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# Comparative Analysis of Lucas-Type Sequence.
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# Comparative Analysis of Lucas-Type Sequence
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Modern cryptography algorithms like RSA need primality tests to generate large random primes.\
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Specifically, RSA uses the product of two prime numbers to generate the public and private keys; if these primes are predictable, it makes it easier for an attacker to break the encryption scheme.\
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Large random primes are constructed in practice by generating pseudorandom numbers and then doing a primality test such as the Fermat primality test or something more powerful such as the Miller–Rabin primality test.\
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These primality tests fail for certain numbers called **pseudoprimes**.\
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My research focuses on analyzing the class of Perrin-type primality tests- **Lucas-Type Sequence**: \
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My research focuses on analyzing the class of Perrin-type primality tests- **Lucas-Type Sequence**:\
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## Lucas-Type Sequence
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$$V_{n+2} = c_1 V_{n+1} + c_0 V_{n}, \quad V_{0} = 2, \quad V_{1} = c_1$$\

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