Multivariate Public Key Cryptosystem Security and Efficiency
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Solution Overview
Problem
Multivariate public key cryptosystems (MPKCs) face security and efficiency challenges, with existing designs being vulnerable to attacks and inefficient for practical applications, especially in small electronic devices like smartcards and RFID.
Innovation Solution
The introduction of 'internal perturbation plus' (IPP), 'enhanced internal perturbation' (EIP), and 'multi-layer Oil-Vinegar construction' (MOVC) methods to enhance the security and efficiency of MPKCs, making them more resistant to attacks and suitable for use in small devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing MPKC designs are used, then the system can provide basic cryptographic functionality, but the security is vulnerable to attacks and efficiency is insufficient for practical applications
Solution Approach 1:
The patent segments the cryptographic system into multiple layers with different security requirements. The encryption layer uses fewer variables for efficiency, while the decryption layer uses more variables for security. This segmentation allows the system to achieve both high security and efficiency by assigning different functional requirements to different parts of the system.
Solution Approach 2:
The patent changes key parameters of the MPKC system, specifically using a finite field with a larger number of elements (q > 2) and employing polynomial transformations with controlled degrees. These parameter changes improve both security resistance against known attacks and computational efficiency for practical applications.
2Reliability
If more variables are added to the polynomial equations to improve security, then the system becomes more resistant to attacks, but the computational complexity and processing time increase
Solution Approach 1:
The patent applies local quality by having different numbers of variables in different parts of the system. The encryption function uses a smaller set of variables for fast computation, while the decryption function uses a larger set for security. This localized differentiation allows each part to optimize for its specific function without compromising the other.
Solution Approach 2:
The patent introduces dynamic elements through the use of affine transformations and polynomial compositions that can be efficiently evaluated. The system dynamically balances security and efficiency by using structured polynomial forms that maintain security properties while enabling optimized computation through pre-computation and caching techniques.
3Reliability
If the polynomial degree is increased to enhance security, then the system becomes more resistant to algebraic attacks, but the computational overhead and implementation complexity increase
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing certain polynomial transformations and their inverses. The system prepares lookup tables and pre-processed cryptographic materials during key generation, which reduces the complexity of real-time computations during encryption and decryption operations.
Solution Approach 2:
The patent substitutes complex mechanical polynomial inversion with more efficient computational methods. Instead of directly inverting high-degree polynomials, the system uses composed transformations of lower-degree polynomials that are easier to compute and invert, replacing the mechanical complexity with algorithmic efficiency.
Data Source
AI summary
Multivariate public key cryptosystems (MPKC) are public key cryptosystems, whose public key are a set of multivariate polynomials over a finite field (or ring). MPKC can be used for encryption, authentication and signatures. The invention develops three new methods that could be applied to a multivariate public key cryptosystem to produce new multivariate public key cryptosystems that are better in terms of security and efficiency. These three methods are called the internal perturbation plus (IPP), the enhanced internal perturbation (EIP) and the multi-layer Oil-Vinegar construction (MOVC). These three methods can be combined in any 2 or all 3 to be applied to a multivariate public key cryptosystem to produce new multivariate public key cryptosystems as well.