Multivariate Cryptographic System for RFID Security
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current public key cryptography methods, such as RSA and elliptic curve cryptography, are computationally slow and resource-intensive, making them inefficient for use in constrained environments like RFID technology and expensive to implement in payment terminals, and may be vulnerable to future attacks due to sub-exponential complexity.
Innovation Solution
A cryptographic method using a composite encryption function composed of a quadratic multivariate system, a linear error-correcting code, and a random function, which adds redundancy and noise to the encryption process, making it more resistant to attacks and efficient in terms of computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If RSA or elliptic curve cryptography is used, then security is provided, but computational speed and resource efficiency deteriorate
Solution Approach 1:
The patent changes the fundamental parameters of the cryptographic system by switching from traditional RSA/elliptic curve mathematics to multivariate quadratic polynomial systems over finite fields. This parameter change enables significantly faster computation while maintaining security through the hardness of solving multivariate quadratic equations
Solution Approach 2:
The patent substitutes the mathematical structure of traditional public key cryptography with a completely different mathematical framework based on multivariate quadratic systems. This substitution replaces the computationally intensive modular exponentiation and elliptic curve operations with efficient polynomial arithmetic and syndrome decoding operations
2Reliability
If RSA keys are stored in constrained environments like RFID chips, then security is maintained, but device complexity and cost increase
Solution Approach 1:
The patent employs cryptographic parameters and keys that can be implemented with minimal hardware resources, making them suitable for disposable or low-cost devices like RFID tags. The multivariate quadratic system allows security to be achieved with far fewer logic gates than traditional RSA key storage requirements
Solution Approach 2:
The patent changes the cryptographic parameters from large RSA moduli requiring tens of thousands of logic gates to compact multivariate quadratic systems with thousands of parameters, dramatically reducing the hardware footprint while maintaining security levels
3Reliability
If traditional public key cryptography is used in payment terminals, then security is provided, but processing time and energy consumption increase
Solution Approach 1:
The patent substitutes traditional public key verification mechanisms with multivariate quadratic system verification that operates through efficient polynomial evaluation and syndrome decoding, dramatically reducing verification time for payment transactions while maintaining security
Data Source
AI summary
The present invention relates to a method making it possible to perform a cryptographic task on at least one numerical datum in an electronic component, and comprises a step of at least partial use of an encryption function. This encryption function comprises a base encryption function (h) obtained by the addition between an intermediate function (g) emanating from a composition of a coding function (L) with a first function (f), and a second function (E). This method can be applied to the encryption of a datum or to the decryption of a datum. The present invention also relates to a method of generating a public key and a device able to implement one of these methods.