AES SubBytes Optimization in Multi-Party Computation
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Solution Overview
Problem
The efficiency of Advanced Encryption Standard (AES) computations in secure multi-party computation (MPC) settings is hindered by the non-linear layers, particularly the SubBytes operation, which requires significant resources and is less efficient compared to plain implementations.
Innovation Solution
The implementation of special SubBytes tuples and algebraic operations in the MP-SPDZ framework, utilizing arithmetic circuits (AES-BD) or table look-ups (AES-LT), to optimize AES computations in MPC by embedding elements from GF(28) into GF(240), reducing communication and storage requirements through bit decomposition and efficient data handling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If AES SubBytes operation is implemented in MPC using standard methods, then security is maintained, but computation efficiency deteriorates significantly
Solution Approach 1:
The patent precomputes multiplication tables (T0, T1, T2, T3) during an offline phase before the actual AES encryption. These tables contain all possible products of basis elements in GF(2^40), allowing the online phase to perform Sbox operations using only precomputed lookups and XOR operations, eliminating expensive real-time multiplications in the MPC protocol
Solution Approach 2:
The patent changes the field representation from standard GF(2^8) to an embedded representation in GF(2^40). By representing each GF(2^8) element as a polynomial in a larger field with basis elements {1, w, w^2, w^3}, the multiplication operations can be decomposed into precomputable components, transforming a computationally intensive operation into efficient table lookups
2Speed
If AES is implemented in MP-SPDZ using GF(2^40) embedding, then Sbox computation speed improves, but storage requirements increase
Solution Approach 1:
The patent segments the multiplication operation into four separate precomputed tables (T0, T1, T2, T3), each storing products for one basis element position. This segmentation allows the system to store data in a structured, compressed format where each table contains only the necessary products for its specific basis element, reducing redundant storage
3Reliability
If standard AES rounds are computed in MPC, then encryption security is maintained, but communication overhead increases
Solution Approach 1:
The patent precomputes and distributes all multiplication tables during an offline phase, so that during the online encryption phase, parties only need to exchange XOR results and table indices. This eliminates the need for real-time multiplication protocols, reducing online communication to simple XOR operations and index exchanges
Solution Approach 2:
The patent replaces expensive real-time multiplication operations with copies of precomputed multiplication tables. Instead of performing actual multiplications in the MPC protocol, parties copy relevant entries from the precomputed tables based on their secret-shared inputs, transforming computational complexity into simple memory access operations
Data Source
AI summary
A distributed computer network utilizing cryptography that includes one or more processors, wherein the one or more processors are programmed to receive a secret input state and one or more tuples, mask the secret input state with the one or more tuple and utilize a reveal to compute a masked input, compute six multiplications on the masked input, compute multiplication of two secret values to output an intermediate output, mask a third secret value from the intermediate output and reveal the third secret value to compute an interaction, compute a multiparty-computation multiplication with the interaction, and output a final secret value in response to computing the multiparty-computation multiplication.