complex_secret_share

Documentation

Index

• Variables
• func ComplexSecretRetrieve(shares map[int]*big.Int) ([]byte, error)
• func ComplexSecretSplit(totalShareNumber, minimumShareNumber int, secret []byte) (shares map[int]*big.Int, err error)

Variables

var (
	InvaildTotalShareNumberError = errors.New("The totalShareNumber must be greater than one.")
	InvaildShareNumberError      = errors.New("The minimumShareNumber must be smaller than the totalShareNumber.")
)

var (
	EmptyMessageError = errors.New("The message to be signed should not be empty")
)

Functions

func ComplexSecretRetrieve

func ComplexSecretRetrieve(shares map[int]*big.Int) ([]byte, error)

Shamir's Secret Sharing algorithm, can be considered as: A way to split a secret to W shares, the secret can only be retrieved if more than T(T <= W) shares are combined together.

This is the retrieve process:

1. Decode each share i.e. the byte slice to a (x, y) pair
2. Use lagrange interpolation formula, take the (x, y) pairs as input points to compute a polynomial f(x) which is able to match all the given points.
3. Give x = 0, then the secret number S can be computed
4. Now decode number S, then the secret is retrieved

func ComplexSecretSplit

func ComplexSecretSplit(totalShareNumber, minimumShareNumber int, secret []byte) (shares map[int]*big.Int, err error)

Shamir's Secret Sharing algorithm, can be considered as: A way to split a secret to W shares, the secret can only be retrieved if more than T(T <= W) shares are combined together.

This is the split process:

1. Encode the secret to a number S
2. Choose a lot of random numbers as coefficients, in order to make a random polynomials F(x) of degree T-1, the variable is X, the const(x-intercept) is S
3. For this polynomial, Give x diffent values, for example, x++ each time, then compute y = F(x)
4. So we get W shares, which are (x, y) pairs
5. Now encode each pair to a byte slice