In the RSA encryption system, are there not multiple messages m that give the same cipher text c?

Asked Sep 14 '15 at 14:27

Active Sep 14 '15 at 14:32

Viewed 26 times

For example:

p = 5, q = 11, n = 55

$\phi$(55) = 40

e = 3, $\phi$(55) and 3 are relatively prime

m = 3, then: $3^3 mod(55) = 27$

m = 113, then: $113^3 mod(55) = 27$

I heard that e and $\phi$(n) have to be relatively prime in order for the encryption to give unique solutions, but it seems that even if they are, multiple values for m gives the same encrypted c value. Is this not a problem? Or am I missing something or doing something wrong? I am asking if it is a problem that multiple values of m give the same cipher text c.

edited Sep 14 '15 at 14:32

asked Sep 14 '15 at 14:27

maurits

I am asking if it is a problem that multiple values of m give the same cipher text c. – maurits Sep 14 '15 at 14:32
Since $113 = 2 \cdot 55 + 3 \equiv 3 \pmod {55}$ these are considered the same value in modular arithmetic. You need restrict it to $0 \leq m < n$ if you want to treat $m$ as an integer. – CodesInChaos Sep 14 '15 at 14:38
Oh okay, that answers my question perfectly, since 113 is larger than 55. Thank you! – maurits Sep 14 '15 at 14:38
$113\equiv 3 \bmod{55}$ – mikeazo Sep 14 '15 at 14:38

In the RSA encryption system, are there not multiple messages m that give the same cipher text c?

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