Editing NTRUEncrypt (section)

==Encryption==

Alice, who wants to send a secret message to Bob, puts her message in the form of a polynomial '''m''' with coefficients in <math>[-p/2, p/2]</math> . In modern applications of the encryption, the message polynomial can be translated in a binary or ternary representation.
After creating the message polynomial, Alice chooses randomly a polynomial '''r''' with small coefficients (not restricted to the set {-1,0,1}), that is meant to obscure the message.

With Bob's public key '''h''' the encrypted message '''e''' is computed:
:<math> \textbf{e} =  \textbf{r} \cdot \textbf{h} + \textbf{m} \pmod q </math>

This ciphertext hides Alice's messages and can be sent safely to Bob.

'''Example''':
Assume that Alice wants to send a message that can be written as polynomial
:<math> \textbf{m} = -1 + X^3 - X^4-X^8+X^9+X^{10} </math>	
and that the randomly chosen ‘blinding value’ can be expressed as
:<math> \textbf{r} = -1+X^2+X^3+X^4-X^5-X^7 </math>

The ciphertext '''e''' that represents her encrypted message to Bob will look like
:<math> \textbf{e} = \textbf{r} \cdot \textbf{h} + \textbf{m} \pmod {32} = 14 + 11X+26X^2+24X^3+14X^4+16X^5+30X^6+7X^7+25X^8+6X^9+19X^{10} \pmod {32} </math>