Method for performing polynomial multiplication operations
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Solution Overview
Problem
Existing cryptographic devices, particularly those with low CPU power and memory, face prohibitive costs in performing polynomial multiplications between large polynomials due to the lack of dedicated coprocessors, making them vulnerable to quantum computer attacks.
Innovation Solution
A method that transforms polynomial multiplication into integer multiplication by concatenating polynomial coefficients with added zeros, using a cryptographic co-processor to perform this operation efficiently, and applies masking techniques to protect against side-channel attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If polynomial multiplication is performed using existing methods (Karatsuba, Toom-Cook, NTT) on devices with low CPU power and memory, then the computational cost remains prohibitive, but using a cryptographic co-processor with integer multiplier reduces the computational cost significantly
Solution Approach 1:
The patent uses an intermediary transformation that converts polynomial multiplication into integer multiplication. By representing polynomials as integers through coefficient concatenation and using integer multiplication as an intermediary operation, the system leverages the cryptographic co-processor's integer multiplier to achieve efficient polynomial multiplication without requiring dedicated polynomial multiplication hardware.
Solution Approach 2:
The patent replaces the mechanical/computational system of polynomial multiplication with a different system - integer multiplication. This substitution allows the use of a cryptographic co-processor designed for integer operations to perform polynomial multiplication, avoiding the need for complex polynomial multiplication algorithms and reducing computational cost.
2Measurement precision
If polynomial coefficients are concatenated directly without zero insertion, then the multiplication result contains carry interference that prevents accurate coefficient retrieval, but inserting zeros increases the integer size and memory usage
Solution Approach 1:
The patent applies local quality by inserting zeros only in specific positions within the concatenated integer representation. Rather than uniformly increasing the size of all integers, zeros are strategically placed between coefficient groups to prevent carry interference in critical regions while minimizing overall memory usage. This localized modification achieves accurate coefficient retrieval without excessive memory consumption.
Data Source
AI summary
Provided is a method for performing a cryptographic algorithm, performed by a cryptographic device comprising a cryptographic co-processor comprising an integer multiplier, said cryptographic algorithm comprising a polynomial multiplication between a first input polynomial A[X] and a second input polynomial B[X], wherein the first input polynomial A[X] and the second input polynomial B[X] comprise Nc coefficients and said coefficients of the first and second input polynomials are of size Nb bits, with Nc and Nb non-zero integers. A polynomial result is computed for a polynomial multiplication between said first input polynomial A[X] and said second input polynomial B[X] by generating (S11) a concatenated integer for each input polynomial as a concatenation of the coefficients of said input polynomial, each coefficient being extended to a size Ne with Ne≥┌log2 Nc┐+2*Nb by inserting zeros as Most Significant Bits of said concatenated coefficients. Other embodiments disclosed.