Matrix Multiply Accumulate Instruction for Groestl Hashing
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Solution Overview
Problem
Conventional systems using AES instructions are inefficient in performing the MixBytes transformation of the Groestl Secure Hashing algorithm, requiring numerous cycles and operations due to the complexity of Galois Field (GF) multiplications and XOR operations.
Innovation Solution
The implementation of a new instruction, MAC_BYTE_MATRIX_GF2, which performs a matrix multiply accumulate operation to accelerate the MixBytes transformation by processing each row of the state matrix independently with circulant constants, reducing the number of cycles required for the transformation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional AES instructions are used to perform MixBytes transformation, then the transformation can be completed, but the cycle count is high (60 cycles) due to complex GF multiplications and XOR operations
Solution Approach 1:
The patent combines multiple GF(2^8) multiplication operations and XOR operations into a single matrix multiply-accumulate instruction. The instruction performs the MixBytes transformation by multiplying a state matrix with a circulant key matrix and accumulating the results, reducing 60 separate cycles into one atomic operation that completes in 4 cycles.
Solution Approach 2:
The matrix multiply-accumulate instruction is designed to perform multiple cryptographic operations simultaneously - it handles both the multiplication by circulant constants and the accumulation with the state matrix in a single instruction. This multi-functional approach eliminates the need for separate instructions for each operation, significantly reducing the total cycle count.
2Reliability
If numerous GF multiplications and XOR operations are performed sequentially, then the MixBytes transformation is completed correctly, but the processing time increases significantly
Solution Approach 1:
The circulant key matrix is pre-computed from the key material before the actual transformation. This preliminary preparation allows the MixBytes operation to proceed with simple matrix multiply-accumulate instructions rather than performing complex GF multiplications during the transformation itself, reducing processing time while maintaining correctness.
Solution Approach 2:
The patent replaces the sequential mechanical execution of multiple GF multiplication and XOR instructions with a single optimized matrix multiply-accumulate operation. This substitution maintains the mathematical correctness of the transformation while dramatically reducing the number of operational steps required, thereby reducing processing time.
Data Source
AI summary
A method is described. The method includes iteratively performing for each position in a result matrix stored in a third register, multiplying a value at a matrix position stored in a first register with a value at a matrix position stored in a second register to obtain a first multiplicative value, where the positions in the first register and the second register are determined by the position in the result matrix and performing an exclusive or (XOR) operation with the first multiplicative value and a value stored at a result matrix position stored in the third register to obtain a result value.