Method for threshold secret sharing and reconstruction for multi-compartment
View Patent ↗Provided is a method for threshold secret sharing and reconstruction for multi-compartment, and more particularly, to a method for creating a share and reconstructing a secret in a system constituted by a plurality of compartments. The method for threshold secret sharing for multi-compartments may include: an operation of creating, when at least one second compartment is related toward a first compartment in one direction, an encrypted secret value by using an external share which does not belong to the first compartment, but belongs to the at least one second compartment; an operation of creating a first polynomial for defining the first compartment by using the encrypted secret value; and an operation of creating an internal share of the first compartment by using the first polynomial.
1 . A method for threshold secret sharing for multi-compartments performed by an electronic device including a processor, the method comprising:
an operation of creating, by the processor, when at least one second compartment is configured at a higher level than a first compartment in one direction, an encrypted secret value by using an external share which does not belong to the first compartment, but belongs to the at least one second compartment;
an operation of creating, by the processor, a first polynomial for defining the first compartment by using the encrypted secret value; and
an operation of creating, by the processor, an internal share of the first compartment by using the first polynomial.
2 . The method for threshold secret sharing for multi-compartments according to claim 1 , wherein the operation of creating the first polynomial for defining the first compartment by using the encrypted secret value further includes
an operation of creating at least one point having the encrypted secret value as a coordinate value, and
an operation of creating the first polynomial passing through the created point.
3 . The method for threshold secret sharing for multi-compartments according to claim 2 , further comprising:
an operation of creating m points having an encrypted secret value as a coordinate;
an operation of creating the first polynomial passing through m created point.
4 . The method for threshold secret sharing for multi-compartments according to claim 1 , wherein the operation of creating the first polynomial for defining the first compartment by using the encrypted secret value includes
an operation of creating at least one coefficient by using the encrypted secret value; and
an operation of creating the first polynomial by using the encrypted secret value as a coefficient of the first polynomial.
5 . The method for threshold secret sharing for multi-compartments according to claim 4 , further comprising:
an operation of creating m coefficients by using m encrypted secret values as the coefficients of the first polynomial.
6 . The method for threshold secret sharing for multi-compartments according to claim 1 , comprising:
an operation of assigning the internal share to a participant of the first compartment.
7 . A method for threshold secret reconstruction for multi-compartments performed by an electronic device including a processor, the method comprising:
an operation of reconstructing, by the processor, when at least one second compartment is configured at a higher level than a first compartment in one direction, a first polynomial of the first compartment by using at least one internal share which belongs to the first compartment;
an operation of acquiring, by the processor, an encrypted secret value by using the reconstructed first polynomial and an external share which belongs to the at least one second compartment; and
an operation of decrypting, by the processor, the encrypted secret value by using the external share to reconstruct a secret S.
8 . The method for threshold secret reconstruction for multi-compartments according to claim 7 , wherein the operation of decrypting the encrypted secret value includes
an operation of reconstructing the secret S by decrypting a coordinate of a point through which the reconstructed first polynomial passes.
9 . The method for threshold secret reconstruction for multi-compartments according to claim 8 , further comprising:
an operation of acquiring a cryptographic key for decryption from an external share set.
10 . The method for threshold secret reconstruction for multi-compartments according to claim 7 , wherein the operation of decrypting the secret by using the encrypted secret value further includes
an operation of reconstructing the encrypted secret S by decrypting a coefficient of the reconstructed first polynomial.
11 . The method for threshold secret reconstruction for multi-compartments according to claim 10 , further comprising:
an operation of acquiring a cryptographic key for decryption from an external share set.
12 . The method for threshold secret reconstruction for multi-compartments according to claim 7 , wherein the operation of reconstructing the first polynomial for the first compartment by using the at least one internal share which belongs to the first compartment includes
an operation of calculating the first polynomial of the first compartment based on a Lagrange interpolation.
13 . The method for threshold secret sharing for multi-compartments according to claim 1 , wherein creating the first polynomial by using the encrypted secret value establishes an arbitrary access structure enabling a plurality of compartments in a single hierarchical level without using polynomial derivatives, thereby reducing system complexity for hierarchical secret sharing.
14 . The method for threshold secret reconstruction for multi-compartments according to claim 7 , wherein the encrypted secret value enables the processor to reconstruct the secret S by applying a Lagrange interpolation instead of a Birkhoff interpolation, thereby reducing computational complexity.