# Convert messages to elliptic curve points [duplicate]

Let $$E$$ be an elliptic curve; $$\alpha,\beta$$ two points of $$E$$; and $$a$$ a private key such that $$\beta=a\cdot\alpha$$. We choose random integer $$k$$ and plain text $$x\in E$$. Encryption and decryption methods are as follows:

$$\operatorname{Enc}(x,k)=(k\cdot\alpha,x+k\cdot\beta)$$

$$\operatorname{Dec}(y_1,y_2)=y_2-a\cdot y_1$$

How can we convert a message such as "Hello" to a point of $$E$$?

edit: In answer to question "Mapping of message onto elliptic curve and reverse it", we are given a general probabilistic method, and methods that are easy for special cases; for example when the curve is super-singular, or for ordinary curves defined over $$\mathbb F_q$$ with $$q=3\bmod 4$$ and group order divisible by $$4$$. I am looking for methods which are not probabilistic and are applicable to general cases. Do such methods exist?

I will be so thankful for any helpful comments and answers.

• I'm pretty sure the answer is: "There's no known way to map arbitrary integers to points on arbitrary curves in an easily reversible way." – SEJPM Jan 6 '16 at 13:11