# Given a Message and Decryption Key, is it possible to find the Cipher in RSA?

This is a slight reversal from the norm but...

Suppose Alice wants to ensure that everyone knows that a message will be from her. Instead of giving out the encryption key, she broadcasts the decryption key, and encrypts her messages privately. She doesn't care that anybody can read her messages, only that someone can't imitate her.

So if I want to imitate Alice, and all I have is a decryption key and the message, is it possible to fake a message from Alice?

Edit: so to clarify, we'll assume a literate message is valid. We'll also add the constraint that the attacker wants to mimic a specific Message (M), not just any message, or previous messages will do.

• This seems to be trying to reinvent RSA signature, but in a way that I do not quite get. Suggestion: precisely state what receivers do to decide if something received is accepted as coming from Alice; then try to fool that, possibly assuming availability of cryptograms genuinely produced by Alice. For a start, do receivers get one or two numbers? Assuming one, on what grounds exactly will a receiver accept or refuse $0$? $1$? $42$? $N-1$, where $N$ is Alice's public modulus? $C+N$, where $C$ is genuinely from Alice? Assuming two, what about $(0,0)$? $(1,1)$? etc..
– fgrieu
Oct 3, 2017 at 20:23
• I'll edit the question, but for the purposes of the question, lets assume a literate message is valid. I'll also add that+ the attacker has a specific message M which they want to use, and can't just use any message they like. Oct 3, 2017 at 20:34