Difference between revisions of "G"
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Owen Vaughan (talk | contribs) |
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| − | G refers to a distinguished point on the secpt256k1 elliptic curve known as the ''generator'' or ''base point''. | + | *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, G + G + G, ... . Eventually every point on the elliptic curve will be generated in this sequence. Although this property is true for any point on the elliptic curve, the particular choice of G is chosen to be secure against attacks when used in the context of public key cryptography. | + | Using elliptic curve point addition, one may add G to itself over and over again to form the sequence *G, *G + *G, *G + *G + *G, ... . Eventually every point on the elliptic curve will be generated in this sequence. Although this property is true for any point on the elliptic curve, the particular choice of *G is chosen to be secure against attacks when used in the context of public key cryptography. |
| − | G in compressed form is: | + | *G in compressed form is: |
*G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 | *G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 | ||
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*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 | ||
| − | + | ||
| + | The order *n of *G and the cofactor *h are: | ||
*n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141 | *n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141 | ||
*h = 01 | *h = 01 | ||
| + | |||
| + | The order *n is the number of times *G may be added to itself to get the identity. This generators a subgroup of the group of elliptic curve points, and the fact that the cofactor *h of this subgroup is 1 tells us that this subgroup is the whole group, i.e. *G generates the entrie group. | ||
Revision as of 15:50, 12 December 2019
- 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, *G + *G + *G, ... . Eventually every point on the elliptic curve will be generated in this sequence. Although this property is true for any point on the elliptic curve, the particular choice of *G is chosen to be secure against attacks when used in the context of public key cryptography.
- G in compressed form is:
- G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
and in uncompressed form is:
- G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
The order *n of *G and the cofactor *h are:
- n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
- h = 01
The order *n is the number of times *G may be added to itself to get the identity. This generators a subgroup of the group of elliptic curve points, and the fact that the cofactor *h of this subgroup is 1 tells us that this subgroup is the whole group, i.e. *G generates the entrie group.