Definition of avelanche effect and completeness effect
Answers
First of all, the avalanche effect is a desirable effect: it means that a very small change in the input will lead to a very big change in the output.
A security algorithm that doesn't provide this avalanche effect can lead to an easy statistical analysis: if the change of one bit from the input leads to the change of only one bit of the output, then it's easy to guess / try to find the input: just change one bit of it and verify if it was the right one.
How it works in DES: if you take a look at the DES, you'll see that it has 16 rounds and 2 permutations. The real thing happens in the rounds: for each round, the input bits are used to look up for bits that will be used as the output (the S-box). take a look at this presentation, for example. With the shifts that are made at each round, it means that the "index bits" (the ones used to the table look up) come from the "data bits" that come from the previous round.
Changing a single bit in the input will cause more bits to be changed in the following rounds. Slide 6.41 of the above presentation show how many bits will change at each round.
The avalanche effect (“landslide effect”) is a property of block ciphers and cryptographic hash functions algorithms. It is often desired in cryptography. The effect says, that a lot of the output must change, even when the input changes only a little. In good block ciphers this means: A small change in the key or the plaintext should cause a strong change in the ciphertext.
This means that small changes can spread fast, when the algorithm uses iterations. Thus, every bit of the output depends on every bit of the input.
The term avalanche effect was first used by Horst Feistel (Feistel 1973). Later, the concept was identified by Shannon's property of confusion.
If a block cipher or cryptographic hash function does not satisfy the avalanche effect to a significant degree, then it has poor randomization. Thus, a cryptanalyst can make forecasts about the input, if given only the output. This may be sufficient to partially or completely break (crack) the algorithm.
It is one of the primary design objectives when people create a strong cipher or cryptographic hash function. They try to build a good avalanche effect in it. Mathematically this uses the butterfly effect. This is why most block ciphers are product ciphers. It is also why hash functions have large data blocks.
i hope this much is okay for u