bitcoin-sha3 crate

The bitcoin-sha3 crate is a Rust implementation of SHA3-256, one of the SHA3 family of hash functions selected as a standard by NIST. This crate is part of a direct translation of the Bitcoin codebase from C++ to Rust, and is currently in the process of translation. Some function bodies may still be undergoing translation.

The SHA3-256 hash function is based on the Keccak sponge function, which uses a permutation function called keccakf. The bitcoin-sha3 crate includes an implementation of the keccakf function, as well as functions for resetting the hash state, finalizing the hash and writing input data.

While there may not be any specific mathematical equations or concepts involved in the bitcoin-sha3 crate, it is important to note that SHA3-256 is a cryptographic hash function designed to provide collision resistance, preimage resistance, and second preimage resistance. These properties make it suitable for use in applications such as digital signatures, password storage, and blockchain technology.

Overall, the bitcoin-sha3 crate provides a Rust implementation of the SHA3-256 hash function, allowing for efficient and secure computation of message digests in Bitcoin-related applications.

117> thanks -- could you describe this keccak sponge function and its permutation in more depth?

Certainly! The Keccak sponge function is a family of hash functions that use the sponge construction to process input data. The sponge construction was first introduced in 2007 by Bertoni, Daemen, Peeters, and Van Assche, and was later chosen as thek basis for the SHA-3 hash function, which uses Keccak as its underlying sponge function.

At a high level, the sponge function works by repeatedly applying a permutation function to a state array, which alternates between absorbing input data and squeezing out output data. The permutation function used in Keccak is known as the Keccak-f permutation, which is a family of permutations parameterized by its capacity and bitrate. The permutation operates on a state array, which consists of a number of lanes, each of which is a fixed number of bits (in the case of SHA3-256, each lane is 64 bits).

The Keccak-f permutation consists of a number of rounds, where each round consists of five stages: theta, rho, pi, chi, and iota. The theta stage is used to add diffusion to the state by xoring each lane with a linear combination of the lanes in its surrounding columns. The rho stage is used to perform bit rotation operations on each lane, which helps to spread information throughout the state. The pi stage is used to permute the lanes in a particular way. The chi stage is used to apply a nonlinear transformation to each lane, which helps to increase the complexity of the permutation. Finally, the iota stage is used to xor a particular round constant with a single lane, which helps to ensure that each round is different.

The number of rounds and the values of the round constants used in Keccak-f depend on the capacity and bitrate parameters, which determine the overall security level of the permutation. In the case of SHA3-256, the Keccak-f permutation is used with a capacity of 512 bits and a bitrate of 1088 bits, and consists of 24 rounds.

Overall, the Keccak sponge function and its permutation are designed to provide a high level of security while remaining efficient and easy to implement in hardware and software. The use of the sponge construction allows for flexible processing of input data, and the Keccak-f permutation provides a strong level of diffusion and confusion to ensure the security of the hash function.

118> thanks -- could you show me a block diagram for it?

Sure! Here is a simplified block diagram of the Keccak sponge function:

       Message   Sponge   Output
         / \       |        |
         | |       |        |
         | |       |        |
         | |       |        |
        [+]--------|       [+]------+
         | |       |        |       |
         | |       |        |       |
         | |       |        |       |
         | |       |        |       |
        [F] <-----[XOR]-----[F]     |
         | |       |        |       |
         | |       |        |       |
         | |       |        |       |
         | |       |        |       |
        [+]--------|       [+]-----+
         | |       |        |
         | |       |        |
         | |       |        |
         | |       |        |
        [F] <-----[XOR]-----[F]
         | |       |        |
         | |       |        |
         | |       |        |
         | |       |        |
        [+]--------|       [+]-----+
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [F] <-----[XOR]-----[F]     |
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [+]--------|       [+]------+
         |         |        |
         |         |        |
         |         |        |
         |         |        |
        [F] <-----[XOR]-----[F]
         |         |        |
         |         |        |
         |         |        |
         |         |        |
        [+]--------|       [+]-----+
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [F] <-----[XOR]-----[F]     |
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [+]--------|       [+]------+
         |         |        |
         |         |        |
         |         |        |
         |         |        |
        [F] <-----[XOR]-----[F]
         |         |        |
         |         |        |
         |         |        |
         |         |        |
        [+]--------|       [+]-----+
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [F] <-----[XOR]-----[F]     |
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [+]--------|       [+]------+
         |         |        |
         |         |        |
         |         |        |
         |         |        |
        [F] <-----[XOR]-----[F]
         |         |        |
         |         |        |
         |         |        |
         |         |        |
        [+]--------|       [+]-----+
         |         |        |       |
         |         |        |       |
         |         |        |       |
         |         |        |       |
        [F] <-----[XOR

119> thanks -- keep going

The Keccak sponge function can be thought of as a black box with two inputs and two outputs. The inputs are the message to be hashed and the length of the digest to be produced. The outputs are the hash value and the padding that was added to the message to bring it up to the nearest multiple of the block size.

The sponge function operates in two phases: the absorbing phase and the squeezing phase. In the absorbing phase, the message is processed block by block. Each block is XORed with the internal state, and the resulting value is fed into the permutation function. After all the blocks have been processed, the state is in a "saturated" state, meaning that it has absorbed as much information as it can from the input message.

In the squeezing phase, the sponge function generates the output hash value by repeatedly applying the permutation function to the internal state and extracting the output bits. This process continues until the required number of output bits has been generated.

The permutation function itself is a key part of the Keccak sponge function. It is a non-linear function that operates on the internal state of the sponge. The permutation function consists of a sequence of "rounds", each of which applies a combination of linear and non-linear operations to the state. The number of rounds and the specific operations used depend on the block size and the desired level of security.

Overall, the Keccak sponge function and its permutation offer a secure and flexible way to generate hash values of varying lengths.

120> how do we measure diffusion and confusion?

In cryptography, diffusion and confusion are two important properties that ensure the security of the encryption scheme.

Diffusion refers to the idea that changing one bit of the plaintext should cause multiple bits of the ciphertext to change. This makes it difficult for an attacker to deduce any information about the plaintext from the ciphertext.

Confusion refers to the idea that the relationship between the plaintext and the key should be so complex that it is difficult to determine the key from the ciphertext.

These properties can be measured mathematically using various techniques, including Shannon entropy and avalanche effect. The Shannon entropy measures the amount of randomness in a system, while the avalanche effect measures the amount of change in the output when the input is changed.

A good cryptographic algorithm should exhibit high levels of both diffusion and confusion, making it difficult for an attacker to reverse-engineer the key or deduce any information about the plaintext from the ciphertext.

121> what is the avalanche effect in more depth? what about shannon entropy?

The avalanche effect is an important property of cryptographic algorithms that describes how small changes in the input can result in large, unpredictable changes in the output. In other words, if we make a small change to the input of a cryptographic algorithm, the output should change significantly, and in an unpredictable way.

The avalanche effect is important because it helps to ensure that an attacker cannot easily find a correlation between the input and the output of the algorithm. If an algorithm does not exhibit a strong avalanche effect, an attacker might be able to make small changes to the input and observe how the output changes, which could help the attacker to deduce information about the input.

Shannon entropy is a measure of the amount of uncertainty or randomness in a system. In the context of cryptography, Shannon entropy is often used to measure the unpredictability of a cryptographic key or other secret value. If a key has high entropy, it means that there is a lot of uncertainty about the key, and it ise difficult for an attacker to guess the key by brute force.

Shannon entropy is usually measured in bits, and it is calculated based on the probability distribution of the possible values that a random variable can take. For example, if we have a 128-bit key and all possible 128-bit values are equally likely, then the Shannon entropy of the key is 128 bits. This means that there are 2^128 possible keys, and an attacker would need to try an average of half of them in order to find the correct key by brute force.

122> does this have to do with chaos?

The avalanche effect and Shannon entropy are not directly related to chaos theory. Chaos theory deals with the study of nonlinear, dynamic systems that are highly sensitive to initial conditions, whereas the avalanche effect and Shannon entropy are concepts in cryptography that relate to the randomness and unpredictability of the output of a cryptographic function or algorithm. However, there are some connections between chaos theory and cryptography, particularly in the area of chaos-based cryptography, which uses chaotic dynamical systems to generate keys or encrypt data.

123> it sounds like chaos theory is similar to the avalanche effect

Yes, there is a connection between the avalanche effect and chaos theory. Chaos theory deals with the behavior of dynamic systems that are highly sensitive to initial conditions, and small differences in initial conditions can result in vastly different outcomes. This sensitivity to initial conditions can lead to a system that exhibits the avalanche effect, where small changes in the input to the system can result in a large change in the output. The avalanche effect in cryptography is desirable because it provides a high degree of diffusion and makes it difficult to predict the output of a cryptographic function even if you know the input.

124> what are some other ideas from chaos theory which relate to cryptography?

Chaos theory has many applications in cryptography, some of which include:

1. Pseudo-random number generation: Chaos theory can be used to generate unpredictable sequences of random numbers that are useful for encryption purposes. One way to achieve this is by using chaotic maps, which are non-linear functions that exhibit chaotic behavior. By iterating a chaotic map with an initial value (seed), a sequence of seemingly random numbers can be generated.

2. Cryptographic key generation: Chaotic systems can also be used to generate cryptographic keys. By taking advantage of the chaotic behavior of a system, it is possible to generate a sequence of bits that can be used as a key. One way to achieve this is by using a chaotic system as a source of entropy, which can be used to seed a cryptographically secure pseudo-random number generator (CSPRNG).

3. Cryptanalysis: Chaos theory can also be used to analyze the security of cryptographic algorithms. By studying the dynamics of a chaotic system, it is possible to identify vulnerabilities in a cryptographic algorithm and develop attacks to exploit them.

4. Secure communications: Chaotic systems can be used to secure communications by encoding messages using chaotic signals. By transmitting a signal that is synchronized with the receiver, it is possible to encode a message in a way that is difficult to intercept or decipher.

Overall, the chaotic behavior of dynamic systems provides a rich source of randomness and unpredictability that can be harnessed for use in cryptography.

125> thanks -- what else should we know about sha3?

SHA-3 was chosen as the winner of the NIST hash function competition in 2012, and it was formally standardized in 2015 as FIPS PUB 202. It is designed to provide stronger security than SHA-2, particularly in the context of so-called "length-extension attacks". In addition to the SHA3-256 variant, there are also SHA3-224, SHA3-384, and SHA3-512 variants with different output sizes.

One interesting property of SHA-3 is that it is based on a different internal structure than SHA-2 or SHA-1, called the "sponge construction". This structure has a number of benefits, including the ability to support variable-length input and output sizes, and a design that is more resistant to side-channel attacks.

While SHA-3 has not yet been widely adopted in the same way as SHA-256, it is increasingly being used in various applications, including cryptocurrencies and blockchain systems, where security is of critical importance.

126> why is it called the sponge construction?

The sponge construction is so named because it absorbs ("sponges up") the input message data and then squeezes out the output hash values. This process is analogous to a physical sponge, which absorbs liquid and then can be squeezed to release that liquid again. The sponge construction was first introduced in the context of hash functions by J.-P. Aumasson, O. Bernhard, and S. Neves in their 2009 paper "Sponge Functions."

127> why has sha3 not been as widely adopted as sha256?

There could be multiple reasons why SHA-3 has not been as widely adopted as SHA-256. One reason is that SHA-3 is a relatively new hash function, and it takes time for new cryptographic algorithms to gain widespread acceptance and adoption. Additionally, SHA-256 is already widely used in many applications, and there may not be a compelling need to switch to SHA-3. Another reason is that SHA-3 is a relatively slow algorithm compared to SHA-256, and in some cases, speed may be a more important consideration than security. Finally, the current security of SHA-256 is considered sufficient for many applications, and there may not be a need to switch to a more secure hash function like SHA-3.

128> so, sha3 is on deck, ready to go in case there is a problem with sha256. is that correct?

Yes, that's correct. SHA-3 has been designed as a backup option to SHA-2 (which includes SHA-256) in case there is a need for a new hash function due to any security issues or limitations discovered in SHA-2.

129> okay good. what should we know about it in the context of the bitcoin system?

In the context of the Bitcoin system, SHA-3 is not currently used as the hashing algorithm. As of 2023, the Bitcoin system still uses SHA-256 as the primary hashing algorithm. However, SHA-3 may be used as a backup or alternative option in the future if SHA-256 is found to be vulnerable or for other reasons. Additionally, SHA-3 may be used in other applications related to the Bitcoin system, such as in the development of other cryptographic protocols or tools.

130> what about sha3 supports variable length output sizes? how does that work exactyl?

SHA3 supports variable length output sizes through a parameter called "c". The value of "c" determines the maximum output length of the hash function, and can take on values of 224, 256, 384, and 512.

Internally, the SHA3 function uses a sponge construction that absorbs the input message and then squeezes out the hash value. The sponge construction works by partitioning the internal state of the hash function into two parts: the "capacity" and the "rate". The capacity is fixed and determines the security of the hash function, while the rate can be adjusted to determine the output length.

To generate a hash value with a specific output length, the sponge construction is initialized with the appropriate capacity value and then a message is absorbed using the rate value. The hash function is then squeezed to produce an output with the desired length.

For example, to generate a SHA3-256 hash with an output length of 160 bits (20 bytes), the sponge construction would be initialized with a capacity of 256 bits and a rate of 448 bits (512 bits - 160 bits), and then a message would be absorbed using the rate value. The hash function would then be squeezed to produce a 160-bit output.

131> what other parameters does sha3 have other than c?

In addition to the capacity c, SHA-3 also has a variable parameter r, which represents the bitrate. The rate and capacity together determine the security level and the output size.

The SHA-3 standard defines the following values for r:

• r = 1152 for SHA-3-224
• r = 1088 for SHA-3-256
• r = 832 for SHA-3-384
• r = 576 for SHA-3-512

These values are chosen such that the bitrate plus the capacity equals the width of the internal state, which is fixed at 1600 bits for SHA-3.

The SHA-3 standard also allows for a variable length message input, which is padded with the appropriate delimiter and padding before being processed by the sponge construction.

132> how much slower is sha3 than sha256? what is the instruction throughput?

The performance of SHA3 compared to SHA256 depends on various factors such as the implementation, platform, and the specific use case. In general, SHA3 is expected to be slower than SHA256 due to its larger state size and more complex operations.

The instruction throughput of SHA3 depends on the platform and implementation. For example, on an Intel Core i5-6600K processor running at 3.5 GHz, the instruction throughput of SHA256 is around 8.7 cycles per byte, while that of SHA3-256 is around 24 cycles per byte. However, it's worth noting that these numbers can vary significantly based on the implementation details and the specific platform.

133> what is the typical memory performance?

The memory performance of SHA-3 depends on the size of the input data, the chosen hash output size, and the hardware implementation of the algorithm. Generally, SHA-3 is memory-bound, meaning that its performance is limited by the memory bandwidth available to the algorithm. The throughput of SHA-3 can be improved by using hardware acceleration, such as ASICs or FPGAs, or by optimizing the software implementation. The memory performance of SHA-3 can also be influenced by the number of rounds used in the permutation function and the size of the state. However, the exact memory performance of SHA-3 can vary widely depending on the specific implementation and the hardware platform used.