Editing RSA cryptosystem (section)

===Encryption===
After Bob obtains Alice's public key, he can send a message {{mvar|M}} to Alice.

To do it, he first turns {{mvar|M}} (strictly speaking, the un-padded plaintext) into an integer {{mvar|m}} (strictly speaking, the [[Padding (cryptography)|padded]] plaintext), such that {{math|0 &le; ''m'' &lt; ''n''}} by using an agreed-upon reversible protocol known as a [[#Padding schemes|padding scheme]]. He then computes the ciphertext {{mvar|c}}, using Alice's public key {{mvar|e}}, corresponding to

<math display="block">c \equiv m^e \pmod{n}.</math>

This can be done reasonably quickly, even for very large numbers, using [[modular exponentiation]]. Bob then transmits {{mvar|c}} to Alice. Note that at least nine values of {{mvar|m}} will yield a ciphertext {{mvar|c}} equal to
{{mvar|m}},{{efn|Namely, the values of {{mvar|m}} which are equal to −1, 0, or 1 modulo {{mvar|p}} while also equal to −1, 0, or 1 modulo {{mvar|q}}. There will be more values of {{mvar|m}} having {{math|1=''c'' = ''m''}} if {{math|''p''&nbsp;−&nbsp;1}} or {{math|''q''&nbsp;−&nbsp;1}} has other divisors in common with {{math|''e''&nbsp;−&nbsp;1}} besides 2 because this gives more values of {{mvar|m}} such that <math>m^{e-1} \bmod p = 1</math> or <math>m^{e-1} \bmod q = 1</math> respectively.}} but this is very unlikely to occur in practice.