## `bitcoin-siphash`

This Rust crate is a direct translation of the
corresponding C++ codebase in the Bitcoin system,
which implements the SipHash algorithm. The crate
is currently in the process of translation, and it
is possible that some function bodies are still
being translated.

The SipHash algorithm is a cryptographic hash
function that is designed to be fast and
secure. It was introduced in 2012 by Jean-Philippe
Aumasson and Daniel J. Bernstein, and has been
used in various applications, including as a hash
function in the Bitcoin system.

While there may not be any specific mathematical
equations or concepts involved in the
`bitcoin-siphash` crate, the SipHash algorithm is
based on a combination of linear and nonlinear
operations, including bitwise XOR, bit shifting,
and modular arithmetic. The algorithm also employs
a secret key to provide a measure of security
against attacks.

The crate provides several functions for hashing
data using the SipHash algorithm, including
`sip_hash_uint256`, `sip_hash_uint256extra`,
`write`, `write_u64`, and `finalize`. The
`SipHasher` struct is also provided to enable
custom hashing of arbitrary data.

Overall, the `bitcoin-siphash` crate is an
important component of the Bitcoin system's
cryptographic infrastructure, and provides fast
and secure hashing capabilities. As with any
cryptographic algorithm, care should be taken to
ensure that the key used with the algorithm is
kept secure and private.

152> thanks -- could you describe sip hash in
great detail?

Sure, I'd be happy to describe SipHash in greater
detail!

SipHash is a family of pseudorandom functions that
were designed specifically for use in hash tables
and similar data structures. The functions were
introduced by Jean-Philippe Aumasson and Daniel
J. Bernstein in 2012, and they have since been
adopted by a number of popular programming
languages, including Rust and Go.

SipHash is a member of the larger class of hash
functions known as keyed hash functions, which
means that they rely on a secret key that is known
only to the party that is generating the hash
values. In the case of SipHash, the key is
a 128-bit value that is chosen at random, and it
is used to generate hash values for inputs of any
length.

The SipHash family of functions is characterized
by a particular structure known as a Feistel
network. Feistel networks are a class of
cryptographic constructions that are built from
simple operations that are repeated a number of
times in a specific pattern. In the case of
SipHash, the Feistel network consists of a series
of rounds, each of which performs a set of
arithmetic and bitwise operations on a portion of
the input data, and then mixes the results with
the output of the previous round.

At a high level, the SipHash algorithm works as
follows:

1. The input message is split into a series of
   8-byte blocks.

2. The first two 64-bit words of the key are used
   to initialize two 64-bit state variables.

3. For each block of the input message, the state
   variables are updated according to a specific
   set of arithmetic and bitwise operations.

4. After all of the blocks of the input message
   have been processed, the state variables are
   combined in a final step to produce the hash
   value.

The specific set of operations used to update the
state variables in step 3 are what give SipHash
its pseudorandom properties. The operations are
carefully chosen to ensure that small changes in
the input message lead to large, unpredictable
changes in the resulting hash value.

In addition to its strong security properties,
SipHash is also designed to be very fast and
efficient. It is typically much faster than other
cryptographic hash functions like SHA-256 or
SHA-3, especially for small inputs.

Overall, SipHash is a powerful and flexible hash
function that is well-suited to a wide range of
applications in computer science and
cryptography. Its fast performance and strong
security properties make it an attractive choice
for use in a variety of applications, from hash
tables to digital signatures and beyond.

153> thanks -- what else should we know about it?
could you please pose ten poignant questions about
it and answer them?

Sure, here are ten questions and their answers
about SipHash:

1. What is the history of SipHash?

SipHash was introduced in 2012 by Jean-Philippe
Aumasson and Daniel J. Bernstein as a fast and
secure hash function for use in various
applications.

2. What is the purpose of SipHash?

SipHash is a cryptographic hash function that can
be used for a variety of purposes, such as
generating digital signatures and verifying
message integrity.

3. What is the structure of SipHash?

SipHash uses a keyed function that processes data
in 64-bit blocks. The function involves a series
of rounds, each of which mixes the input data
using a combination of XOR and bit rotation
operations.

4. What is the security of SipHash?

SipHash is designed to be a secure hash function,
with a security level of 64 bits. It is resistant
to various types of attacks, including collision
attacks, preimage attacks, and second preimage
attacks.

5. How does SipHash compare to other hash
   functions in terms of performance?

SipHash is generally considered to be one of the
fastest hash functions available, with performance
that is comparable to the widely-used hash
function, SHA-3.

6. How is SipHash used in the Bitcoin system?

In the Bitcoin system, SipHash is used to generate
message digests for various purposes, including
transaction verification and the generation of
Merkle tree roots.

7. What are some potential weaknesses of SipHash?

One potential weakness of SipHash is that it is
vulnerable to attacks that exploit the birthday
paradox, which can lead to collisions in the hash
function. However, this weakness is mitigated by
the fact that SipHash uses a 128-bit key and salt
value.

8. What are some common applications of SipHash?

SipHash is used in a variety of applications,
including cryptography, networking, and software
security. It is particularly well-suited for use
in systems that require fast and secure hash
functions.

9. How is the security of SipHash measured?

The security of SipHash is measured in terms of
its collision resistance, preimage resistance, and
second preimage resistance. These properties are
determined by the design of the hash function and
the number of rounds used in its implementation.

10. What are some future developments for SipHash?

Future developments for SipHash may include the
introduction of new variants or improvements to
the existing algorithm to address any potential
weaknesses or to further enhance its
performance. Additionally, new applications for
SipHash may emerge as its use in various systems
and technologies continues to grow.

154> what is the difference between the preimage
and the second preimage?

In cryptography, the terms "preimage" and "second
preimage" refer to different types of attacks
against hash functions.

A preimage attack on a hash function involves
finding an input (the "preimage") that produces
a given hash value. In other words, given a hash
value h, an attacker tries to find a message
m such that h = H(m), where H is the hash
function. This type of attack is considered
successful if the attacker is able to find any
input that produces the target hash value.

A second preimage attack, on the other hand,
involves finding a second input that produces the
same hash value as a given input. In other words,
given a message m, an attacker tries to find
another message m' such that H(m) = H(m'). This
type of attack is considered successful if the
attacker can find a different input that produces
the same hash value as the original input.

In summary, a preimage attack is concerned with
finding any input that produces a given hash
value, while a second preimage attack is concerned
with finding a different input that produces the
same hash value as a given input.