Shared Domain Public Keys for Lattice Cryptosystem Overhead
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Solution Overview
Problem
The increasing length of public keys in lattice-based cryptosystems leads to significant time and cost for transmission and storage, and the computational burden of generating random matrices from seeds in conventional methods.
Innovation Solution
A lattice-based public key cryptosystem where a part of the public keys is shared among terminals within a specific domain, managed by a server that generates and distributes a common domain public key, reducing the need for individual key generation and transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If individually generated random matrices are used as public keys for each terminal, then security level is improved, but transmission amount and storage cost increase significantly
Solution Approach 1:
The public key is segmented into two parts: a domain public key (random matrix) shared by all terminals in the domain, and an individual public key (secret value) unique to each terminal. This segmentation allows the large random matrix to be shared once rather than transmitted individually to each terminal, reducing transmission amount while maintaining security through the combination of both parts.
Solution Approach 2:
The domain public key serves as a universal component for all terminals within the same domain. This single random matrix is used by multiple terminals to generate their individual public keys, eliminating the need to transmit separate large random matrices to each terminal while still enabling secure individual cryptographic operations.
2Quantity of substance
If seeds are transmitted instead of complete random matrices to reduce transmission amount, then transmission efficiency is improved, but computational burden increases as each terminal must generate the random matrix from the seed
Solution Approach 1:
The domain public key (random matrix) is generated in advance by the key generation server and distributed to all terminals before they need to perform cryptographic operations. This preliminary generation and distribution eliminates the need for each terminal to computationally generate the random matrix from a seed, reducing real-time computational burden while maintaining reduced transmission requirements.
3Reliability
If complete public keys are transmitted to each terminal, then individuality and security are maintained, but time and cost for transmission and storage increase significantly
Solution Approach 1:
The public key is segmented into a shared domain public key and an individual secret value. The domain public key is transmitted once to all terminals in the domain, while only the small individual secret value needs to be transmitted to each terminal. This segmentation maintains individuality through the unique secret value while dramatically reducing transmission time and storage requirements.
Solution Approach 2:
Instead of transmitting complete public keys to each terminal, the system transmits a copy of the domain public key once and individual secret values. Terminals reconstruct their full public keys by combining the shared domain public key with their individual secret values, reducing transmission time while maintaining the ability to perform individual cryptographic operations.
Data Source
AI summary
A server for managing terminals that perform lattice-based public key cryptographic communication according to embodiments of the present disclosure is disclosed. Each of the terminals performs public key cryptographic communication based on a public key including a domain public key and an individual public key, and a randomly determined individual private key, wherein the individual public key is calculated according to the following mathematical formula: IP=f(CP,SK) (wherein IP is an individual public key, SK is an individual private key, CP is a domain public key, and f is an individual public key generation function), and wherein the server includes a communication circuit, a memory configured to store a program including instructions, and a processor that controls the server to perform a plurality of operations by executing the program stored in the memory.