# what does the leading byte represent for the initial point G?

Per SEC 2, the base point $G$ for secp192r1 is as follows:

G = 04 188DA80E B03090F6 7CBF20EB 43A18800 F4FF0AFD 82FF1012
07192B95 FFC8DA78 631011ED 6B24CDD5 73F977A1 1E794811


According to this JavaScript ECDH Key Exchange Demo, when you click the secp192r1 button, the $(x, y)$ coordinates for $G$ are as follows:

• x = 602046282375688656758213480587526111916698976636884684818
• y = 174050332293622031404857552280219410364023488927386650641

$x$ is equal to what you'd get if you converted 188DA80E B03090F6 7CBF20EB 43A18800 F4FF0AFD 82FF1012 from hex to decimal. Same thing for 07192B95 FFC8DA78 631011ED 6B24CDD5 73F977A1 1E794811.

But what does the 04 at the beginning mean?

• Since you found SEC2, this is in SEC1 (2.3.3-4) at the same place. – dave_thompson_085 Jul 2 '17 at 4:37

But what does the 04 at the beginning mean?

It means 'this elliptic curve point is specified in uncompressed format', that is, the $x$ and $y$ coordinates are given explicitly.

The other alternatives are :

• 02, which means 'this is a compressed point, where we give the $x$ coordinate explicitly; of the two possible $y$ coordinates that are compatible with that $x$ coordinate, select the one with the 0 lsbit.

• 03, which is the same, except you select the $y$ coordinate with a 1 lsbit.

The compressed formats are about half as long (saving space), but requires more computation (a modular square root) to use if you perform an operation that requires the $y$ coordinate.

• It looks like for binary curves that it's not quite as simple as "is the square root odd or even". I understand that on an elliptic curve any x axis coordinate that intersects with the curve will do so at two points. It stands to reason that one point would be "higher" (possessing of a larger y) than the other. Maybe "02" and "03" are more generally understood as "high point" and "low point"? – neubert Nov 23 '17 at 23:15
• @neubert: yes, for a binary curve, it becomes "find the two solutions to this quadratic equation". I've never worked with compressed points to binary curves, and I'm not certain which they assign the lables 02 and 03 to. – poncho Nov 27 '17 at 22:54