The ecliptic curve E1: y^2 = x^3+7 over F17 with the base point G is (15, 13) and the second ecliptic curve E2: y^2 = x^3+7 over F31 with the same base point G is (15, 13).
My question is: is there any way to calculate the equivalent point of F31 based on F17? For example: with 7G = (10, 15) of curve F17, how to calculate 7G of F31 ? The result should be 7G = (12, 14) on F31.
Below is all points of two curves:
#----Curve F17-------#
- 1G = (15, 13)
- 2G = (2, 10)
- 3G = (8, 3)
- 4G = (12, 1)
- 5G = (6, 6)
- 6G = (5, 8)
- 7G = (10, 15)
- 8G = (1, 12)
- 9G = (3, 0)
- 10G = (1, 5)
- 11G = (10, 2)
- 12G = (5, 9)
- 13G = (6, 11)
- 14G = (12, 16)
- 15G = (8, 14)
- 16G = (2, 7)
- 17G = (15, 4)
#----Curve F31-------#
- 1G = (15, 13)
- 2G = (29, 17)
- 3G = (1, 22)
- 4G = (20, 19)
- 5G = (21, 17)
- 6G = (23, 23)
- 7G = (12, 14)
- 8G = (11, 27)
- 9G = (25, 22)
- 10G = (7, 19)
- 11G = (27, 27)
- 12G = (5, 9)
- 13G = (0, 24)
- 14G = (4, 12)
- 15G = (22, 23)
- 16G = (3, 13)
- 17G = (13, 18)
- 18G = (17, 23)
- 19G = (24, 4)
- 20G = (24, 27)
- 21G = (17, 8)
- 22G = (13, 13)
- 23G = (3, 18)
- 24G = (22, 8)
- 25G = (4, 19)
- 26G = (0, 7)
- 27G = (5, 22)
- 28G = (27, 4)
- 29G = (7, 12)
- 30G = (25, 9)
- 31G = (11, 4)
