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In RSA, Why Is It Important Choosing E so That It Is Coprime to φ(n)?

How Does This Happen in RSA Malleability?

How to Iteratively Calculate a^emod N with Modulus N Sized 4096 Bits

Where Does the $\varphi(n)$ Part of RSA Come From?

How Does Clifford Cocks 'Non-Secret Encryption' Work?