Aurura modexp (#111)

Port over aurora's modexp implementation.

Signed-off-by: Danno Ferrin <[email protected]>

README.md

@@ -33,7 +33,7 @@ TBD
 
 ### Rust
 
-Rust needs to be installed to compile the altbn128 library. The default way to install it on Linux or OS X is:
+Rust needs to be installed to compile the arithmetic and bls12-381 libraries. The default way to install it on Linux or OS X is:
 
 ```
 curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh

arithmetic/arithmetic/Cargo.toml

@@ -1,15 +1,17 @@
 [package]
 name = "besu-native-arithmetic"
 version = "0.11.0"
-description = "Native arithemetic for EVM."
+description = """Native arithemetic for EVM.
+Derived from aurora - https://github.com/aurora-is-near/aurora-engine/tree/4ecee7ded1e6c78b69416e5b22388357316f7551/engine-modexp - originally CC0-1.0 license."""
 license = "Apache-2.0"
-authors = ["Danno Ferrin <[email protected]>"]
+authors = ["Aurora Labs <[email protected]>", "Danno Ferrin <[email protected]>"]
 repository = "https://github.com/hyperledger/besu-native"
 edition = "2021"
 
 [dependencies]
-num-bigint = "0.4.3"
-num-traits = "0.2.15"
+ibig = { version = "0.3.6", default-features = false, features = ["num-traits"], optional = true }
+num = { version = "0.4.0", default-features = false, features = ["alloc"] }
+hex = { version = "0.4", default-features = false, features = ["alloc"] }
 libc = "0.2"
 
 [lib]

arithmetic/arithmetic/README.md

@@ -0,0 +1,34 @@
+# Besu native `modexp`
+
+Originally from Aurora `modexp` [implementation](https://github.com/aurora-is-near/aurora-engine/tree/4ecee7ded1e6c78b69416e5b22388357316f7551/engine-modexp)
+
+## What this crate is
+
+This crate is an efficient implementation of the EVM `modexp` precompile.
+This crate exposes a single public function
+
+```rust
+pub fn modexp(base: &[u8], exp: &[u8], modulus: &[u8]) -> Vec<u8>
+```
+
+This function takes the base, exponent and modulus as big-endian encoded bytes and returns the result in big-endian as well.
+
+This crate is meant to be an efficient implementation, using as little memory as possible (for example, it does not copy the exponent slice).
+The exponentiation is done using the ["binary method"](https://en.wikipedia.org/wiki/Exponentiation_by_squaring).
+The multiplication steps within the exponentiation use ["Montgomery multiplication"](https://en.wikipedia.org/wiki/Montgomery_modular_multiplication).
+In the case of even modulus, Montgomery multiplication does not apply directly.
+However we can reduce the problem to one involving an odd modulus and one where the modulus is a power of two.
+These two sub-problems can be solved efficiently (the former using Montgomery multiplication, the latter the modular arithmetic is trivial on a binary computer),
+then the results are combined using the [Chinese remainder theorem](https://en.wikipedia.org/wiki/Chinese_remainder_theorem).
+
+The primary academic references for this implementation are:
+
+1. [Analyzing and Comparing Montgomery Multiplication Algorithms](https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf)
+2. [Montgomery Reduction with Even Modulus](http://www.people.vcu.edu/~jwang3/CMSC691/j34monex.pdf)
+3. [A Cryptographic Library for the Motorola DSP56000](https://link.springer.com/content/pdf/10.1007/3-540-46877-3_21.pdf)
+4. [The Art of Computer Programming Volume 2](https://www-cs-faculty.stanford.edu/~knuth/taocp.html)
+
+## What this crate is NOT
+
+This crate is not a general purpose big integer library.
+If you need anything other than `modexp`, then you should use something like [num-bigint](https://crates.io/crates/num-bigint) or [ibig](https://crates.io/crates/ibig).