Add blog link, small pending updates

2 years ago · c63b841899
8 changed files with 73 additions and 333 deletions
--- a/README.md
+++ b/README.md
@ -1,5 +1,9 @@
 # Shamir's Secret Sharing
 This repo contains `Rust` & `Go` implementations of [Shamir's Secret Sharing](https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing) algorithm. The `Go` implementation also has a compiled Web Assembly (WASM) version from the Go code to be used from the browser.
 > Warning: this has been done to study, do not use.

 This repo contains `Rust` & `Go` implementations of [Shamir's Secret Sharing](https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing) algorithm. A blog post explaining the concepts can be found at https://arnaucube.com/blog/shamir-secret-sharing.html .

 The `Go` implementation also has a compiled Web Assembly (WASM) version from the Go code to be used from the browser.

 - `go`: [go-shamirsecretsharing](https://github.com/arnaucube/shamirsecretsharing/tree/master/go-shamirsecretsharing): Go lib + WASM lib
 - `rust`: [shamirsecretsharing-rs](https://github.com/arnaucube/shamirsecretsharing/tree/master/shamirsecretsharing-rs)
--- a/go-shamirsecretsharing/README.md
+++ b/go-shamirsecretsharing/README.md
@ -21,7 +21,7 @@ Call the library from javascript:
 // Create shares from a secret
 // nNeededShares: number of secrets needed
 // nShares: number of shares
 // p: random point
 // p: size of finite field
 // k: secret to share
 createShares(nNeededShares, nShares, p, k);
 ```
@ -29,12 +29,12 @@ createShares(nNeededShares, nShares, p, k);
 ## Usage from Go
 ```go
 // define secret to share
 k, ok := new(big.Int).SetString("123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890", 10)
 k, ok := new(big.Int).SetString("12345678901234567890123456789012345678", 10)
 assert.True(t, ok)

 // define random prime
 p, err := rand.Prime(rand.Reader, bits/2)
 assert.Nil(t, err)
 // define the field
 p, ok := new(big.Int).SetString("170141183460469231731687303715884105727", 10)
 assert.True(t, ok)

 // define how many shares want to generate
 nShares := big.NewInt(int64(6))
--- a/go-shamirsecretsharing/shamirsecretsharing.go
+++ b/go-shamirsecretsharing/shamirsecretsharing.go
@ -6,15 +6,21 @@ import (
 	"math/big"
 )

 const (
 	// bits = 1024
 	bits = 2048
 )
 func randBigInt(p *big.Int) (*big.Int, error) {
 	b := make([]byte, 32)
 	_, err := rand.Read(b)
 	if err != nil {
 		return nil, err
 	}
 	r := new(big.Int).SetBytes(b)
 	rp := new(big.Int).Mod(r, p)
 	return rp, nil
 }

 // Create calculates the secrets to share from given parameters
 // t: number of secrets needed
 // n: number of shares
 // p: random point
 // p: size of finite field
 // k: secret to share
 func Create(t, n, p, k *big.Int) (result [][]*big.Int, err error) {
 	if k.Cmp(p) > 0 {
@ -24,11 +30,11 @@ func Create(t, n, p, k *big.Int) (result [][]*big.Int, err error) {
 	var basePolynomial []*big.Int
 	basePolynomial = append(basePolynomial, k)
 	for i := 0; i < int(t.Int64())-1; i++ {
 		randPrime, err := rand.Prime(rand.Reader, bits/2)
 		x, err := randBigInt(p)
 		if err != nil {
 			return result, err
 		}
 		basePolynomial = append(basePolynomial, randPrime)
 		basePolynomial = append(basePolynomial, x)
 	}

 	//calculate shares, based on the basePolynomial
--- a/go-shamirsecretsharing/shamirsecretsharing_test.go
+++ b/go-shamirsecretsharing/shamirsecretsharing_test.go
@ -2,7 +2,6 @@ package shamirsecretsharing

 import (
 	"bytes"
 	"crypto/rand"
 	"math/big"
 	"testing"

@ -10,11 +9,12 @@ import (
 )

 func TestCreate(t *testing.T) {
 	k, ok := new(big.Int).SetString("123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890", 10)
 	k, ok := new(big.Int).SetString("12345678901234567890123456789012345678", 10)
 	assert.True(t, ok)

 	p, err := rand.Prime(rand.Reader, bits/2)
 	assert.Nil(t, err)
 	// 2 ** 127 - 1
 	p, ok := new(big.Int).SetString("170141183460469231731687303715884105727", 10)
 	assert.True(t, ok)

 	nShares := big.NewInt(int64(6))
 	nNeededShares := big.NewInt(int64(3))
--- a/shamirsecretsharing-rs/.gitignore
+++ b/shamirsecretsharing-rs/.gitignore
@ -1 +1,2 @@
 /target
 Cargo.lock
--- a/shamirsecretsharing-rs/Cargo.lock
+++ b/shamirsecretsharing-rs/Cargo.lock
@ -1,273 +0,0 @@
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--- a/shamirsecretsharing-rs/README.md
+++ b/shamirsecretsharing-rs/README.md
@ -4,7 +4,7 @@ Shamir's Secret Sharing in Rust

 ## Usage
 ```rust
 // create 6 shares from k, given the rand p
 // create 6 shares from k, on the Fp
 // where to recover will be needed 3 shares
 let s = create(3, 6, &p, &k);

--- a/shamirsecretsharing-rs/src/lib.rs
+++ b/shamirsecretsharing-rs/src/lib.rs
@ -1,35 +1,34 @@
 extern crate rand;
 extern crate num;
 extern crate num_bigint;
 extern crate num_traits;
 extern crate rand;

 use std::str::FromStr;

 use num_bigint::RandBigInt;
 use num::pow::pow;
 use num::Integer;

 use num_bigint::RandBigInt;

 use num_bigint::{BigInt, ToBigInt};
 use num_traits::{Zero, One};
 use num_traits::{One, Zero};

 fn modulus(a: &BigInt, m: &BigInt) -> BigInt {
    ((a%m) + m) % m
    ((a % m) + m) % m
 }

 pub fn create(t: u32, n: u32,p: &BigInt, k: &BigInt) -> Vec<[BigInt;2]> {
 pub fn create(t: u32, n: u32, p: &BigInt, k: &BigInt) -> Vec<[BigInt; 2]> {
    // t: number of secrets needed
    // n: number of shares
    // p: random point
    // p: size of finite field
    // k: secret to share
    if k>p {
    if k > p {
        println!("\nERROR: need k<p\n");
    }

    // generate base_polynomial
    let mut base_polynomial: Vec<BigInt> = Vec::new();
    base_polynomial.push(k.clone());
    for _ in 0..t as usize-1 {
    for _ in 0..t as usize - 1 {
        let mut rng = rand::thread_rng();
        let a = rng.gen_bigint(1024);
        base_polynomial.push(a);
@ -37,11 +36,11 @@ pub fn create(t: u32, n: u32,p: &BigInt, k: &BigInt) -> Vec<[BigInt;2]> {

    // calculate shares, based on the base_polynomial
    let mut shares: Vec<BigInt> = Vec::new();
    for i in 1..n+1 {
    for i in 1..n + 1 {
        let mut p_res: BigInt = Zero::zero();
        let mut x = 0;
        for pol_elem in &base_polynomial {
            if x==0 {
            if x == 0 {
                p_res = p_res + pol_elem;
            } else {
                let i_pow = pow(i, x);
@ -49,23 +48,23 @@ pub fn create(t: u32, n: u32,p: &BigInt, k: &BigInt) -> Vec<[BigInt;2]> {
                p_res = p_res + curr_elem;
                p_res = modulus(&p_res, p);
            }
            x = x+1;
            x = x + 1;
        }
        shares.push(p_res);
    }
    pack_shares(shares)
 }

 fn pack_shares(shares: Vec<BigInt>) -> Vec<[BigInt;2]> {
    let mut r: Vec<[BigInt;2]> = Vec::new();
 fn pack_shares(shares: Vec<BigInt>) -> Vec<[BigInt; 2]> {
    let mut r: Vec<[BigInt; 2]> = Vec::new();
    for i in 0..shares.len() {
        let curr: [BigInt;2] = [shares[i].clone(), (i+1).to_bigint().unwrap()];
        let curr: [BigInt; 2] = [shares[i].clone(), (i + 1).to_bigint().unwrap()];
        r.push(curr);
    }
    r
 }

 fn unpack_shares(s: Vec<[BigInt;2]>) -> (Vec<BigInt>, Vec<BigInt>) {
 fn unpack_shares(s: Vec<[BigInt; 2]>) -> (Vec<BigInt>, Vec<BigInt>) {
    let mut shares: Vec<BigInt> = Vec::new();
    let mut is: Vec<BigInt> = Vec::new();
    for i in 0..s.len() {
@ -100,9 +99,9 @@ pub fn kalinski_inv(a: &BigInt, modulo: &BigInt) -> BigInt {
    // This Phase I indeed is the Binary GCD algorithm , a version o Stein's algorithm
    // which tries to remove the expensive division operation away from the Classical
    // Euclidean GDC algorithm replacing it for Bit-shifting, subtraction and comparaison.
    // 
    //
    // Output = `a^(-1) * 2^k (mod l)` where `k = log2(modulo) == Number of bits`.
    // 
    //
    // Stein, J.: Computational problems associated with Racah algebra.J. Comput. Phys.1, 397–405 (1967).
    let phase1 = |a: &BigInt| -> (BigInt, u64) {
        assert!(a != &BigInt::zero());
@ -114,35 +113,31 @@ pub fn kalinski_inv(a: &BigInt, modulo: &BigInt) -> BigInt {
        let mut k = 0u64;

        while v > BigInt::zero() {
            match(u.is_even(), v.is_even(), u > v, v >= u) {
            match (u.is_even(), v.is_even(), u > v, v >= u) {
                // u is even
                (true, _, _, _) => {

                    u = u >> 1;
                    s = s << 1;
                },
                }
                // u isn't even but v is even
                (false, true, _, _) => {

                    v = v >> 1;
                    r = &r << 1;
                },
                }
                // u and v aren't even and u > v
                (false, false, true, _) => {

                    u = &u - &v;
                    u = u >> 1;
                    r = &r + &s;
                    s = &s << 1;
                },
                }
                // u and v aren't even and v > u
                (false, false, false, true) => {

                    v = &v - &u;
                    v = v >> 1;
                    s = &r + &s;
                    r = &r << 1;
                },
                }
                (false, false, false, false) => panic!("Unexpected error has ocurred."),
            }
            k += 1;
@ -155,8 +150,8 @@ pub fn kalinski_inv(a: &BigInt, modulo: &BigInt) -> BigInt {

    // Phase II performs some adjustments to obtain
    // the Montgomery inverse.
    // 
    // We implement it as a clousure to be able to grap the 
    //
    // We implement it as a clousure to be able to grap the
    // kalinski_inv scope to get `modulo` variable.
    let phase2 = |r: &BigInt, k: &u64| -> BigInt {
        let mut rr = r.clone();
@ -166,13 +161,13 @@ pub fn kalinski_inv(a: &BigInt, modulo: &BigInt) -> BigInt {
            match rr.is_even() {
                true => {
                    rr = rr >> 1;
                },
                }
                false => {
                    rr = (rr + modulo) >> 1;
                }
            }
        }
        rr 
        rr
    };

    let (r, z) = phase1(&a.clone());
@ -180,7 +175,7 @@ pub fn kalinski_inv(a: &BigInt, modulo: &BigInt) -> BigInt {
    phase2(&r, &z)
 }

 pub fn lagrange_interpolation(p: &BigInt, shares_packed: Vec<[BigInt;2]>) -> BigInt {
 pub fn lagrange_interpolation(p: &BigInt, shares_packed: Vec<[BigInt; 2]>) -> BigInt {
    let mut res_n: BigInt = Zero::zero();
    let mut res_d: BigInt = Zero::zero();
    let (shares, sh_i) = unpack_shares(shares_packed);
@ -198,7 +193,8 @@ pub fn lagrange_interpolation(p: &BigInt, shares_packed: Vec<[BigInt;2]>) -> Big
        }
        let numerator: BigInt = &shares[i] * &lagrange_numerator;

        let quo: BigInt = (&numerator / &lagrange_denominator) + (&lagrange_denominator ) % &lagrange_denominator;
        let quo: BigInt =
            (&numerator / &lagrange_denominator) + (&lagrange_denominator) % &lagrange_denominator;
        if quo != Zero::zero() {
            res_n = res_n + quo;
        } else {
@ -218,7 +214,6 @@ pub fn lagrange_interpolation(p: &BigInt, shares_packed: Vec<[BigInt;2]>) -> Big
    r
 }


 #[cfg(test)]
 mod tests {

@ -227,15 +222,16 @@ mod tests {

    #[test]
    fn test_create_and_lagrange_interpolation() {
        let mut rng = rand::thread_rng();
        let p = rng.gen_biguint(1024).to_bigint().unwrap();
        println!("p: {:?}", p);
        let k = BigInt::parse_bytes(b"123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890", 10).unwrap();
        // 2 ** 127 - 1
        let p = BigInt::parse_bytes(b"170141183460469231731687303715884105727", 10).unwrap();
        println!("p: {:?}", p.to_string());

        let k = BigInt::parse_bytes(b"12345678901234567890123456789012345678", 10).unwrap();

        let s = create(3, 6, &p, &k);
        // println!("s: {:?}", s);

        let mut shares_to_use: Vec<[BigInt;2]> = Vec::new();
        let mut shares_to_use: Vec<[BigInt; 2]> = Vec::new();
        shares_to_use.push(s[2].clone());
        shares_to_use.push(s[1].clone());
        shares_to_use.push(s[0].clone());
@ -263,10 +259,16 @@ mod tests {
        // Tested: 182687704666362864775460604089535377456991567872
        // Expected for: inverse_mod(a, l) computed on SageMath:
        // `7155219595916845557842258654134856828180378438239419449390401977965479867845`.
        let modul3 = BigInt::from_str("7237005577332262213973186563042994240857116359379907606001950938285454250989").unwrap();
        let modul3 = BigInt::from_str(
            "7237005577332262213973186563042994240857116359379907606001950938285454250989",
        )
        .unwrap();
        let d = BigInt::from_str("182687704666362864775460604089535377456991567872").unwrap();
        let res4 = kalinski_inv(&d, &modul3); 
        let expected4 = BigInt::from_str("7155219595916845557842258654134856828180378438239419449390401977965479867845").unwrap();
        let res4 = kalinski_inv(&d, &modul3);
        let expected4 = BigInt::from_str(
            "7155219595916845557842258654134856828180378438239419449390401977965479867845",
        )
        .unwrap();
        assert_eq!(expected4, res4);
    }
 }