Public Key Combination Verification for Compact Multisignature Scripts
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Solution Overview
Problem
Existing blockchain transactions that utilize multisignature protocols face increased operational and storage requirements due to the linear scaling of redeem script size with the number of signatures and participants, leading to higher network propagation and storage needs.
Innovation Solution
A computer-implemented method that involves deriving a group public key from a combination of public keys and their gradients, using elliptic curve point addition outside the script, and verifying this combination within the script, reducing the need to store multiple public keys and optimizing processing steps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional multisignature protocols are used with N public keys, then security and access control are improved, but redeem script size and storage requirements increase linearly with N
Solution Approach 1:
The patent combines N public keys into a single aggregated public key through elliptic curve point addition. Instead of storing and processing N separate public keys in the redeem script, the system merges them into one aggregated key that represents the collective authority of all N participants, thereby reducing script size while maintaining the security requirement that multiple signatures are needed to redeem.
Solution Approach 2:
The aggregated public key serves multiple functions: it represents the combined authority of N participants, enables compact storage in the redeem script, and maintains compatibility with standard elliptic curve cryptography operations. This single structure replaces what would otherwise require N separate key storage locations and multiple verification operations.
2Reliability
If N public keys are stored in the redeem script, then multisignature verification is enabled, but network propagation speed decreases due to larger transaction size
Solution Approach 1:
By merging N public keys into a single aggregated public key, the transaction size is reduced from O(N) to O(1) with respect to the number of participants. This single aggregated key is stored in the redeem script and used for verification, enabling fast network propagation while still supporting multisignature verification through the mathematical properties of elliptic curve aggregation.
3Reliability
If multiple public keys are processed in the redeem script, then access control is secured, but processing time and computational operations increase
Solution Approach 1:
The aggregation of N public keys into a single aggregated public key is performed in advance, before the redeem script execution. This preliminary action moves the computationally intensive point addition operations out of the critical verification path, so that during transaction redemption, the system only needs to perform a single signature verification against the aggregated key rather than N separate verifications.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method enhances the efficiency and security of blockchain transactions by minimizing the storage and processing requirements while maintaining secure and reliable resource transfer or access control.
Implementation Method 1
A computer-implemented method that involves deriving a group public key from a combination of public keys and their gradients, using elliptic curve point addition outside the script
Data Source
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AI summary
A computer-implemented method is disclosed. The method includes obtaining a first blockchain transaction configured to be redeemable to permit access to, or transfer control of, a resource, wherein the first blockchain transaction has an output comprising a public key combination verification function. The function comprises a plurality of public keys including a first public key and a second public key, each public key being a point on an elliptic curve, and a group public key being the elliptic curve point addition of the first and second public keys. A first gradient value is determined, being the gradient of the line between the first and second public keys. A second blockchain transaction is provided, the second transaction comprising an input comprising the public keys, the first gradient value, and the group public key. The first blockchain transaction is configured to be redeemable to permit access to, or transfer control of, a resource on successful application of the public key combination verification function to the input to verify that the group public key is derived from a combination of the public keys.