System and method for securely sharing cryptographic material

Patent metadata

Field	Value
Publication number	US-12574221-B2
Application number	US-202418610175-A
Country	US
Kind code	B2
Filing date	Mar 19, 2024
Priority date	Dec 13, 2017
Publication date	Mar 10, 2026
Grant date	Mar 10, 2026

Abstract

Systems and methods described herein relate to techniques in which multiple parties each generate and exchange quantities that are based on a shared secret (e.g., powers of the shared secret) without exposing the shared secret. According to a protocol, two or more parties may exchange sets of elliptic curve points generated over polynomials that can be used, by each of the two or more parties, to determine a power of a shared secret. The protocol may be utilised as part of determining parameters for a smart contract that is broadcast to a blockchain network (e.g., Bitcoin). Based on the protocol, an additional party (e.g., a third party different from the two or more parties) may perform a computational task such as execution of the smart contract.

First claim

What is claimed is:

1 . A computer-implemented method comprising:
at each of a plurality of participants, determining respective polynomial; collectively agreeing, among the plurality of participants, upon a set of points: at each of the plurality of participants, evaluating its respective polynomial in the set of points to obtain a respective plurality of values; at each of the plurality of participants, distributing powers of its respective plurality of values to the other participants, and receiving corresponding powers of values from the other participants; at each of the plurality of participants, using the powers of the values determine a power of a sum of the respective polynomials of the participants, wherein the power of the sum corresponds to a power of a secret; and collectively generating, among the plurality of participants and based on the power of the secret, a blockchain transaction.

2 . The computer-implemented method according to claim 1 , wherein the set of points are a set of elliptic curve points.

3 . The computer-implemented method according to claim 1 , wherein determining the power of the sum of polynomials is based on a Lagrange interpolation.

4 . The computer-implemented method according to claim 1 , further comprising determining, based at least in part on the power of the secret, a common reference string that is determinable by the plurality of participants.

5 . The computer-implemented method according to claim 1 , wherein off-chain communications are utilised in the distribution of the powers of the values of the polynomials to the participants.

6 . The computer-implemented method according to claim 1 , wherein the plurality of participants is exactly two participants.

7 . The computer-implemented method according to claim 1 , wherein the secret is determined based on the power of the sum of polynomials evaluated at a particular point.

8 . The computer-implemented method according to claim 7 , wherein the particular point is an intersection point.

9 . The computer-implemented method according to claim 1 , wherein the set of points excludes an intersection point.

10 . The computer-implemented method according to claim 1 , wherein the polynomials evaluated in the set of points are of at least order 2 .

11 . The computer-implemented method according to claim 1 , wherein each point of the set of points is a different point.

12 . A system, comprising:
a processor; and memory including executable instructions that, as a result of execution by the processor, causes the system to execute operations, the operations comprising: at each of a plurality of participants, determining a respective polynomial; collectively agreeing, among the plurality of participants, upon a set of points; at each of the plurality of participants, evaluating its respective polynomial in the set of points to obtain a respective plurality of values; at each of the plurality of participants, distributing powers of its respective plurality of values to the other participants, and receive corresponding powers of values from the other participants; at each of the plurality of participants, using the powers of the values to determine a power of a sum of the respective polynomials of the participants, wherein the power of the sum corresponds to a power of a secret; and collectively generating, among the plurality of participants and based on the power of the secret, a blockchain transaction.

13 . The system of claim 12 , wherein the operations further comprise determining, based at least in part on the power of the secret, a common reference string that is determinable by the plurality of participants.

14 . A non-transitory computer-readable storage medium having stored thereon executable instructions that, as a result of being executed by a processor of a computer system, cause the computer system to execute operations, the operations comprising:
at each of a plurality of participants, determining a respective polynomial; collectively agreeing, among the plurality of participants, upon a set of points; at each of the plurality of participants, evaluating its respective polynomial in the set of points to obtain a respective plurality of values; at each of the plurality of participants, distributing powers of its respective plurality of values to the other participants, and receive corresponding powers of values from the other participants; at each of the plurality of participants, using the powers of the values to determine a power of a sum of the respective polynomials of the participants, wherein the power of the sum corresponds to a power of a secret; and collectively generating, among the plurality of participants and based on the power of the secret, a blockchain transaction.

15 . The non-transitory computer-readable storage medium of claim 14 , wherein the operations further comprise determining, based at least in part on the power of the secret, a common reference string that is determinable by the plurality of participants.

Assignees

• Nchain Licensing Ag

Inventors

• Covaci Alexandra
• Madeo Simone
• Motylinski Patrick
• Vincent Stephane

Classifications

• H04L9/50

  using hash chains, e.g. blockchains or hash trees · CPC title

• H04L9/3093

  involving Lattices or polynomial equations, e.g. NTRU scheme · CPC title

• H04L9/3066

  involving algebraic varieties, e.g. elliptic or hyper-elliptic curves · CPC title

• H04L9/14

  using a plurality of keys or algorithms · CPC title

• H04L9/3236

  using cryptographic hash functions · CPC title