Inverse Calculation Circuit for Elliptic Curve Cryptography
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Solution Overview
Problem
Existing inverse calculation circuits for elliptic curve cryptography are vulnerable to timing attacks and differential power analysis (DPA) attacks, which compromise the security of decryption processes.
Innovation Solution
The implementation of a second Montgomery inverse algorithm that introduces random numbers to vary the calculation time and power consumption, making it difficult for attackers to predict the inverse calculation process, combined with a random number generator to generate first and second random numbers that prevent specific types of attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a conventional inverse calculation circuit is used for elliptic curve cryptography, then the calculation speed is fast and the structure is simple, but the circuit is vulnerable to timing attacks and differential power analysis attacks
Solution Approach 1:
The patent introduces a random number generation step before the inverse calculation process. This preliminary action of generating random numbers and using them to control calculation paths ensures that each execution varies in timing and power consumption, thereby preventing timing attacks and DPA attacks while maintaining the core inverse calculation functionality
Solution Approach 2:
The patent makes the inverse calculation circuit dynamic by using random numbers to selectively activate different calculation paths or operations. This dynamic behavior causes variation in execution time and power consumption patterns across different executions, making the circuit robust against side-channel attacks while preserving cryptographic correctness
2Reliability
If random numbers are introduced to prevent timing and DPA attacks, then the security robustness is improved, but the calculation time increases and power consumption varies
Solution Approach 1:
The patent changes the parameter of calculation path selection based on random numbers rather than altering the fundamental inverse calculation algorithm. By dynamically selecting from pre-defined calculation paths that all lead to the correct mathematical result, the system adds security without significantly increasing computational complexity or execution time
3Object-affected harmful factors
If the inverse calculation process is made unpredictable through random numbers, then resistance to decryption attacks is improved, but the power consumption increases
Solution Approach 1:
The patent designs the random number-controlled calculation paths to perform multiple functions: they not only prevent timing and DPA attacks but also ensure correct cryptographic output. The same random number mechanism serves both security and correctness verification purposes, avoiding additional power-consuming operations
Data Source
AI summary
In an inverse calculation circuit, an inverse calculation method, and a storage medium encoded with a computer readable computer program code, a random number generator generates a first random number and a second random number; and an inverter receives a plurality of first bits expressing a first element of a finite field(s) as first inputs, receives a plurality of second bits expressing a second element of a finite field(s) as second inputs. In response to the first and second random numbers, the inverter outputs a plurality of third bits expressing the inverse elements of the first element. The first random number prevents a different power analysis (DPA) decryption attack, and the second random number prevents a timing decryption attack.