9.6In this problem we will decrypt a message that was encrypted using an ElGamal scheme based on the elliptic curve E:y^2 = x^3 +4x +20 mod 29. The scheme works as follows: Bob selects a primitive point P, a private key b and calculates his public key B=bP. He then sends to Alice E, P and B. Suppose that Alice wants to send Bob the message m=(m_x,m_y) (this is a point on E and the first element of the pair, m_x, is her real message) . She selects a random number i (between 2 and #E-1), calculates A=iP, and sends to Bob the ciphertext M={A;[m+iB]}. Note that M is a pair of points on E. Bob can then decript Alice's message by calculating [m+iB]-bA. Assume P=(8,10) and b=5. Bob's public key will be B

In this problem we will decrypt a message that was encrypted using an ElGamal scheme based on the elliptic curve E:y y2=x3+4x+20mod29. The scheme works as follows: Bob selects a primitive point P, a private key b and calculates his public key B=bP. He then sends to Alice E, P and B. Suppose that Alice wants to send Bob the message m=(mx,m_y) (this is a point on E and the first element of the pair, mx, is her real message). She selects a random number i (between 2 and #E1 ), calculates A=iP, and sends to Bob the ciphertext M={A;[m+iB]}. Note that M is a pair of points on E. Bob can then decript Alice's message by calculating [m+iiB]bA. Assume P=(8,10) and b=5. Bob's public key will be B= After sending Alice E,P and B he receives from her the ciphertext M={(6,17);(1,24)}. Bob first calculates bA= and then subtracts this point from (1,24) (sent to him by Alice) obtaining Alice's real message was x_m=