throw out rust because im stupid
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||||||
"windows_x86_64_msvc",
|
|
||||||
]
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_aarch64_gnullvm"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "32a4622180e7a0ec044bb555404c800bc9fd9ec262ec147edd5989ccd0c02cd3"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_aarch64_msvc"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "09ec2a7bb152e2252b53fa7803150007879548bc709c039df7627cabbd05d469"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_i686_gnu"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "8e9b5ad5ab802e97eb8e295ac6720e509ee4c243f69d781394014ebfe8bbfa0b"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_i686_gnullvm"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "0eee52d38c090b3caa76c563b86c3a4bd71ef1a819287c19d586d7334ae8ed66"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_i686_msvc"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "240948bc05c5e7c6dabba28bf89d89ffce3e303022809e73deaefe4f6ec56c66"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_x86_64_gnu"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "147a5c80aabfbf0c7d901cb5895d1de30ef2907eb21fbbab29ca94c5b08b1a78"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_x86_64_gnullvm"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "24d5b23dc417412679681396f2b49f3de8c1473deb516bd34410872eff51ed0d"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "windows_x86_64_msvc"
|
|
||||||
version = "0.52.6"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "589f6da84c646204747d1270a2a5661ea66ed1cced2631d546fdfb155959f9ec"
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "zerocopy"
|
|
||||||
version = "0.7.35"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "1b9b4fd18abc82b8136838da5d50bae7bdea537c574d8dc1a34ed098d6c166f0"
|
|
||||||
dependencies = [
|
|
||||||
"byteorder",
|
|
||||||
"zerocopy-derive",
|
|
||||||
]
|
|
||||||
|
|
||||||
[[package]]
|
|
||||||
name = "zerocopy-derive"
|
|
||||||
version = "0.7.35"
|
|
||||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
|
||||||
checksum = "fa4f8080344d4671fb4e831a13ad1e68092748387dfc4f55e356242fae12ce3e"
|
|
||||||
dependencies = [
|
|
||||||
"proc-macro2",
|
|
||||||
"quote",
|
|
||||||
"syn",
|
|
||||||
]
|
|
||||||
10
Cargo.toml
10
Cargo.toml
|
|
@ -1,10 +0,0 @@
|
||||||
[package]
|
|
||||||
name = "ec_crypto"
|
|
||||||
version = "0.1.0"
|
|
||||||
edition = "2021"
|
|
||||||
|
|
||||||
[dependencies]
|
|
||||||
rand = "0.8.5"
|
|
||||||
num = "0.4.3"
|
|
||||||
discrete-logarithm = "1.0.0"
|
|
||||||
rug = "1.26.1"
|
|
||||||
93
keygen.py
Normal file
93
keygen.py
Normal file
|
|
@ -0,0 +1,93 @@
|
||||||
|
from fractions import Fraction
|
||||||
|
import random
|
||||||
|
from dataclasses import dataclass
|
||||||
|
from sympy.ntheory.residue_ntheory import nthroot_mod
|
||||||
|
from itertools import cycle
|
||||||
|
|
||||||
|
@dataclass
|
||||||
|
class ec:
|
||||||
|
a: int
|
||||||
|
b: int
|
||||||
|
p: int
|
||||||
|
|
||||||
|
def ec_add(self, p1, p2):
|
||||||
|
if all(v1 == v2 for v1, v2 in zip(p1, p2)):
|
||||||
|
#print("H")
|
||||||
|
if self.p:
|
||||||
|
dy = Fraction((3*p1[0]**2 + self.a), 2*p1[1])
|
||||||
|
else:
|
||||||
|
dy =(3*p1[0]**2 + self.a) / (2*p1[1])
|
||||||
|
else:
|
||||||
|
if self.p:
|
||||||
|
dy = Fraction((p2[1] - p1[1]), (p2[0] - p1[0]))
|
||||||
|
else:
|
||||||
|
dy = (p2[1] - p1[1]) / (p2[0] - p1[0])
|
||||||
|
res_x = dy ** 2 - p1[0] - p2[0]
|
||||||
|
res_y = (dy * (p1[0] - res_x) - p1[1])
|
||||||
|
if self.p != None:
|
||||||
|
res_x = int(res_x % self.p)
|
||||||
|
res_y = int(res_y % self.p)
|
||||||
|
return (res_x, res_y)
|
||||||
|
return (float(res_x), float(res_y))
|
||||||
|
def ec_mul(self, p, s):
|
||||||
|
for _ in range(s):
|
||||||
|
p = self.ec_add(p, p)
|
||||||
|
return p
|
||||||
|
def __getitem__(self, pos):
|
||||||
|
x = pos[0]
|
||||||
|
x_given = type(x) != slice
|
||||||
|
if x_given: value = x**3+self.a*x+self.b
|
||||||
|
else: raise ValueError()
|
||||||
|
solutions = [(x % self.p, s) for s in nthroot_mod(value, 2, self.p, True)]
|
||||||
|
return solutions
|
||||||
|
|
||||||
|
@dataclass
|
||||||
|
class Person:
|
||||||
|
name: str
|
||||||
|
private: tuple[int, int]
|
||||||
|
public: tuple[int, int]
|
||||||
|
shared: tuple[int, int]
|
||||||
|
|
||||||
|
def gen_keys(self, start, curve: ec):
|
||||||
|
self.private = random.randint(0, curve.p)
|
||||||
|
self.public = curve.ec_mul(start, self.private)
|
||||||
|
print(f"[{self.name}]: private: {self.private} -> public: {self.public[1]}")
|
||||||
|
return
|
||||||
|
|
||||||
|
def gen_shared(self, public, curve: ec):
|
||||||
|
self.shared = curve.ec_mul(public, self.private)
|
||||||
|
return
|
||||||
|
|
||||||
|
def diffie_hellman(curve: ec, alice, bob):
|
||||||
|
gen = (4, 10)
|
||||||
|
alice.gen_keys(gen, curve)
|
||||||
|
bob.gen_keys(gen, curve)
|
||||||
|
alice.gen_shared(bob.public, curve)
|
||||||
|
bob.gen_shared(alice.public, curve)
|
||||||
|
assert(alice.shared == bob.shared)
|
||||||
|
print(f"[{alice.name}|{bob.name}] generated equal shared keys")
|
||||||
|
|
||||||
|
def xor(data, key):
|
||||||
|
key = str(key)
|
||||||
|
data = data.encode() if isinstance(data, str) else data
|
||||||
|
key = key.encode() if isinstance(key, str) else key
|
||||||
|
return bytearray(a ^ b for a, b in zip(data, cycle(key)))
|
||||||
|
|
||||||
|
def send(self, msg, target):
|
||||||
|
encrypted = Person.xor(msg, self.shared[1])
|
||||||
|
print(f"[{self.name}] sent message '{msg}' to {target.name}")
|
||||||
|
target.recv(encrypted, self)
|
||||||
|
|
||||||
|
def recv(self, msg, source):
|
||||||
|
decrypted = str(Person.xor(msg, self.shared[1]), encoding='utf-8')
|
||||||
|
print(f"[{self.name}] received message '{decrypted}' from {source.name}")
|
||||||
|
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
curve = ec(0, 7, 1109)
|
||||||
|
alice = Person("alice", 0, 0, 0)
|
||||||
|
bob = Person("bob", 0, 0, 0)
|
||||||
|
|
||||||
|
Person.diffie_hellman(curve, alice, bob)
|
||||||
|
alice.send("Hello world", bob)
|
||||||
|
|
||||||
132
src/keygen.rs
132
src/keygen.rs
|
|
@ -1,132 +0,0 @@
|
||||||
use core::str;
|
|
||||||
use std::u32;
|
|
||||||
|
|
||||||
use num::{pow::Pow, Integer};
|
|
||||||
use rand::{distributions::Standard, prelude::Distribution};
|
|
||||||
|
|
||||||
use crate::utils::*;
|
|
||||||
|
|
||||||
struct EllipticCurve<BigInt>
|
|
||||||
where
|
|
||||||
BigInt: Integer,
|
|
||||||
{
|
|
||||||
a: BigInt,
|
|
||||||
b: BigInt,
|
|
||||||
r#mod: BigInt,
|
|
||||||
}
|
|
||||||
impl<BigInt> EllipticCurve<BigInt>
|
|
||||||
where
|
|
||||||
BigInt: Integer + std::marker::Copy + Pow<usize, Output = BigInt>,
|
|
||||||
Standard: Distribution<BigInt>,
|
|
||||||
{
|
|
||||||
pub fn new(a: BigInt, b: BigInt, r#mod: BigInt) -> Self {
|
|
||||||
EllipticCurve { a, b, r#mod }
|
|
||||||
}
|
|
||||||
|
|
||||||
pub fn y(&self, x: BigInt) -> BigInt {
|
|
||||||
(x.pow(3) + self.b * x + self.a) % self.r#mod
|
|
||||||
}
|
|
||||||
pub fn random(&self) -> (BigInt, BigInt) {
|
|
||||||
let mut start = rand::random::<BigInt>() % self.r#mod;
|
|
||||||
let i_count = rand::random::<i8>();
|
|
||||||
|
|
||||||
for _ in 0..i_count {
|
|
||||||
start = self.y(start);
|
|
||||||
}
|
|
||||||
|
|
||||||
(start, self.y(start))
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
pub struct Person {
|
|
||||||
pub name: String,
|
|
||||||
private_key: Option<u32>,
|
|
||||||
pub public_key: Option<u32>,
|
|
||||||
pub shared_key: Option<u32>,
|
|
||||||
pub gen: Option<u32>,
|
|
||||||
pub r#mod: Option<u32>,
|
|
||||||
}
|
|
||||||
impl Person {
|
|
||||||
pub fn new(name: &str) -> Self {
|
|
||||||
Person {
|
|
||||||
name: name.to_string(),
|
|
||||||
private_key: None,
|
|
||||||
public_key: None,
|
|
||||||
shared_key: None,
|
|
||||||
gen: None,
|
|
||||||
r#mod: None,
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
pub fn gen_keys(&mut self, start: u32, r#mod: u32) {
|
|
||||||
let private = rand::random::<u32>() % r#mod;
|
|
||||||
self.private_key = Some(private.into());
|
|
||||||
let public = mod_pow(start, private.into(), r#mod);
|
|
||||||
self.public_key = Some(public);
|
|
||||||
self.gen = Some(start);
|
|
||||||
self.r#mod = Some(r#mod);
|
|
||||||
eprintln!(
|
|
||||||
"[{}] private: {} -> public: {}",
|
|
||||||
self.name,
|
|
||||||
self.private_key.unwrap(),
|
|
||||||
self.public_key.unwrap()
|
|
||||||
);
|
|
||||||
}
|
|
||||||
|
|
||||||
pub fn gen_shared(&mut self, public: u32, r#mod: u32) {
|
|
||||||
self.shared_key = Some(mod_pow(public, self.private_key.unwrap(), r#mod))
|
|
||||||
}
|
|
||||||
|
|
||||||
pub fn diffie_hellman(p1: &mut Self, p2: &mut Self) {
|
|
||||||
let m: u32 = 1109;
|
|
||||||
let curve = EllipticCurve::new(0, 7, m);
|
|
||||||
let gen = curve.random().1;
|
|
||||||
|
|
||||||
eprintln!(
|
|
||||||
"Start params: x³+{}x+{}, mod {}, generator {}",
|
|
||||||
0, 7, m, gen
|
|
||||||
);
|
|
||||||
|
|
||||||
p1.gen_keys(gen, m.into());
|
|
||||||
p2.gen_keys(gen, m.into());
|
|
||||||
p1.gen_shared(p2.public_key.unwrap(), m.into());
|
|
||||||
p2.gen_shared(p1.public_key.unwrap(), m.into());
|
|
||||||
assert_eq!(p1.shared_key, p2.shared_key);
|
|
||||||
eprintln!(
|
|
||||||
"[{}] Shared key for {}: {}",
|
|
||||||
p1.name,
|
|
||||||
p2.name,
|
|
||||||
p1.shared_key.unwrap()
|
|
||||||
);
|
|
||||||
}
|
|
||||||
|
|
||||||
fn xor_cipher(msg: &[u8], key: u32) -> Vec<u8> {
|
|
||||||
let key_bytes = key.to_le_bytes();
|
|
||||||
let key_len = key_bytes.len();
|
|
||||||
|
|
||||||
msg.iter()
|
|
||||||
.enumerate()
|
|
||||||
.map(|(i, &byte)| byte ^ key_bytes[i % key_len])
|
|
||||||
.collect()
|
|
||||||
}
|
|
||||||
|
|
||||||
pub fn send(&self, msg_raw: &[u8], target: &Self) {
|
|
||||||
let encrypted_raw = Self::xor_cipher(msg_raw, self.shared_key.unwrap());
|
|
||||||
let encrypted = str::from_utf8(&encrypted_raw).unwrap_or("not displayable");
|
|
||||||
let msg = str::from_utf8(&msg_raw).unwrap_or("not displayable");
|
|
||||||
eprintln!(
|
|
||||||
"[{}] Sending message '{}' ({}) to {}",
|
|
||||||
self.name, msg, encrypted, target.name
|
|
||||||
);
|
|
||||||
target.recv(&encrypted_raw, self);
|
|
||||||
}
|
|
||||||
fn recv(&self, msg_raw: &[u8], source: &Self) {
|
|
||||||
let decrypted_raw = Self::xor_cipher(msg_raw, self.shared_key.unwrap());
|
|
||||||
let decrypted = str::from_utf8(&decrypted_raw).unwrap_or("not displayable");
|
|
||||||
let msg = str::from_utf8(&msg_raw).unwrap_or("not displayable");
|
|
||||||
eprintln!(
|
|
||||||
"[{}] Received message '{}' ({}) from {}",
|
|
||||||
self.name, decrypted, msg, source.name
|
|
||||||
);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
48
src/main.rs
48
src/main.rs
|
|
@ -1,48 +0,0 @@
|
||||||
use discrete_logarithm::discrete_log_pollard_rho;
|
|
||||||
use keygen::Person;
|
|
||||||
use rug::Integer;
|
|
||||||
use utils::mod_pow;
|
|
||||||
|
|
||||||
mod keygen;
|
|
||||||
mod utils;
|
|
||||||
|
|
||||||
fn main() {
|
|
||||||
let mut alice = Person::new("alice");
|
|
||||||
let mut bob = Person::new("bob");
|
|
||||||
Person::diffie_hellman(&mut alice, &mut bob);
|
|
||||||
alice.send(b"Hello World", &bob);
|
|
||||||
|
|
||||||
let alice_priv = discrete_log_pollard_rho(
|
|
||||||
&Integer::from(alice.r#mod.unwrap()),
|
|
||||||
&Integer::from(alice.public_key.unwrap()),
|
|
||||||
&Integer::from(alice.gen.unwrap()),
|
|
||||||
None,
|
|
||||||
).unwrap();
|
|
||||||
let bob_priv = discrete_log_pollard_rho(
|
|
||||||
&Integer::from(bob.r#mod.unwrap()),
|
|
||||||
&Integer::from(bob.public_key.unwrap()),
|
|
||||||
&Integer::from(bob.gen.unwrap()),
|
|
||||||
None,
|
|
||||||
);
|
|
||||||
eprintln!(
|
|
||||||
"[mallory] Calculated {}'s private key {} from {}'s public key {}",
|
|
||||||
alice.name,
|
|
||||||
&alice_priv,
|
|
||||||
alice.name,
|
|
||||||
alice.public_key.unwrap()
|
|
||||||
);
|
|
||||||
eprintln!(
|
|
||||||
"[mallory] Calculated {}'s private key {} from {}'s public key {}",
|
|
||||||
bob.name,
|
|
||||||
bob_priv.unwrap(),
|
|
||||||
bob.name,
|
|
||||||
bob.public_key.unwrap()
|
|
||||||
);
|
|
||||||
eprintln!(
|
|
||||||
"[mallory] Calculated {}'s and {}'s shared secret {}",
|
|
||||||
alice.name,
|
|
||||||
bob.name,
|
|
||||||
mod_pow(bob.public_key.unwrap(), alice_priv.to_u32_wrapping(), alice.r#mod.unwrap())
|
|
||||||
);
|
|
||||||
//Some(mod_pow(public, self.private_key.unwrap(), r#mod
|
|
||||||
}
|
|
||||||
28
src/utils.rs
28
src/utils.rs
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@ -1,28 +0,0 @@
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use num::Integer;
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/**
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* Discrete/Modular exponentiation
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*
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* Highly memory efficient because the full result is never stored, but shortened by defined modulo instead.
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* We can use that because the prime divisor required for our algorithm is guarenteed to be smaller
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* than n.
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*
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* Counterpart function to the discrete logarithm.
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*/
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pub fn mod_pow<T>(mut base: T, mut exp: T, r#mod: T) -> T
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where
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T: Integer + Copy + std::ops::DivAssign + From<u8>,
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u64: From<T>,
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u128: From<T>,
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{
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let mut result: T = T::one();
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base = base % r#mod;
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while exp > T::zero() {
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if exp.is_odd() {
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result = (result * base) % r#mod;
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}
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base = (base * base) % r#mod;
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exp /= T::from(2);
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|
||||||
}
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result
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}
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||||||
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