Difference between revisions of "G"
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The symbol ''G'' refers to a distinguished point on the secpt256k1 elliptic curve known as the ''generator'' or ''base'' point. | The symbol ''G'' refers to a distinguished point on the secpt256k1 elliptic curve known as the ''generator'' or ''base'' point. | ||
| − | Using elliptic curve point addition, one may add G to itself over and over again to form the sequence | + | Using elliptic curve point addition, one may add ''G'' to itself over and over again to form the sequence |
''G'', ''G'' + ''G'' = 2''G'', ''G'' + ''G'' + ''G'' = 3''G'', ... | ''G'', ''G'' + ''G'' = 2''G'', ''G'' + ''G'' + ''G'' = 3''G'', ... | ||
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''G'' = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 | ''G'' = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 | ||
| − | and in uncompressed form is: | + | and in uncompressed form it is: |
''G'' = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8 | ''G'' = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8 | ||
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*''h'' = 01 | *''h'' = 01 | ||
| − | The order ''n'' is the number of times ''G'' | + | The order ''n'' is the number of times ''G'' must be added to itself to get the identity. The cofactor ''h'' = 1 tells us that moreover ''n'' is the order of the entire group of elliptic curve points, and therefore ''G'' is a generator of this group. |
Revision as of 16:01, 12 December 2019
The symbol G refers to a distinguished point on the secpt256k1 elliptic curve known as the generator or base point.
Using elliptic curve point addition, one may add G to itself over and over again to form the sequence
G, G + G = 2G, G + G + G = 3G, ...
and eventually every point on the elliptic curve will be generated in this sequence.
In compressed form G is given by:
G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
and in uncompressed form it is:
G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
This particular choice of G is chosen to be secure against attacks when used in the context of public key cryptography.
The order of G and the cofactor are:
- n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
- h = 01
The order n is the number of times G must be added to itself to get the identity. The cofactor h = 1 tells us that moreover n is the order of the entire group of elliptic curve points, and therefore G is a generator of this group.