AES Encryption via Polynomial Ring Transformation
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Solution Overview
Problem
Existing AES encryption methods are vulnerable to side-channel attacks, such as DPA and DFA, due to the structure of the AES algorithm and the operations performed on individual bytes, which can be exploited to infer the encryption key, and current countermeasures like masking and redundancy are not effective against all types of attacks.
Innovation Solution
The method involves representing the AES state as a polynomial in a polynomial ring using irreducible polynomials and the Chinese Remainder Theorem, applying AES encryption operations in this polynomial ring, and reconverting to the AES finite field, while adding randomization and constant check bytes to enhance security against side-channel attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If AES encryption is performed using standard byte-by-byte operations, then the encryption process is simple and fast, but the system becomes vulnerable to side-channel attacks
Solution Approach 1:
The patent transforms the AES state representation from a 4x4 byte matrix to a polynomial in the ring Z2[z]/(z^16+1). This dimensional transformation allows operations to be performed on the entire state as a single polynomial entity rather than individual bytes, increasing security against side-channel attacks while maintaining computational efficiency through polynomial arithmetic properties
Solution Approach 2:
The patent changes the mathematical field parameters from standard GF(2^8) byte operations to polynomial ring Z2[z]/(z^16+1) operations. This parameter change fundamentally alters how AES operations are computed, making side-channel attacks more difficult while preserving the cryptographic security and performance characteristics of AES
2Reliability
If masking techniques are applied to protect against passive side-channel attacks, then security against DPA is improved, but protection against active DFA attacks is not effective
Solution Approach 1:
The polynomial ring transformation provides universal protection against both passive attacks (DPA) and active attacks (DFA) simultaneously. The inherent properties of polynomial arithmetic in this ring structure make the system resistant to masking-based attacks while also providing natural protection against error injection, eliminating the need for separate countermeasures for different attack types
3Reliability
If the AES state is represented as a polynomial in a polynomial ring, then the hypothesis space increases and interdependence of bit changes increases, but the computational operations become more complex
Solution Approach 1:
The patent replaces traditional mechanical byte-by-byte AES operations with polynomial arithmetic operations in Z2[z]/(z^16+1). This substitution leverages the algebraic properties of polynomial rings, where operations like multiplication and addition can be performed efficiently on the entire state polynomial, maintaining computational speed while increasing security through the expanded hypothesis space and bit interdependence
Data Source
AI summary
A polynomial representation (bi(x)) in an AES finite field(Z2[x](r(x)))of input bytes (bi) of a state matrix (B) is obtained. A plurality (1) of irreducible polynomials (fi(y)) and a moving map (ψi) are used to map each polynomial (bi(x)) of the polynomial representation into a respective field of polynomials(Z2[y](fi(y)))computed with respect to one of the irreducible polynomials (fi(y)), to obtain respective moved polynomials (αi(y)). The moved polynomials (αi(y)) are mapped into a polynomial (a(z)) of a polynomial ring(Z2[z](p(z))),obtained by applying an isomorphism (ω) between the fields of polynomials(Z2[y](fi(y)))and the polynomial ring(Z2[z](p(z)))based upon the Chinese remainder theorem (CRT). AES encryption is applied to the polynomial (a(z)). The polynomial (a(z)) is reconverted into the AES finite field(Z2[x](r(x)))to obtain an encrypted state matrix (CB).