Symmetric-Key Cryptographic Sortition for Post-Quantum Leader Election
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Solution Overview
Problem
Existing Verifiable Random Functions (VRFs) used in distributed applications like proof-of-stake blockchains are computationally expensive and lack post-quantum security, making them inefficient and vulnerable to quantum attacks.
Innovation Solution
A cryptographic sortition method using an n-time-secure VRF based on symmetric-key primitives, involving a block cipher and Merkle Trees, ensures post-quantum security while reducing computational costs by limiting key usage to a fixed number of evaluations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If state-of-the-art VRFs based on elliptic curves or bilinear maps are used, then post-quantum security is not provided, but computational cost is reduced
Solution Approach 1:
The patent changes the cryptographic parameter foundation from elliptic curves/bilinear maps to lattice-based cryptography. This parameter change provides post-quantum security while the symmetric-key block cipher structure keeps computational costs manageable through efficient encryption operations.
Solution Approach 2:
The patent extracts and uses only the essential cryptographic functionality needed for sortition - a symmetric-key block cipher with limited evaluation次数. By removing unnecessary cryptographic complexity and focusing on core encryption/verification functions, computational overhead is reduced while maintaining security.
2Reliability
If recently proposed post-quantum secure VRFs based on lattices are used, then post-quantum security is provided, but computational cost increases
Solution Approach 1:
The patent segments the cryptographic system into a symmetric-key block cipher component and a Merkle tree verification component. The block cipher handles the computationally intensive encryption with limited evaluations, while the Merkle tree provides efficient verification. This segmentation reduces overall computational burden compared to full lattice-based VRFs.
Solution Approach 2:
The patent uses a symmetric-key block cipher that is computationally inexpensive and can be efficiently implemented in hardware. The key set is designed for limited use (n-time secure), making it a disposable resource that provides adequate security for the specific sortition application without the overhead of more complex post-quantum schemes.
3Productivity
If an n-time-secure VRF based on symmetric-key primitives is used, then computational cost is reduced and post-quantum security is provided, but key usage is limited to a fixed number of evaluations
Solution Approach 1:
The patent performs preliminary action by committing to a set of n secret keys in advance through a Merkle tree structure. This preliminary commitment allows the system to efficiently handle up to n evaluations without requiring key management infrastructure during the actual sortition process, balancing flexibility with computational efficiency.
Solution Approach 2:
The patent introduces a Merkle tree as an intermediary structure that manages the limited key set. The Merkle tree provides a flexible interface for selecting and verifying keys without exposing the underlying limitation of having only n keys, thus mediating between the fixed key constraint and the need for adaptable key usage in different sortition scenarios.
Data Source
AI summary
A method for cryptographic sortition among a group of parties includes committing, by a first party, to a set of n party-specific secret keys k1, kn for a block cipher E and obtaining, by the first and a second party, a common input x and an index r. The method further includes encrypting, by the first party, the input x with the r-th key kr of the committed keys k1, . . . , kn, thereby generating an output y1 of the block-cipher E, and publishing the output y1 with the key kr used for encryption. The method further includes encrypting, by the second party, the common input x with the published key kr, thereby generating an output y1′ of the block-cipher E, and comparing the generated output y1′ with the published output y1. The method can be used to optimize the cryptographic sortition and support secure decision making.