Self-Correcting Cryptographic Calculation Device for Flexible Parameter Settings
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Solution Overview
Problem
The self-correcting cryptographic technique described in existing patents is limited in flexibility as it requires two natural numbers a and b to be coprime, and fails when a' and b' do not satisfy the relation a'a + b'b = 1.
Innovation Solution
A calculation device and method that calculates f(x) b< x1 and f(x) a< x2, with results u and v, and outputs (u b'< v a'< ) 1/d< for d = a'a + b'b, enabling the technique to function even when a and b are not coprime and a' and b' do not satisfy the relation, thus enhancing flexibility in setting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If two natural numbers a and b are required to be coprime and a' and b' must satisfy a'a + b'b = 1, then the self-correcting technique can ensure correct calculation, but the flexibility in setting parameters is reduced
Solution Approach 1:
The patent changes the mathematical parameters from requiring coprime numbers with a'a + b'b = 1 to allowing any integers with a'a + b'b = d. This parameter transformation enables the system to work with non-coprime numbers while maintaining correctness through the generalized formula (u^b')^(a') * (v^a')^(b') = 1/d, thereby resolving the contradiction between reliability and flexibility
Solution Approach 2:
Instead of requiring the traditional condition a'a + b'b = 1 and then correcting deviations, the patent inverts the approach by directly setting a'a + b'b = d where d can be any integer, and building the correction mechanism around this generalized condition. This inversion allows greater flexibility in parameter selection while ensuring correct results
Data Source
AI summary
A first calculation unit is capable of calculating f(x)bx1 and sets a calculation result of f(x)bx1 to u, and a second calculation unit is capable of calculating f(x)ax2 and sets a calculation result of f(x)ax2 to v. A final calculation unit outputs (ub'va')l/d for d=a'a+b'b when the calculation result u and the calculation result v satisfy ua=vb. Here, G and H are groups, f is a function for mapping an element x of the group H to the group G, x1 and X2 are random variables values of which are in the group G, a realization of the random variable X1 is x1, a realization of the random variable X2 is x2, and a, b, a', and b' are integers.