Avalanche effect: Wikis

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Encyclopedia

In cryptography, the avalanche effect refers to a desirable property of cryptographic algorithms, typically block ciphers and cryptographic hash functions. The avalanche effect is evident if, when an input is changed slightly (for example, flipping a single bit) the output changes significantly (e.g., half the output bits flip). In the case of quality block ciphers, such a small change in either the key or the plaintext should cause a drastic change in the ciphertext. The actual term was first used by Horst Feistel,[1] although the concept dates back to at least Shannon's diffusion.

The SHA1 hash function exhibits good avalanche effect. When a single bit is changed the hash sum becomes completely different.

If a block cipher or cryptographic hash function does not exhibit the avalanche effect to a significant degree, then it has poor randomization, and thus a cryptanalyst can make predictions about the input, being given only the output. This may be sufficient to partially or completely break the algorithm. Thus, the avalanche effect is a desirable condition from the point of view of the designer of the cryptographic algorithm or device.

Constructing a cipher or hash to exhibit a substantial avalanche effect is one of the primary design objectives. This is why most block ciphers are product ciphers. It is also why hash functions have large data blocks. Both of these features allow small changes to propagate rapidly through iterations of the algorithm, such that every bit of the output should depend on every bit of the input before the algorithm terminates.

Strict avalanche criterion

The strict avalanche criterion (SAC) is a generalization of the avalanche effect. It is satisfied if, whenever a single input bit is complemented, each of the output bits changes with a probability of one half. The SAC builds on the concepts of completeness and avalanche and was introduced by Webster and Tavares in 1985.[2]

Bit independence criterion

The bit independence criterion (BIC) states that output bits j and k should change independently when any single input bit i is inverted, for all i, j and k.

References

1. ^ Horst Feistel, "Cryptography and Computer Privacy." Scientific American, Vol. 228, No. 5, 1973. (JPEG format scanned)
2. ^ A. F. Webster and Stafford E. Tavares, "On the design of S-boxes", Advances in Cryptology - Crypto '85 (Lecture Notes in Computer Science), vol. 219, pp. 523-534, 1985.

Simple English

```hash function has good avalanche effect. When a single bit is changed the hash sum becomes completely different.]]
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In cryptography, the avalanche effect refers to an attractive property of block ciphers and cryptographic hash functions algorithms.

The avalanche effect is satisfied if:

1. If the output changes significantly (e.g., half the output bits flip) cause of a slight change in input (e.g., flipping a single bit)
2. In "quality" block ciphers, such a small change in either the key or the plaintext should cause a strong change in the ciphertext.

Both of above features allow small changes to propagate rapidly through iterations of the algorithm, in such a way that every bit of the output should depend on every bit of the input before the algorithm terminates.

The term avalanche effect was first used by Horst Feistel (Feistel 1973), although the concept was identified by Shannon's property of confusion.

If a block cipher or cryptographic hash function does not exhibit the avalanche effect to a significant degree, then it has poor randomization, and 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.

One of the primary design objectives in constructing a "quality" cipher or cryptographic hash function is to build a good avalanche effect. This is why most block ciphers are product ciphers. It is also why hash functions have large data blocks.

Strict avalanche criterion

The Strict Avalanche Criterion (SAC) is a property of boolean functions of importance to cryptography. A function is said to satisfy the strict avalanche criterion if, whenever a single input bit is complemented, each of the output bits should change with a probability of one half.

The SAC was built on the concepts of completeness and avalanche and introduced by Webster and Tavares in 1985.

Bit independence criterion

The Bit independence criterion (BIC) states that output bits j & k should change independently when any single input bit i is inverted, for all i, j and k.

References

• A. F. Webster and Stafford E. Tavares, "On the design of S-boxes", Advances in Cryptology - Crypto '85 (Lecture Notes in Computer Science), vol. 219, pp. 523-534, 1985.
• Practical example (32 bits), taken from the extensive justification of the hash function HSH 11/13
• Horst Feistel, "Cryptography and Computer Privacy." Scientific American, Vol. 228, No. 5, 1973. (JPEG format scanned)