Hello The elliptic curve parameters: p=29 a=26 b=7 Check non-singularity condition: 4 a^3 + 27 b^2 mod p = 26 Constructing point (2,3): P=(2,3) Constructing zero point: P=infinity Eqality tests (1=true, 0=false) P=(2,3), Q(2,4), R(1,3) P==P: 1, P==Q: 0, P==R: 0 Assignment test P=(2,3), Q(2,4), R(1,3) P=Q; Q=R; P=(2,4), Q(1,3), R(1,3) Addition test: Case 1 P=infinity, Q=infinity, P+Q=infinity Addition test: Case 2a P=(2,3), Q=infinity, P+Q=(2,3) Addition test: Case 2b P=infinity, Q=(2,3), P+Q=(2,3) Addition test: Case 3 P=(2,3), Q=(2,-3), P+Q=infinity Addition test: Case 4 P=(2,3), Q=(3,5), P+Q=(28,3) Addition test: Case 5 P=(2,3), P+P=(20,28) (P+P)-P=(2,3) Modsqrt test modsqrt(1)=1 modsqrt(2) does not exist modulo 29 modsqrt(3) does not exist modulo 29 modsqrt(4)=27 modsqrt(5)=18 modsqrt(6)=8 modsqrt(7)=23 modsqrt(8) does not exist modulo 29 modsqrt(9)=26 findPoint test findPoint(1): (1,18)...verified findPoint(2): (2,26)...verified findPoint(3): (3,24)...verified findPoint(4): (4,1)...verified findPoint(5): (5,1)...verified findPoint(6): No point with x-coordinate 6 findPoint(7): No point with x-coordinate 7 findPoint(8): No point with x-coordinate 8 findPoint(9): (9,10)...verified Times test 1 times (4,16) = (4,16)...verified 2 times (4,16) = (14,8)...verified 3 times (4,16) = (7,27)...verified 4 times (4,16) = (25,23)...verified 5 times (4,16) = (13,10)...verified 6 times (4,16) = (6,24)...verified 7 times (4,16) = (6,5)...verified 8 times (4,16) = (13,19)...verified 9 times (4,16) = (25,6)...verified 5 x (4 x (7,27))=(13,19) 20 x (7,27))=(13,19)