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Mathematical Cryptography | focusing on the math in public key cryptography

focusing on the math in public key cryptography

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Dan Ma | Mathematical Cryptography

https://mathcrypto.wordpress.com/author/mathcrypto

Focusing on the math in public key cryptography. Skip to primary content. Skip to secondary content. Author Archives: Dan Ma. Pepin’s Primality Test. October 30, 2016. A Fermat number is of the form. Is a nonnegative integer. A Fermat prime is a Fermat number that is a prime number. The first five Fermat numbers. Are known to be prime. Pierre de Fermat (1601-1665) conjectured that all Fermat numbers are prime. In 1732, Euler discovered a counterexample by showing that. Theorem 1 (Pepin’s Test). In fact, ...

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Mathematical Cryptography | focusing on the math in public key cryptography | Page 2

https://mathcrypto.wordpress.com/page/2

Focusing on the math in public key cryptography. Skip to primary content. Skip to secondary content. Newer posts →. A formula for generating strong pseudoprimes. November 19, 2014. We show in the previous post. Is a strong pseudoprime to base 2 whenever. Be a prime number that is larger than 5. Then the following number is a strong pseudoprime to base 2. Proof of Theorem 1. First step is to show that. Is a composite number. Note that. Is divisible by 5. it follows that. Furthermore, for any odd integer.

3

Another version of the primality test using a theorem of Lucas | Mathematical Cryptography

https://mathcrypto.wordpress.com/2014/12/03/another-version-of-the-primality-test-using-a-theorem-of-lucas

Focusing on the math in public key cryptography. Skip to primary content. Another version of the primality test using a theorem of Lucas. December 3, 2014. In the previous post. In the previous post. We discuss and prove the following theorem. Be a positive integer. Then. Is prime if and only if there exists some integer. For all prime factor. In the statement of the theorem is a primitive root modulo. Be a positive integer. Then. Is prime if and only if for each prime factor. There exists some integer.

4

A primality proving algorithm using a theorem of Lucas | Mathematical Cryptography

https://mathcrypto.wordpress.com/2014/12/01/a-primality-proving-algorithm-using-a-theorem-of-lucas

Focusing on the math in public key cryptography. Skip to primary content. A primality proving algorithm using a theorem of Lucas. December 1, 2014. In this post we discuss a theorem that can be used as a primality test that actually proves primality rather than just giving strong evidence for primality. The theorem is originally due to Lucas in 1891. The version we discuss here is proved by Lehmer [1]. The primality test using the theorem is a limited one since the test requires that. For all prime factor.

5

Pepin’s Primality Test | Mathematical Cryptography

https://mathcrypto.wordpress.com/2016/10/30/pepins-primality-test

Focusing on the math in public key cryptography. Skip to primary content. Pepin’s Primality Test. October 30, 2016. A Fermat number is of the form. Is a nonnegative integer. A Fermat prime is a Fermat number that is a prime number. The first five Fermat numbers. Are known to be prime. Pierre de Fermat (1601-1665) conjectured that all Fermat numbers are prime. In 1732, Euler discovered a counterexample by showing that. Theorem 1 (Pepin’s Test). Is a prime number if and only if. Describes all possible base...

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Focusing on the math in public key cryptography. Skip to primary content. Skip to secondary content. Pepin’s Primality Test. October 30, 2016. A Fermat number is of the form. Is a nonnegative integer. A Fermat prime is a Fermat number that is a prime number. The first five Fermat numbers. Are known to be prime. Pierre de Fermat (1601-1665) conjectured that all Fermat numbers are prime. In 1732, Euler discovered a counterexample by showing that. Theorem 1 (Pepin’s Test). Is a prime number if and only if.

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