Finite Field Multiplication Masking for Secure Cryptography
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Solution Overview
Problem
Existing methods for securing data in cryptographic applications, especially in software implementations, face challenges when applying non-linear functions due to inefficiencies and increased silicon area requirements, and are not effective in masking data from attackers observing electronic circuits.
Innovation Solution
A method for representing and processing elements of a finite field using a plurality of values, where multiplication is performed by picking random values and applying specific addition and multiplication operations to maintain masking, allowing non-linear functions to be applied without compromising data security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If multiple masks are used to mask the same data item, then security against attacks is improved, but the complexity of processing the masked data increases
Solution Approach 1:
The data item is segmented into multiple masked representations (d values), where each value represents a portion of the original data combined with random masks. This segmentation allows the data to be processed in distributed form while maintaining security, as each individual masked value reveals no information about the original data.
Solution Approach 2:
The patent introduces a new dimension of processing by associating each masked value with an integer index and processing them in a structured sequence. The method transforms the problem from simple parallel masking to an ordered processing sequence where each step builds upon previous results, enabling systematic handling of multiple masks.
2Adaptability or versatility
If non-linear functions are applied to masked data, then cryptographic functionality is improved, but the masking security is compromised due to increased observable electrical phenomena
Solution Approach 1:
The patent applies preliminary actions by pre-processing the masked data values in a specific sequence before applying the non-linear function. Random values are introduced and processed in advance to ensure that when the non-linear function is applied, the masking properties are preserved. This preliminary structuring prevents the emergence of observable electrical phenomena that would compromise security.
Solution Approach 2:
Random values serve as intermediaries between the original data and the non-linear function application. These random values are introduced at strategic points in the processing sequence to mask the intermediate results, ensuring that even when non-linear operations are performed, the underlying data remains protected from observation through electrical phenomena.
3Reliability
If software implementation is used to avoid circuit glitches, then security against certain attacks is improved, but processing efficiency deteriorates
Solution Approach 1:
The patent changes the parameters of processing by introducing a structured sequence with specific ordering rules and integer associations. This parameter change enables the software implementation to process masked data more efficiently by avoiding random access patterns and reducing the number of required operations, thereby improving productivity while maintaining security.
Data Source
AI summary
A method for determining a representation of a product of a first element and a second element is disclosed comprising, picking a random value for each pair of a first integer between 1 and d and a second integer greater than the first integer, adding the random value to the product of a first value and a second value, and adding the result of the first addition and the product of the first value and the second value. Then summing, for each integer between 1 and d, a product of the first and second values associated with the integer, the random values associated with the pairs of which the first integer is the integer concerned, and the values obtained for the pairs of which the second integer is the integer concerned.