Montgomery Multiplication Operand Ordering for Power Analysis Protection
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Solution Overview
Problem
Existing encryption technologies are vulnerable to differential power analysis attacks, which can expose secret keys during decryption processes, particularly in symmetric key encryption algorithms like Montgomery multiplications.
Innovation Solution
The proposed method involves repeating Montgomery multiplications with arbitrary changes in the order of operations and operands, combined with blinding and unblinding processes using random numbers, to protect the secret key from exposure during decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Montgomery multiplications are performed in a fixed order with fixed operands, then the decryption process is simple and efficient, but the secret key is vulnerable to differential power analysis attacks
Solution Approach 1:
The patent applies dynamics by making the order of Montgomery multiplications and the order of operands variable rather than fixed. A random number determines the operation sequence, transforming the static decryption process into a dynamic one that adapts to random patterns, thereby preventing differential power analysis while maintaining computational efficiency
Solution Approach 2:
The patent changes the parameter of operation order by introducing a random number that dynamically determines the sequence of Montgomery multiplications and operand arrangement. This parameter change ensures that each decryption operation follows a different pattern, making power analysis ineffective while preserving the mathematical correctness of the decryption result
2Reliability
If the order of Montgomery multiplications and operands is arbitrarily changed to prevent power analysis, then security is improved, but the decryption process becomes more complex
Solution Approach 1:
The patent changes the operational parameters by using a random number to dynamically determine the sequence of Montgomery multiplications and operand ordering. Although the sequence varies, the underlying mathematical operations remain the same, ensuring that decryption remains computationally straightforward while achieving security against power analysis
Solution Approach 2:
The random number serves as an intermediary that mediates between the fixed mathematical requirements of decryption and the variable security requirements. It determines the operation sequence without altering the fundamental decryption logic, thus maintaining ease of operation while improving security
Data Source
AI summary
Provided is a decryption method of an encryption algorithm. In the decryption method, a secret key can be received. A plurality of Montgomery multiplications can be repeated on a cipher text until a modular exponentiation of the secret key. When the repeated Montgomery multiplications are performed, an order of the plurality of Montgomery multiplications or an order of operands can be arbitrarily changed.