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Hash Collections

Collections such as maps and sets are fundamental data structures. sp_std exposes them via BTreeMap and BTreeSet respectively. These map closely to the implementations in Rust's standard library. However, the standard library also contains HashMap and HashSet. Let's look into why those types are not also exposed in sp_std.

Trees vs. Hashes

Trees and hashes are two distinct approaches to implementing the interface of a map or set. Fundamentally, trees operate by comparing items: a node in the tree contains an item, and might contain references to a set of items less than the node item, and a set of items greater than the node item. Tree-based maps and sets have O(log n) performance characteristics for insert, remove, and contains, where n is the number of items currently contained in the collection.

Hashes, on the other hand, lay out a number of "buckets" in memory. Each bucket contains a list of items. Their method of operation is to hash each item: reduce it via some hash function into a number. Then, they use the hash value to select which bucket should contain the item. Finally, in the event that the bucket is not empty, items are handled in unordered manner; the list is scanned linearly. Hash-based maps and sets have O(1) performance characteristics for insert, remove, and contains: their performance does not depend on the number of items they contain.

Clearly, hash-based implementations are faster than tree-based implementations for large n. However, most modern hash implementations require non-determinism in order to operate properly.

Non-determinism in hash collections

The transform from an arbitrary hashable piece of data into a hash bucket for a particular hash table typically occurs in two phases: first, the data is hashed into a single number, the hash value. Then, the hash value is transformed into the index of a particular bucket. While in principle an attack could target either phase of that process, in practice, existing attacks focus on the hasher, because that requires less knowledge about the program's internal state.

In 2003, researchers discovered an attack on hash collections which operate in this way. In 2011, other researchers demonstrated a way to use this attack on software written in several languages popular at the time.

The attack is simple: generate a large number of inputs, all of which hash into the same bucket. This means that instead of taking constant time for an insert, you need to spend time proportional to the number of items already in the bucket. This in turn transforms the total cost required to insert a list of n items from O(n) to O(n**2).

The mitigation was also simple: generate a random value at program initialization, then include that value in the hash function's input. This makes it impossible to pre-compute a set of inputs which will generate a collision. In 2012, it was shown that a cryptographic hash function is necessary to effectively defend against hash-flooding attacks. The same presentation introduced SipHash for that purpose. That hash function and strategy remains the state of the art as of 2021, and forms the basis for hashes in many languages, including Rust.

However, the foundation of the strategy remains a single, random number. This is incompatible with blockchain applications.

Non-determinism on the blockchain

Blockchains are fundamentally consensus engines. At heart, this means that all the validators have to do the same thing.

It's trivial to imagine a runtime which intentionally behaves non-deterministically based on things like the location of hashmap values in memory. That's straightforward operator error; it will only happen to users who are doing things they shouldn't.

However, non-determinism can occur for other reasons. Consider a hashmap implementation which uses the max quantity of items in a bucket as a heuristic for when to resize itself. Now consider how that system behaves as it runs out of memory. Some nodes will believe that the block is invalid: they happened to generate internal hash seeds which prompted them to grow past the memory limits. Other nodes will believe that the block is valid: their seeds prompted less growth, resulting in successful block execution. This forks the blockchain.

This particular scenario is straightforward to guard against; just make resizing behavior a simple function of total items contained, without any bucket size heuristics. However, it illustrates the broader case: it is very difficult to encapsulate non-determinism in a way which is deterministic across nodes. Parity has chosen not to spend the R&D effort which would be required to solve that problem.

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