Optical Fourier NTRU Cryptosystem for Fast Multinomial Encryption
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Solution Overview
Problem
Current public-key cryptosystems, such as RSA and elliptic-curve algorithms, are vulnerable to quantum attacks, lacking future-proofness, and existing NTRU-like cryptosystems face challenges in efficient optical implementation due to reliance on polynomial operations.
Innovation Solution
A bi-variate NTRU-like cryptosystem (NTRU2D) using multinomial algebra over a ring of the form Z[X,Y]/<XN1-1, YN2-1> for optical implementation, employing optical Fourier transforms to accelerate multinomial multiplication and decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional public-key cryptosystems (RSA, elliptic-curve) are used, then they provide secure key exchange, but they are vulnerable to quantum attacks and lack future-proofness
Solution Approach 1:
The patent changes the mathematical foundation from traditional number-theoretic problems (RSA) or elliptic curve problems to lattice-based problems using NTRU cryptosystem. This parameter change in the underlying mathematical problem makes the system resistant to quantum attacks while maintaining future-proofness, as lattice problems are believed to be hard even for quantum computers.
2Reliability
If NTRU-like cryptosystems are used for post-quantum security, then quantum resistance is achieved, but optical implementation efficiency is reduced due to reliance on polynomial operations
Solution Approach 1:
The patent replaces traditional electronic computational methods with optical computing methods. By implementing polynomial multiplication and inversion operations using optical Fourier transforms, the system achieves both quantum security through NTRU-based cryptography and high processing speed through optical acceleration, eliminating the bottleneck of electronic computation for these mathematical operations.
Solution Approach 2:
The patent introduces optical Fourier transforms as an intermediary mechanism to bridge the gap between cryptographic operations and physical implementation. The optical domain serves as an intermediary that can efficiently perform the heavy computational tasks required by NTRU, translating mathematical operations into physical optical processes that are both secure and fast.
3Productivity
If optical Fourier transforms are used to accelerate multinomial multiplication, then computational speed increases, but device complexity increases
Solution Approach 1:
The patent segments the optical computing system into distinct functional modules: input encoding unit, optical Fourier transform unit, multiplication unit, and output decoding unit. This segmentation allows each component to be optimized independently and simplifies the overall system design and implementation, making the complex optical computation manageable through modular architecture.
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
Enhances security against quantum attacks and reduces computational complexity and power consumption by leveraging optical devices for efficient multinomial operations.
Implementation Method 1
The invention has particular applications which are quantum secure (that is, would not be easy to break by a quantum computer) and which thus have long term security as required by banking applications for example
Data Source
AI summary
A crypto-method of securely communicating a message; the method comprises the steps of selecting a ring R′ of bi or multi variate multinomials; generating a private key which has a multinomial f; generating a public key which has a multinomial h; encrypting by representing said message as a multinomial m in R′, selecting a random multinomial r, and computing an encrypted message; and decrypting said message using said private key.