half of the bits changes, it says each bit have 50% changes. One bit could change and all the other bits could stay the same. Very unlikely but it is possible.

     – Biv Dec 21 '16 at 21:36
  • @Biv, thanks for the clarification, I was obviously remembering wrong. – kodlu Dec 21 '16 at 21:47