binaryfield.go

package adss

import (
	"crypto/subtle"
	"io"
)

// This implementation has been copied over from hashicorp's vault/shamir implementation
// with some minor modifications to make it compatible with our shamir implementations.

// 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, randReader io.Reader) (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
	if _, err := randReader.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 b 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
}

// Tables taken from http://www.samiam.org/galois.html
// They use 0xe5 (229) as the generator

var (
	// logTable provides the log(X)/log(g) at each index X
	logTable = [256]uint8{
		0x00, 0xff, 0xc8, 0x08, 0x91, 0x10, 0xd0, 0x36,
		0x5a, 0x3e, 0xd8, 0x43, 0x99, 0x77, 0xfe, 0x18,
		0x23, 0x20, 0x07, 0x70, 0xa1, 0x6c, 0x0c, 0x7f,
		0x62, 0x8b, 0x40, 0x46, 0xc7, 0x4b, 0xe0, 0x0e,
		0xeb, 0x16, 0xe8, 0xad, 0xcf, 0xcd, 0x39, 0x53,
		0x6a, 0x27, 0x35, 0x93, 0xd4, 0x4e, 0x48, 0xc3,
		0x2b, 0x79, 0x54, 0x28, 0x09, 0x78, 0x0f, 0x21,
		0x90, 0x87, 0x14, 0x2a, 0xa9, 0x9c, 0xd6, 0x74,
		0xb4, 0x7c, 0xde, 0xed, 0xb1, 0x86, 0x76, 0xa4,
		0x98, 0xe2, 0x96, 0x8f, 0x02, 0x32, 0x1c, 0xc1,
		0x33, 0xee, 0xef, 0x81, 0xfd, 0x30, 0x5c, 0x13,
		0x9d, 0x29, 0x17, 0xc4, 0x11, 0x44, 0x8c, 0x80,
		0xf3, 0x73, 0x42, 0x1e, 0x1d, 0xb5, 0xf0, 0x12,
		0xd1, 0x5b, 0x41, 0xa2, 0xd7, 0x2c, 0xe9, 0xd5,
		0x59, 0xcb, 0x50, 0xa8, 0xdc, 0xfc, 0xf2, 0x56,
		0x72, 0xa6, 0x65, 0x2f, 0x9f, 0x9b, 0x3d, 0xba,
		0x7d, 0xc2, 0x45, 0x82, 0xa7, 0x57, 0xb6, 0xa3,
		0x7a, 0x75, 0x4f, 0xae, 0x3f, 0x37, 0x6d, 0x47,
		0x61, 0xbe, 0xab, 0xd3, 0x5f, 0xb0, 0x58, 0xaf,
		0xca, 0x5e, 0xfa, 0x85, 0xe4, 0x4d, 0x8a, 0x05,
		0xfb, 0x60, 0xb7, 0x7b, 0xb8, 0x26, 0x4a, 0x67,
		0xc6, 0x1a, 0xf8, 0x69, 0x25, 0xb3, 0xdb, 0xbd,
		0x66, 0xdd, 0xf1, 0xd2, 0xdf, 0x03, 0x8d, 0x34,
		0xd9, 0x92, 0x0d, 0x63, 0x55, 0xaa, 0x49, 0xec,
		0xbc, 0x95, 0x3c, 0x84, 0x0b, 0xf5, 0xe6, 0xe7,
		0xe5, 0xac, 0x7e, 0x6e, 0xb9, 0xf9, 0xda, 0x8e,
		0x9a, 0xc9, 0x24, 0xe1, 0x0a, 0x15, 0x6b, 0x3a,
		0xa0, 0x51, 0xf4, 0xea, 0xb2, 0x97, 0x9e, 0x5d,
		0x22, 0x88, 0x94, 0xce, 0x19, 0x01, 0x71, 0x4c,
		0xa5, 0xe3, 0xc5, 0x31, 0xbb, 0xcc, 0x1f, 0x2d,
		0x3b, 0x52, 0x6f, 0xf6, 0x2e, 0x89, 0xf7, 0xc0,
		0x68, 0x1b, 0x64, 0x04, 0x06, 0xbf, 0x83, 0x38}

	// expTable provides the anti-log or exponentiation value
	// for the equivalent index
	expTable = [256]uint8{
		0x01, 0xe5, 0x4c, 0xb5, 0xfb, 0x9f, 0xfc, 0x12,
		0x03, 0x34, 0xd4, 0xc4, 0x16, 0xba, 0x1f, 0x36,
		0x05, 0x5c, 0x67, 0x57, 0x3a, 0xd5, 0x21, 0x5a,
		0x0f, 0xe4, 0xa9, 0xf9, 0x4e, 0x64, 0x63, 0xee,
		0x11, 0x37, 0xe0, 0x10, 0xd2, 0xac, 0xa5, 0x29,
		0x33, 0x59, 0x3b, 0x30, 0x6d, 0xef, 0xf4, 0x7b,
		0x55, 0xeb, 0x4d, 0x50, 0xb7, 0x2a, 0x07, 0x8d,
		0xff, 0x26, 0xd7, 0xf0, 0xc2, 0x7e, 0x09, 0x8c,
		0x1a, 0x6a, 0x62, 0x0b, 0x5d, 0x82, 0x1b, 0x8f,
		0x2e, 0xbe, 0xa6, 0x1d, 0xe7, 0x9d, 0x2d, 0x8a,
		0x72, 0xd9, 0xf1, 0x27, 0x32, 0xbc, 0x77, 0x85,
		0x96, 0x70, 0x08, 0x69, 0x56, 0xdf, 0x99, 0x94,
		0xa1, 0x90, 0x18, 0xbb, 0xfa, 0x7a, 0xb0, 0xa7,
		0xf8, 0xab, 0x28, 0xd6, 0x15, 0x8e, 0xcb, 0xf2,
		0x13, 0xe6, 0x78, 0x61, 0x3f, 0x89, 0x46, 0x0d,
		0x35, 0x31, 0x88, 0xa3, 0x41, 0x80, 0xca, 0x17,
		0x5f, 0x53, 0x83, 0xfe, 0xc3, 0x9b, 0x45, 0x39,
		0xe1, 0xf5, 0x9e, 0x19, 0x5e, 0xb6, 0xcf, 0x4b,
		0x38, 0x04, 0xb9, 0x2b, 0xe2, 0xc1, 0x4a, 0xdd,
		0x48, 0x0c, 0xd0, 0x7d, 0x3d, 0x58, 0xde, 0x7c,
		0xd8, 0x14, 0x6b, 0x87, 0x47, 0xe8, 0x79, 0x84,
		0x73, 0x3c, 0xbd, 0x92, 0xc9, 0x23, 0x8b, 0x97,
		0x95, 0x44, 0xdc, 0xad, 0x40, 0x65, 0x86, 0xa2,
		0xa4, 0xcc, 0x7f, 0xec, 0xc0, 0xaf, 0x91, 0xfd,
		0xf7, 0x4f, 0x81, 0x2f, 0x5b, 0xea, 0xa8, 0x1c,
		0x02, 0xd1, 0x98, 0x71, 0xed, 0x25, 0xe3, 0x24,
		0x06, 0x68, 0xb3, 0x93, 0x2c, 0x6f, 0x3e, 0x6c,
		0x0a, 0xb8, 0xce, 0xae, 0x74, 0xb1, 0x42, 0xb4,
		0x1e, 0xd3, 0x49, 0xe9, 0x9c, 0xc8, 0xc6, 0xc7,
		0x22, 0x6e, 0xdb, 0x20, 0xbf, 0x43, 0x51, 0x52,
		0x66, 0xb2, 0x76, 0x60, 0xda, 0xc5, 0xf3, 0xf6,
		0xaa, 0xcd, 0x9a, 0xa0, 0x75, 0x54, 0x0e, 0x01}
)