Post
Topic
Board Development & Technical Discussion
Re: Pollard's kangaroo ECDLP solver
by
BorisTheHorist
on 31/03/2022, 04:01:47 UTC
paniker this is meaning that you can change the n's

modular elliptic curve

Total of all the wallets n is the last number. n= 115792089237316195423570985008687907852837564279074904382605163141518161494337 (In Dec)

n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 (In HEX)

Half way of n n//2 = 57896044618658097711785492504343953926418782139537452191302581570759080747169

57896044618658097711785492504343953926418782139537452191302581570759080747169 Lenght Bits = 255

very nice and thanks to boris.. you still here..

yes I am still here, this was the only thing I have found so far.

Half way of n
n//2 is wrong, check in above posts, mention clearly formula for div
thankx

do you mean the last "6" ,
115792089237316195423570985008687907852837564279074904382605163141518161494337 ?


There seems to be some confusion here. the largest possible private key is 115792089237316195423570985008687907852837564279074904382605163141518161494336 or in hex FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140
which is the "prime" at 2^256 - 2^32 - 2^9 -2^8 - 2^7 - 2^6 - 2^4 - 1

Zero cannot be a private key therefor there are 115,792,089,237,316,195,423,570,985,008,687,907,852,837,564,279,074,904,382,605,163,141,518,161,494,336 valid private keys
It turns out there are only                                     57,896,044,618,658,097,711,785,492,504,343,953,926,418,782,139,537,452,191,302,581,570,759,080,747,168 valid public x coordinates

It really is not straight forward to grasp as it took me time though it happens at half of the largest key which is 57896044618658097711785492504343953926418782139537452191302581570759080747168 or in hex 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0
 
you see 57.........168 and 57.........169 have both the same public x coordinate and opposite y parity (fancy word for even/odd)

removing the lead 03 or 02 It turns out that every public x coord from 1 to 57.........168 is exactly equal to the public x coord at the same spot in the sequence from 115........336 to 57.........169 importantly 115........336>57.........169

finally, if you search every private key from 1 to 57,896,044,618,658,097,711,785,492,504,343,953,926,418,782,139,537,452,191,302,581,570,759,080,747,168 (exactly half the normal range) for a public x coord (the majority of a compressed public key) you would find it whether or not the original private key was larger or small than 57.........169 however a leading 03 would be 02 and vice versa therefor the limitation doesn't apply to the resulting addresses.