Cryptosystem Using Linearly Dependent Equations for Chosen-Plaintext Security
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Solution Overview
Problem
Modern cryptographic systems face security limitations, including susceptibility to brute force attacks and computational intensity, making them resource-intensive and costly, while theoretically unbreakable methods are difficult to implement.
Innovation Solution
A cryptosystem utilizing a system of linearly dependent equations and a system randomization number to provide additional strength against known-plaintext and chosen-plaintext attacks, offering semantic security and ciphertext indistinguishability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If computationally-secure cryptography processes are used, then security against brute force attacks is improved, but computational resource consumption increases
Solution Approach 1:
The secret key is divided into multiple key packages (k1, k2, k3, etc.), and the randomization number is divided into multiple random number packages (r1, r2, r3, etc.). This segmentation allows the cryptographic operations to be distributed across multiple components, reducing the computational burden on any single operation while maintaining overall security strength.
Solution Approach 2:
The patent changes the parameter structure by using a system of linearly dependent equations with multiple key packages and random number packages instead of traditional single-key cryptography. This parameter transformation enables the system to achieve enhanced security through mathematical complexity rather than relying solely on computational intensity.
2Ease of operation
If traditional cryptographic processes are used, then implementation simplicity is maintained, but security against chosen-plaintext attacks is weakened
Solution Approach 1:
The patent introduces random number packages (r1, r2, r3, etc.) as intermediaries between the secret key packages and the plaintext. These random number packages act as mediators that obscure the relationship between the key and the ciphertext, providing protection against chosen-plaintext attacks while maintaining a relatively simple implementation structure.
Solution Approach 2:
The cryptographic system uses a composite structure combining multiple key packages, multiple random number packages, and a system of linearly dependent equations. This composite approach integrates multiple security layers into a unified system that maintains ease of operation while significantly improving security against chosen-plaintext attacks.
3Reliability
If a one-time pad is used, then unbreakability is achieved, but implementation difficulty increases
Solution Approach 1:
The patent introduces dynamic elements through the use of random number packages that are generated and applied in each encryption operation. This dynamic approach allows the system to achieve strong security properties similar to one-time pad while using a more practical key management structure with multiple key packages that can be reused.
Solution Approach 2:
The patent moves from the traditional single-dimensional one-time pad approach to a multi-dimensional system using multiple key packages and multiple random number packages organized in a system of linearly dependent equations. This dimensional expansion provides equivalent or superior security with reduced implementation complexity.
Data Source
AI summary
Aspects and features of a cryptosystem and authentication for the cryptosystem, and a method or process for the cryptosystem, are described. In one example, a method for cryptographic communications includes storing a secret key, generating a system randomization number, and encrypting a plain data package into an encrypted data package by application of the plain data package, the secret key, and the system randomization number to a system of equations for encryption. The system of equations can be a system of linearly dependent equations in one example. Among other benefits, the cryptosystem relies upon the system of linearly dependent equations and the system randomization number to provide additional strength against known-plaintext attacks, chosen-plaintext attacks, and other types of attacks. The system is more semantically secure and offers ciphertext indistinguishability in a new approach using the system of linearly dependent equations.