Question

The observations above also provide an answer to another important security question. We know that people often use $e=65537$ as an encryption exponent. What if they also chose the same value of $n$ ? What would be the security implications?

   The observations above also provide an answer to another important security question. We know that people often use $e=65537$ as an encryption exponent. What if they also chose the same value of $n$ ? What would be the security implications?
 
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Modern Cryptography and Elliptic Curves: A Beginner’s Guide
Modern Cryptography and Elliptic Curves: A Beginner’s Guide
Thomas R. Shemanske 1st Edition
Chapter 5, Problem 5 ↓

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The question refers to the use of the RSA encryption algorithm, where $e$ is the public exponent and $n$ is the modulus, which is the product of two prime numbers. The common choice for $e$ is 65537 due to its properties that make encryption efficient.  Show more…

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The observations above also provide an answer to another important security question. We know that people often use $e=65537$ as an encryption exponent. What if they also chose the same value of $n$ ? What would be the security implications?
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