Same RSA keys, same message, different encrypts

Question

I generate private/public keys, and a small text file,

openssl genrsa -out priv.pem
openssl rsa  -out pub.pem -in priv.pem -pubout
echo "A" > plain.txt

When you encrypt the text file with the public key twice, as so,

openssl rsautl -encrypt -pubin -inkey pub.pem -in plain.txt -out cipher.txt

you will see that the two cipher.txt differ. This is what I do not understand.

You might want to check out my answer [here](http://stackoverflow.com/questions/16325057/why-does-rsa-encrypted-text-give-me-different-results-for-the-same-text) — Chiara Hsieh, Aug 20 '13 at 10:45
This should answer your question: http://security.stackexchange.com/questions/33752/will-encrypting-the-same-file-with-gpg-and-the-same-key-produce-the-same-ciphert — Gaston, Aug 20 '13 at 13:03

score 3 · Accepted Answer · edited Feb 08 '16 at 19:25

When you encrypt the text file with the public key twice ... you will see that the two cipher.txt differ. This is what I do not understand.

This is called probabilistic encryption (versus deterministic encryption). Its that way by design so that the same message encrypted twice does not produce the same cipher text. Its due to the masking function and padding functions used by RSA.

If encryption produced the same cipher text, then your adversary could gain information. For example, if your adversary sees a message he does not understand but observers your army attacks his army the next morning, he might guess that the message was "Attack at dawn". If he sees that same encrypted message again, he's probably going to be ready for an attack at dawn the next day.

The folks on the crypto stack exchange might be able to help you further if you want the details of MGFs, OAEP and the like. Also, Dr. Steve Bellovin has a very approachable introduction to cryptography at An Introduction to Cryptography.

Same RSA keys, same message, different encrypts

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