This is part 3 of a series on omission-tolerant integrity protection and related topics. See also part 1 and part 2. A technical report on the topic is available on this site and in the IACR ePrint Archive.
When a cryptographic hash is used as a checksum of a bit string, security depends on the collision resistance of the hash function. When the root label of a typed hash tree is used as an omission-tolerant checksum of a set of key-value pairs, security also depends on the collision resistance of a hash function, in this case of the hash function that is used to construct the typed hash tree. (It may also depend on the preimage resistance of the hash function depending on how the set is encoded, as we shall see in another post of this series.) The formal proof of security in the technical report is therefore based on a formal definition of collision resistance. But, surprising as this may seem, there is no standard, widely used, formal definition of collision resistance for the keyless, or unkeyed hash functions such as SHA256 that are used in practice.
Collision resistance is hard to define
The concept of a hash function collision is simple and clear enough: it is a pair of distinct elements of the domain of the hash function that have the same image. The concept of collision resistance, on the other hand, is difficult to define. The reason for this, as explained for example by Katz and Lindell in their Introduction to Modern Cryptography (Chapman & Hall/CRC, 2nd edition, 2014, bottom of page 155), is that collisions exist, and for any collision there exists a trivial algorithm that hardcodes the collision and outputs it in constant time.Continue reading “Mapping a Formal Definition of Collision Resistance to Existing Implementations of Hash Functions”