Perform the additions 1 2752 2 3636 in the group of the curv

Perform the additions

1. (2,7)+(5,2)

2. (3,6)+(3,6)

in the group of the curve y^2 x^3+2x+2 mod 17. Use only a pocket calculator

Solution

for x=2

y^2 x^3+2x+2 mod 17

y^2 2^3+2(4)+2 mod17
y^2 16+2 mod17
y^2 16+2
y^2 18

y 4.24

For x=5

y^2 x^3+2x+2 mod 17

y^2   5^3+2(5)+2 mod 17

y^2   125 + 10 +2

y^2   137

y 11.70

1. (2,7)+(5,2) = ( 2+7 ,4.24 + 11.70 ) =(9, 15.94)

For x = 3

y^2   x^3+2x+2 mod 17

y^2 3^3+2(3)+2 mod17

y^2 27 + 6 + 2

y^2 35

y = 5.916

2. (3,6)+(3,6) = ( 3+3, 5.916 + 5.916 ) =( 6, 11.832 )

Perform the additions 1. (2,7)+(5,2) 2. (3,6)+(3,6) in the group of the curve y^2 x^3+2x+2 mod 17. Use only a pocket calculatorSolutionfor x=2 y^2 x^3+2x+2 mod

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