I strongly advise working through this entire question before submitting your answers. If you're on the wrong track, you should realise this when none of the answers for the next step make sense. Alice wishes to Bob to send her a message using Elliptic Curve Elgamal. She chooses a prime, p=37p=37, and then chooses the elliptic curve, EE: y2=x3+2x+5y2=x3+2x+5 She stumbles around trying to choose a point, PP, on the curve. She choose an x-coordinate of 33 for the point, then tries to find a value for y by trial and error. Which of her attempts is correct? 23 36 13 3 Now, she randomly choose a private key, a=8a=8. What is the value of her public key, QAQA? (18,8) (34,3) (11,10) (22,2) Alice publishes (p,E,P,QA)(p,E,P,QA). Bob wishes to send Alice the message, m=10m=10. He uses this as the x-coordinate of a point, PmPm. What is the value of PP? (10,17) (10,27) (10,35) (10,11) Bob choose the random number k=17k=17. What is the ciphertext Bob sends to Alice? ((27,24),(16,10)) mod 37 ((4,22),(23,9) mod 37 ((27,24),(21,24)) mod 37 ((4,22),(21,24) mod 37
I strongly advise working through this entire question before submitting your answers. If you're on the wrong track, you should realise this when none of the answers for the next step make sense.
Alice wishes to Bob to send her a message using Elliptic Curve Elgamal. She chooses a prime, p=37p=37, and then chooses the elliptic curve, EE:
She stumbles around trying to choose a point, PP, on the curve. She choose an x-coordinate of 33 for the point, then tries to find a value for y by trial and error.
Which of her attempts is correct?
Now, she randomly choose a private key, a=8a=8. What is the value of her public key, QAQA?
Alice publishes (p,E,P,QA)(p,E,P,QA).
Bob wishes to send Alice the message, m=10m=10. He uses this as the x-coordinate of a point, PmPm. What is the value of PP?
Bob choose the random number k=17k=17.
What is the ciphertext Bob sends to Alice?
Here we have curve,
y^2=x^3+2x+5.
Given,Prime no.p=37.
Now,as per Elliptic Curve Cryptography
algorithm first we have find out Generator Point.
For that G(x,y), x point is given us. x=3
Now for y point
y^2=x^3+2x+5 mod 37
here if we put x=3
then y^2=27+6+5 mod 37=38 mod 37=1 mod 37=1
Now,similarly on right side if we put y=36
then 36*36 mod 37=1
so correct value for y is 36.
Now G(3,36)
so her correct attempt is 36.
Now,
Moving ahead......
Private key is a=8
now for public key Qa=a*G(3,36)
Now,
Qa=8*G(3,36)
let's take=z=(3,36), we have to find out 8z.
Here,y^2=x^3+Ax+B
so ,A=2,B=5
now z=(3,36) For 2z=(x2,x3),3z(x3,y3)........................8z(x8,y8).
For finding 2z
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