Masked Value Decomposition Using the SecMod44 Gadget
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Solution Overview
Problem
Existing cryptographic solutions for Dilithium, a post-quantum digital signature scheme, are inefficient and complex due to the lack of an effective method to compute mod 44 on Boolean shares, leading to increased implementation and verification overhead across different security levels.
Innovation Solution
A method for computing mod 44 on Boolean shares using basic bit manipulation operations such as shifting and standard Boolean masked addition/subtraction, reducing the complexity and overhead by integrating a SecMod44 gadget that supports all security levels of Dilithium with minimal changes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional methods are used to compute mod 44 on Boolean shares, then security is maintained, but implementation complexity and verification overhead increase significantly
Solution Approach 1:
The patent segments the mod 44 computation into multiple intermediate steps operating on Boolean shares. Instead of computing mod 44 directly on the full value, the method breaks it down into sequential operations on segmented Boolean representations, where each segment is processed independently and then combined. This segmentation reduces implementation complexity by allowing parallel processing and simplifying each individual computational step while maintaining the security properties of the overall operation.
2Productivity
If efficient mod 44 computation is implemented, then productivity improves, but security vulnerabilities to side-channel attacks may increase
Solution Approach 1:
The patent introduces Boolean shares as intermediary representations between the input value and the mod 44 computation. These Boolean shares act as mediators that allow efficient computation while maintaining security. The computation operates on these intermediary Boolean representations rather than directly on the secret value, preventing side-channel attacks from observing intermediate values. The Boolean shares are properly managed through the computation steps and combined to produce the correct result, thus achieving both efficiency and security.
3Reliability
If standard cryptographic operations are used, then security is ensured, but code size and verification overhead increase
Solution Approach 1:
The patent changes the parameter representation from standard integer arithmetic to Boolean share representations. By transforming the computational parameters into Boolean domains and operating throughout the computation using Boolean operations, the method achieves more compact code implementation. The Boolean parameter representation allows for more efficient storage and manipulation, reducing code size while maintaining the cryptographic security properties through proper Boolean arithmetic operations.
Data Source
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AI summary
The disclosure relates to decomposition of masked values in a cryptographically secure digital signing system. Example embodiments include a method of decomposing mod 44 an N bit Boolean share input (b'B,k), where N>12, the method comprising: i) reducing (302-305) a number of bits in the Boolean share input (b'B,k) by adding a lower 11:0 bits of the input (b'B,k) to an upper portion of the input left shifted by 2 bits to provide a first intermediate result ( t1B,13) having M bits; ii) reducing (306-309) a number of bits of the first intermediate result ( t1B,13) by adding a lower 6:0 portion of the intermediate result to an upper portion left shifted by 2 bits and subtracted from a multiple of 44 to provide a second intermediate result ( t3B,8); and iii) adjusting (310-316) the second intermediate result ( t3B,8) by adding and/or subtracting 44 to provide an output ( w1B,k′) having a value within an interval of 0:43, the output ( w1B,k′) being a mod 44 representation of the input (b'B,k).