Modular Multiplication Lookup Table for Side-Channel Resistance
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Solution Overview
Problem
Current cryptographic systems, particularly those using modular multiplication in post-quantum cryptography, are vulnerable to side-channel attacks that exploit power consumption and electromagnetic fields, necessitating a countermeasure to enhance security.
Innovation Solution
A device and method incorporating a random number generator, processing circuit, and memory to perform modular multiplication using a lookup table, where the processing circuit generates a random generator, creates and writes the lookup table to memory, and accesses it independently of input values to produce a result, ensuring consistent power consumption and reducing predictability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional modular multiplication is used in cryptographic operations, then the operation can be performed efficiently, but the system becomes vulnerable to side-channel attacks that exploit power consumption and electromagnetic fields
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing multiplication results in lookup tables before the actual cryptographic operation. The processing circuit generates random numbers, creates generators, and builds lookup tables in advance, so that during the modular multiplication operation, only table lookups are needed rather than performing complex multiplication calculations in real-time. This pre-computation approach enhances security by making the actual operation simpler and less susceptible to side-channel analysis.
Solution Approach 2:
The patent introduces lookup tables as an intermediary between the input operands and the multiplication result. Instead of directly multiplying inputs a and b, the system uses pre-computed tables that map input combinations to their products. This intermediary structure randomizes the computation path and decouples the relationship between input values and power consumption patterns, thereby protecting against side-channel attacks while maintaining computational efficiency.
2Reliability
If lookup tables are used for modular multiplication, then side-channel attack resistance is improved through consistent power consumption, but memory requirements and table generation overhead increase
Solution Approach 1:
The patent applies parameter changes by dynamically generating random numbers and using them to create variable generators for the lookup tables. Rather than using fixed, predetermined tables, the system changes the parameters (random numbers, generators) each time a cryptographic operation is performed. This approach maintains security by ensuring consistent power consumption patterns while managing memory usage through on-demand table generation and deletion after use.
Solution Approach 2:
The patent implements dynamics by making the lookup table structure adaptive and transient rather than static and permanent. The processing circuit generates lookup tables dynamically based on randomly generated parameters, uses them for the multiplication operation, and then clears them from memory. This dynamic approach allows the system to balance security requirements with memory resource constraints, as tables are created only when needed and removed afterward.
Data Source
AI summary
A device includes a random number generator configured to generate a random number, a memory configured to store at least one lookup table, and a processing circuit configured to generate a generator based on the random number, create the at least one lookup table based on the generator, and write the created at least one lookup table to the memory, wherein the processing circuit is configured to access the memory based on a first input and a second input, and generate a result of a modular multiplication of the first input by the second input based on the at least one lookup table.