Strict Avalanche Criterion and Avalanche criterion?

Question

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

Answer 1

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)

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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.

Related questions:

• Hash functions and the Avalanche effect
• Calculation of the avalanche effect coefficient

Answer 2

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.