Difference between revisions of "G"

 
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G is the Bitcoin Generator point.
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The symbol ''G'' refers to a distinguished point on the secpt256k1 elliptic curve known as the ''generator'' or ''base'' point.  
  
G in compressed form is:
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Using elliptic curve point addition, one may add ''G'' to itself over and over again to form the sequence
  
*G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
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''G'', ''G'' + ''G'' = 2''G'', ''G'' + ''G'' + ''G'' = 3''G'', ... 
and in uncompressed form is:
 
  
*G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
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and eventually every point on the elliptic curve will be generated in this sequence.
Finally the order n of G and the cofactor are:
 
  
*n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
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*h = 01
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In compressed form ''G'' is given by:
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''G'' = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
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 +
and in uncompressed form it is:
 +
 
 +
''G'' = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
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The order of ''G'' and the cofactor are:
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*''n'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
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*''h'' = 01
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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.

Latest revision as of 14:16, 18 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

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.