9.5In this problem we will encrypt a message using an ElGamal's scheme based on the elliptic curve E:y^2 = x^3 +x +6 mod 11. ElGamal's 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 for example, the first element of the pair, m_x, can be her real message) . She selects a random number i, 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 decrypt m by calculating [m+iB]-bA. Assume P=(2,7) and b=7. Bob's public key will be B= . Alice selects i=3. What is the largest i that Alice could select? Alice calculates A=iP= . Alice's secret message is m=(10,9). Calculate the corresponding M: the second pair in M is=[m+iB]= . Bob first calculates bA= and then subtracts this point from [m+iB] that he received from Alice, obtaining

In this problem we will encrypt a message using an ElGamal's scheme based on the elliptic curve E:y2=x3+x+6 mod 11. ElGamal's 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,my) (this is a point on E and for example, the first element of the pair, m_x, can be her real message). She selects a random number i, 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 decrypt m by calculating [m+iB]bA. Assume P=(2,7) and b=7. Bob's public key will be B= Alice selects i=3. What is the largest i that Alice could select? Alice calculates A=iP= Alice's secret message is m=(10,9). Calculate the corresponding M : the second pair in M is =[m+iB]= . Bob first calculates bA= and then subtracts this point from [m+iB] that he received from Alice, obtaining