Break El Gamal for Elliptic Curves There  is  an  elliptic  curve  El  Gamal  digital  signature  scheme. Alice fixes an elliptic curve $E$, a prime $p$, a point $A$ on $E$, a secret integer $a$, and computes $B = aA$.  She makes $(E, p, A, B)$ public. To sign a message m (which is an integer), she computes a point $R = (x, y)$ on $E$ and an integer $s$, and sends $(m, R, s)$. The verification is $xB + sR = mA$.
Eve chooses $R1 = B − A = (x1, y1)$.
How do I find an integer $s1$ and message $m1$ so that $(m1, R1, s1)$ is a valid signature?
I referred to this to relate the normal El Gamal to the one on the Elliptic curve, but am not able to do so. Also, why is hashing required in such situations to prevent such forgery?
Well, one obvious method (which assumes that either there's a point on the elliptic curve with $x=0$, or the verifier doesn't check if $R$ is on the curve) is:
$$m1 = 0$$
$$R1 = (0, y)$$
$$s1 = 0$$
This satisfies the verification equation...