Add blog link, small pending updates

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)

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))

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

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))

shamirsecretsharing-rs/.gitignore

@@ -1 +1,2 @@
 /target
+Cargo.lock

shamirsecretsharing-rs/Cargo.lock

@@ -1,273 +0,0 @@
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-# It is not intended for manual editing.
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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);
 

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);
     }
 }