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FSS - Coggle Diagram
FSS
Shamir's secret sharing technique
Linear Function: f(0) can be anything in case of single point
In case of 2 points, f(0) can be only be one value
In Secret Sharing, they distribute the data in the form of shares as multiple partitions to compute the original data based on each single one
3 points generate only single quadratic line, where 2 points generates so many lines
Pattern: If we use the polynomial of degree 1 to split the secret, we can retrieve it through more than one share and more than two shares in degree 2 and vice versa
Elgamal technique
key generation
Prime number, generator and random number
Encryption
Random number and compute the secret ciphertexts to be share secretly
Decryption
decrypt both ciphers to get the initial value
Threshold ElGamal
Key Generation
Having same attributes as initially but here it computes the random number based on degree value
shares data based on public key and the secret sharing key
Encryption
compute ciphertexts values
Decryption
TTP involved based on decryption sharing of data
Compute random values of plain text degree based on shares
each users shares involved as to decrypt the complete value exactly
they are unable to compute the secret a
If logarithm problem is hard, unable to learn the shares to originate the actual secret
means same secret reuse for multiple shares
no exposure leads towards the reuse
But in Shamir's technique the secret never be reuse
Lagrange Interpolation in Secret Sharing
Prime number and degree value to reconstruct the polynomial
If output is 1 then it reconstructed exact value otherwise based on polynomials
reconstruct on the basis of constant polynomial values
Where other coefficients generated randomly