257 lines
6.5 KiB
Go
257 lines
6.5 KiB
Go
package shamir
|
|
|
|
import (
|
|
"crypto/rand"
|
|
"crypto/subtle"
|
|
"fmt"
|
|
)
|
|
|
|
const (
|
|
// ShareOverhead is the byte size overhead of each share
|
|
// when using Split on a secret. This is caused by appending
|
|
// a one byte tag to the share.
|
|
ShareOverhead = 1
|
|
)
|
|
|
|
// polynomial represents a polynomial of arbitrary degree
|
|
type polynomial struct {
|
|
coefficients []uint8
|
|
}
|
|
|
|
// makePolynomial constructs a random polynomial of the given
|
|
// degree but with the provided intercept value.
|
|
func makePolynomial(intercept, degree uint8) (polynomial, error) {
|
|
// Create a wrapper
|
|
p := polynomial{
|
|
coefficients: make([]byte, degree+1),
|
|
}
|
|
|
|
// Ensure the intercept is set
|
|
p.coefficients[0] = intercept
|
|
|
|
// Assign random co-efficients to the polynomial, ensuring
|
|
// the highest order co-efficient is non-zero
|
|
for p.coefficients[degree] == 0 {
|
|
if _, err := rand.Read(p.coefficients[1:]); err != nil {
|
|
return p, err
|
|
}
|
|
}
|
|
return p, nil
|
|
}
|
|
|
|
// evaluate returns the value of the polynomial for the given x
|
|
func (p *polynomial) evaluate(x uint8) uint8 {
|
|
// Special case the origin
|
|
if x == 0 {
|
|
return p.coefficients[0]
|
|
}
|
|
|
|
// Compute the polynomial value using Horner's method.
|
|
degree := len(p.coefficients) - 1
|
|
out := p.coefficients[degree]
|
|
for i := degree - 1; i >= 0; i-- {
|
|
coeff := p.coefficients[i]
|
|
out = add(mult(out, x), coeff)
|
|
}
|
|
return out
|
|
}
|
|
|
|
// interpolatePolynomial takes N sample points and returns
|
|
// the value at a given x using a lagrange interpolation.
|
|
func interpolatePolynomial(x_samples, y_samples []uint8, x uint8) uint8 {
|
|
limit := len(x_samples)
|
|
var result, basis uint8
|
|
for i := 0; i < limit; i++ {
|
|
basis = 1
|
|
for j := 0; j < limit; j++ {
|
|
if i == j {
|
|
continue
|
|
}
|
|
num := add(x, x_samples[j])
|
|
denom := add(x_samples[i], x_samples[j])
|
|
term := div(num, denom)
|
|
basis = mult(basis, term)
|
|
}
|
|
group := mult(y_samples[i], basis)
|
|
result = add(result, group)
|
|
}
|
|
return result
|
|
}
|
|
|
|
// div divides two numbers in GF(2^8)
|
|
func div(a, b uint8) uint8 {
|
|
if b == 0 {
|
|
// leaks some timing information but we don't care anyways as this
|
|
// should never happen, hence the panic
|
|
panic("divide by zero")
|
|
}
|
|
|
|
var goodVal, zero uint8
|
|
log_a := logTable[a]
|
|
log_b := logTable[b]
|
|
diff := (int(log_a) - int(log_b)) % 255
|
|
if diff < 0 {
|
|
diff += 255
|
|
}
|
|
|
|
ret := expTable[diff]
|
|
|
|
// Ensure we return zero if a is zero but aren't subject to timing attacks
|
|
goodVal = ret
|
|
|
|
if subtle.ConstantTimeByteEq(a, 0) == 1 {
|
|
ret = zero
|
|
} else {
|
|
ret = goodVal
|
|
}
|
|
|
|
return ret
|
|
}
|
|
|
|
// mult multiplies two numbers in GF(2^8)
|
|
func mult(a, b uint8) (out uint8) {
|
|
var goodVal, zero uint8
|
|
log_a := logTable[a]
|
|
log_b := logTable[b]
|
|
sum := (int(log_a) + int(log_b)) % 255
|
|
|
|
ret := expTable[sum]
|
|
|
|
// Ensure we return zero if either a or be are zero but aren't subject to
|
|
// timing attacks
|
|
goodVal = ret
|
|
|
|
if subtle.ConstantTimeByteEq(a, 0) == 1 {
|
|
ret = zero
|
|
} else {
|
|
ret = goodVal
|
|
}
|
|
|
|
if subtle.ConstantTimeByteEq(b, 0) == 1 {
|
|
ret = zero
|
|
} else {
|
|
// This operation does not do anything logically useful. It
|
|
// only ensures a constant number of assignments to thwart
|
|
// timing attacks.
|
|
goodVal = zero
|
|
}
|
|
|
|
return ret
|
|
}
|
|
|
|
// add combines two numbers in GF(2^8)
|
|
// This can also be used for subtraction since it is symmetric.
|
|
func add(a, b uint8) uint8 {
|
|
return a ^ b
|
|
}
|
|
|
|
// Split takes an arbitrarily long secret and generates a `parts`
|
|
// number of shares, `threshold` of which are required to reconstruct
|
|
// the secret. The parts and threshold must be at least 2, and less
|
|
// than 256. The returned shares are each one byte longer than the secret
|
|
// as they attach a tag used to reconstruct the secret.
|
|
func Split(secret []byte, parts, threshold int) ([][]byte, error) {
|
|
// Sanity check the input
|
|
if parts < threshold {
|
|
return nil, fmt.Errorf("parts cannot be less than threshold")
|
|
}
|
|
if parts > 255 {
|
|
return nil, fmt.Errorf("parts cannot exceed 255")
|
|
}
|
|
if threshold < 2 {
|
|
return nil, fmt.Errorf("threshold must be at least 2")
|
|
}
|
|
if threshold > 255 {
|
|
return nil, fmt.Errorf("threshold cannot exceed 255")
|
|
}
|
|
if len(secret) == 0 {
|
|
return nil, fmt.Errorf("cannot split an empty secret")
|
|
}
|
|
|
|
// Allocate the output array, initialize the final byte
|
|
// of the output with the offset. The representation of each
|
|
// output is {y1, y2, .., yN, x}.
|
|
out := make([][]byte, parts)
|
|
for idx := range out {
|
|
out[idx] = make([]byte, len(secret)+1)
|
|
out[idx][len(secret)] = uint8(idx) + 1
|
|
}
|
|
|
|
// Construct a random polynomial for each byte of the secret.
|
|
// Because we are using a field of size 256, we can only represent
|
|
// a single byte as the intercept of the polynomial, so we must
|
|
// use a new polynomial for each byte.
|
|
for idx, val := range secret {
|
|
p, err := makePolynomial(val, uint8(threshold-1))
|
|
if err != nil {
|
|
return nil, fmt.Errorf("failed to generate polynomial: %v", err)
|
|
}
|
|
|
|
// Generate a `parts` number of (x,y) pairs
|
|
// We cheat by encoding the x value once as the final index,
|
|
// so that it only needs to be stored once.
|
|
for i := 0; i < parts; i++ {
|
|
x := uint8(i) + 1
|
|
y := p.evaluate(x)
|
|
out[i][idx] = y
|
|
}
|
|
}
|
|
|
|
// Return the encoded secrets
|
|
return out, nil
|
|
}
|
|
|
|
// Combine is used to reverse a Split and reconstruct a secret
|
|
// once a `threshold` number of parts are available.
|
|
func Combine(parts [][]byte) ([]byte, error) {
|
|
// Verify enough parts provided
|
|
if len(parts) < 2 {
|
|
return nil, fmt.Errorf("less than two parts cannot be used to reconstruct the secret")
|
|
}
|
|
|
|
// Verify the parts are all the same length
|
|
firstPartLen := len(parts[0])
|
|
if firstPartLen < 2 {
|
|
return nil, fmt.Errorf("parts must be at least two bytes")
|
|
}
|
|
for i := 1; i < len(parts); i++ {
|
|
if len(parts[i]) != firstPartLen {
|
|
return nil, fmt.Errorf("all parts must be the same length")
|
|
}
|
|
}
|
|
|
|
// Create a buffer to store the reconstructed secret
|
|
secret := make([]byte, firstPartLen-1)
|
|
|
|
// Buffer to store the samples
|
|
x_samples := make([]uint8, len(parts))
|
|
y_samples := make([]uint8, len(parts))
|
|
|
|
// Set the x value for each sample and ensure no x_sample values are the same,
|
|
// otherwise div() can be unhappy
|
|
checkMap := map[byte]bool{}
|
|
for i, part := range parts {
|
|
samp := part[firstPartLen-1]
|
|
if exists := checkMap[samp]; exists {
|
|
return nil, fmt.Errorf("duplicate part detected")
|
|
}
|
|
checkMap[samp] = true
|
|
x_samples[i] = samp
|
|
}
|
|
|
|
// Reconstruct each byte
|
|
for idx := range secret {
|
|
// Set the y value for each sample
|
|
for i, part := range parts {
|
|
y_samples[i] = part[idx]
|
|
}
|
|
|
|
// Interpolte the polynomial and compute the value at 0
|
|
val := interpolatePolynomial(x_samples, y_samples, 0)
|
|
|
|
// Evaluate the 0th value to get the intercept
|
|
secret[idx] = val
|
|
}
|
|
return secret, nil
|
|
}
|