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kelalaka
kelalaka
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In rsaRSA encryption, why does the public exponent (usually, 'e') have to be coprime with Φ$\varphi(n)$?

I have seen that there areis a similar question here but none that really answers the question. I understand that if I choose the 'encryptionencryption exponent e'$e$ not coprime with Φ(n) than$\varphi(n)$ then there is not a unique way to decrypt a message. 

What I am wondering is what is the mathemathicalmathematical reason behind this? It seems to me that since m^(kΦ(n)+1) = m mod N$m^{(k \varphi(n)+1)} = m \bmod N$ and d$d$ is defined as (kΦ(n)+1)/e$(k\varphi(n)+1)/e$ then d*e$d\cdot e$ is always going to be kΦ(n)+1 $k\varphi(n) +1$. What am I missing?

In rsa encryption, why does the public exponent (usually, 'e') have to be coprime with Φ(n)?

I have seen that there are similar question here but none that really answers the question. I understand that if I choose the 'encryption exponent e' not coprime with Φ(n) than there is not a unique way to decrypt a message. What I am wondering is what is the mathemathical reason behind this? It seems to me that since m^(kΦ(n)+1) = m mod N and d is defined as (kΦ(n)+1)/e then d*e is always going to be kΦ(n)+1 . What am I missing?

In RSA encryption, why does the public exponent (usually, 'e') have to be coprime with $\varphi(n)$?

I have seen that there is a similar question here but none that really answers the question. I understand that if I choose the encryption exponent $e$ not coprime with $\varphi(n)$ then there is not a unique way to decrypt a message. 

What I am wondering is what is the mathematical reason behind this? It seems to me that since $m^{(k \varphi(n)+1)} = m \bmod N$ and $d$ is defined as $(k\varphi(n)+1)/e$ then $d\cdot e$ is always going to be $k\varphi(n) +1$. What am I missing?

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user79517
user79517
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In rsa encryption, why does the public exponent (usually, 'e') have to be coprime with Φ(n)?

I have seen that there are similar question here but none that really answers the question. I understand that if I choose the 'encryption exponent e' not coprime with Φ(n) than there is not a unique way to decrypt a message. What I am wondering is what is the mathemathical reason behind this? It seems to me that since m^(kΦ(n)+1) = m mod N and d is defined as (kΦ(n)+1)/e then d*e is always going to be kΦ(n)+1 . What am I missing?