Encryption Method Using Polynomial Factorization for Low-Power Devices
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Solution Overview
Problem
Existing public-key encryption systems face challenges in balancing security and computational efficiency, particularly on devices with reduced power, such as smartphones, due to reliance on complex mathematical problems and high computational resources, making them vulnerable to cryptoanalytic attacks and impractical for small devices.
Innovation Solution
An encryption/decryption method using a public-key step with non-linear numerical sum functions and a symmetric key step, where public keys are generated using a Hash sum modulus function with a two-dimensional matrix of private values, avoiding prime numbers and employing non-perfect hash functions to enhance security and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If complex mathematical problems are used for encryption, then security against attacks is improved, but processing speed and computational power requirements worsen
Solution Approach 1:
The patent changes the mathematical parameters from traditional prime number factorization to polynomial factorization over finite fields. This parameter change maintains security through the hardness of polynomial factorization while enabling more efficient computation that can be optimized for both software and hardware implementation, thus improving processing speed without sacrificing security.
2Adaptability or versatility
If asymmetric encryption methods are used, then messages of any length can be encrypted, but processing time and computational resources increase
Solution Approach 1:
The patent segments the encryption process into two distinct phases: an asymmetric encryption phase using polynomial-based public-key cryptography for key exchange and initialization, and a symmetric encryption phase using the derived shared key for actual message encryption. This segmentation allows the system to handle messages of any length while minimizing processing time by using the fast symmetric encryption for the bulk data transmission.
3Reliability
If traditional public-key methods are used, then secure message transmission is achieved, but implementation on low-power devices becomes impractical
Solution Approach 1:
The patent substitutes the traditional mechanical/mathematical approach of prime number factorization with polynomial factorization over finite fields. This substitution creates a more computationally efficient system that maintains cryptographic security while reducing the hardware complexity and power consumption requirements, making it suitable for implementation on low-power devices such as smartphones and embedded systems.
Data Source
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AI summary
Encryption and decryption method comprising: a first public-key step with: a) a first public key which is exchanged between at least two mutually communicating entities and which is used for encrypting a first message; b) a private key for each of said at least two mutually communicating entities which is used for decrypting said first message encrypted using said public key; a second symmetric key encryption/decryption step with a secret (or session) key for encryption/decryption of second messages transmitted between said at least two communicating entities, said secret key being exchanged between the at least two communicating entities using the first public-key encryption step and said encryption/decryption secret key forming the first message and the trapdoor consisting of the secret key creating function, while the second message consist of information to be exchanged between the two communicating entities and while keys are not calculated using prime numbers and wherein the public key is generated by a non-linear numerical sum function having always a numerical value as output. The method provides also a particular encryption/decryption private-key method which is used in said second step or it is used also independently of said first step.