For example we set a secret key integer to be P itself and get the corresponding public level coordinates, X and Y.
For example we set one other secret key integer to be 100 and likewise get the general public level, X and Y
We are able to carry out level addition on these factors and get a ensuing level, let’s name it (X_res, Y_res). Working from this straightforward instance, how can we get the integer worth of the key key that has (X_res, Y_res) as a public level?
For instance, if we do an easier level addition on the general public factors that correspond to the key key integers of 5 and three, we see that the ensuing level is the same as the general public level of the key integer is 8. This settlement between integer house additions and X,Y coordinate level additions appears to not work when the key key sum (in common integer house) exceeds P.
EDIT for a concrete instance
Outline public level of secret key: P
P_pub_point =(81492650628084235722910989215906994493388504323515224987714237725258561550612, 87307511589070331933464849403175870764418577084225550789428258636190124681705)
Outline public level of secret key: 100
one_hundred_point = (107303582290733097924842193972465022053148211775194373671539518313500194639752, 103795966108782717446806684023742168462365449272639790795591544606836007446638)
Do common level addition on the 2 public factors. Word that in integer house the sum of the key keys exceeds the sector most of P.
point_add(P_pub_point, one_hundred_point) = (71798214916470796948816991074259493502633106513666296340686716953572259972185, 113239714757063610655437050885246101255391392638754681964040793217602244196713)
Questions:
- Is the results of this level addition right? Or ought to the purpose addition operation be modified when the integer house sum exceeds P to get the proper level?
- How can we all know the integer worth of the key key that produces the general public level
(71798214916470796948816991074259493502633106513666296340686716953572259972185, 113239714757063610655437050885246101255391392638754681964040793217602244196713)? On condition that we all know all the opposite secret key values, I would assume this needs to be straightforward to get.
Concerning query (1), given this reply (2nd paragraph from backside), possibly the the operand must be negated earlier than level addition in an effort to get the proper reply? The publish creator stated, concerning the purpose at infinity:
“(the place level subtraction is similar as level addition with negation
of the operand)”