Which Hashing Algorithm Has No Collision Attacks?

Several good answers have already been provided on this topic, but the question remains intriguing. When we consider a hashing algorithm in its purest form, it is theoretically impossible to avoid collisions entirely, except in a few specific cases. A hashing algorithm’s primary function is to provide nearly perfect entropy, ensuring that no information about the source data can be practically extracted from the hash. In fact, some hashing algorithms incorporate elements of encryption to enhance their security.

Theoretical Limitations of Hashing Algorithms

Think about the basics of hashing: when you take a sequence of bytes—let's say 1000 bytes—and apply a cryptographic hash function like SHA-512, you are significantly reducing the data from 8000 bits to just 512 bits. This reduction dramatically increases the likelihood of collisions. With 8000 bits, there are (2^{8000}) possible values, whereas with 512 bits, there are only (2^{512}) possible values. In reality, each digest will have approximately (2^{7488}) possible corresponding 1000-byte inputs. Thus, it is almost certain that multiple source data inputs will produce the same hash digest, unless the source data itself is limited to the size of the hash output.

Secure Hash Functions and Collision Resistance

While there is no single hashing algorithm that can be guaranteed to have no collision attacks, several algorithms are considered to be highly resistant to such attacks. Specifically, SHA-2 (including variants like SHA-224, SHA-256, SHA-384, and SHA-512), SHA-3, and their variants (like SHAKE-128 and SHAKE-256) have so far not shown any efficient collision attacks. The Keccak and BLAKE2 families of hash functions are also noted for their strong security properties.

The security of a hash function against collision attacks is generally dependent on the output size. For instance, SHA-256 and SHA-512 are designed to provide 128-bit and 256-bit security respectively, meaning that the maximum theoretical resistance to collision attacks is half the output size. SHA-3–256 and SHA-3–512, for example, offer 128-bit and 256-bit security respectively, which is considered adequate for most practical purposes.

Lesser-Known Secure Hash Algorithms

Other secure hash algorithms, like Hardened SHA-1 and RIPEMD-160, have also not reported published collisions. However, these algorithms are nowadays often considered insufficient for high-security applications due to their lower bit security levels (80-bit for SHA-1 and RIPEMD-160). As such, they are often not recommended for critical systems that require 128-bit or higher security.

Conclusion

While it is highly unlikely to find a hashing algorithm with no collision attacks, there are certainly those that are extremely resistant to them, especially those that follow the SHA-2, SHA-3, Keccak, and BLAKE2 families. For most modern applications, these algorithms provide a robust solution against collision attacks, ensuring the integrity and security of the data being hashed.

For further reading, you may refer to the Wikipedia article on hash functions for an in-depth overview and additional details on these algorithms.