Plactic Monoid Key Agreement Using Knuth Multiplication for Quantum Resistance
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Quantum computers pose a threat to traditional key agreement schemes like Diffie-Hellman, as algorithms such as Shor's quantum algorithm can potentially break the security of these schemes, necessitating the development of post-quantum resistant key agreement methods.
Innovation Solution
Utilizing semigroups, specifically the plactic monoid, for key agreement by employing Knuth multiplication to create shared secrets through semistandard tableaus, ensuring security against quantum attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Diffie-Hellman key agreement is used, then key exchange can be performed efficiently, but security is compromised against quantum computer attacks
Solution Approach 1:
The patent changes the mathematical parameters from traditional Diffie-Hellman (modular exponentiation in finite fields) to plactic monoid operations (Knuth multiplication of semistandard Young tableaux). This parameter change provides quantum resistance while maintaining the key exchange functionality, resolving the contradiction between security and system complexity.
Solution Approach 2:
The patent substitutes the traditional cryptographic mechanism (modular exponentiation) with a completely different mathematical mechanism (plactic monoid operations involving Young tableaux and Knuth multiplication). This substitution replaces the vulnerable Diffie-Hellman structure with a quantum-resistant alternative while preserving the essential key agreement function.
2Reliability
If plactic monoid operations are used for key agreement, then quantum resistance is achieved, but computational complexity increases
Solution Approach 1:
The patent performs preliminary actions by pre-computing and storing the semistandard Young tableaux representations of private keys and public parameters. This preliminary preparation reduces the computational burden during actual key exchange operations, mitigating the productivity loss from using complex plactic monoid operations.
Solution Approach 2:
The patent segments the key agreement process into distinct phases: key generation, public parameter computation, and shared secret derivation. Each phase uses optimized plactic monoid operations specific to that stage, improving overall computational efficiency while maintaining quantum resistance.
Data Source
Figure 1
Figure 2
Figure 3A~3B
AI summary
A method for key agreement between a first party and a second party over a public communications channel, the method including selecting, by the first party, a first value "a"; multiplying the first value "a" by a second value "b" using Knuth multiplication to create a third value "d", the third value "d" being a semistandard tableau; sending the third value "d" to the second party; receiving, from the second party, a fourth value "e", the fourth value being a second semistandard tableau comprising the second value "b" multiplied by a fifth value "c" selected by the second party; and creating a shared secret by multiplying the first value "a" with the fourth value "e" using Knuth multiplication, wherein the shared secret matches the third value "d" multiplied by the fifth value "c" using Knuth multiplication.