Most of you’re aware of the method:
s1 x k1 = z1 + r1 x d1 mod n
In case you have two of them associated like this:
s1 x k1 = z1 + r1 x d1 mod n (1)
s2 x k1 = z2 + r1 x d1 mod n (2)
There may be the method:
(s1 – s2) x k1 = (z1 – z2) mod n (3)
to seek out,k1.And from that d1.
There additionally particular circumstances then you could find d1,from the method:
k2 = k1 – 1 or m,m
k2 = k1 /2 or m,m
Additionally,i learn in lots of posts right here,that k1 and k2 or (in particular circumstances) d1 and d2,can’t be associated in a algebric and logic approach,beacouse after all,shall be a method that can discover k1,k2,d1 and d2.
Now,i discovered with a easy derivation a method:
s1 x k1 = z1 + r1 x d1 (4)
s2 x k2 = z2 + r2 x d1 (5)
a x k1 – b x k2 = c (6)
Now the paradox,from my viewpoint:
I admit that my superior algebra is weak,however i need to guarantee that if somebody is best then me
might help me to show i’m proper or show me mistaken and assist me and in the long run assist you to,the reader.
I can show with out,that i name invisible information/stealth information,that this method is true.By invisible information /stealth information,i imply to have two actual or synthetic tx (transactions),the place i can use invisible information aka actual worth of k1,k2 or d1,to examine the knowledge straight.
However right here is the factor: even i can show in any transactions wherever,relation between a x k1 and b x k2 is c,via numbers,logic and method(4),(5) and (6) solely,with out invisible information,i can’t extract k1,k2 or d,even in a two associated k1,k2 transaction made public right here on this discussion board.
I attempted two modes to extract k1,k2 or d,but it surely gave me zero division.
Why,if i can show with algebra and logic which might be associated?
I believe first as a result of my superior algebra is just not excessive sufficient or second could be a rule that may not be damaged associated with how these equations are made.Are you able to assist me?
Be aware.I’m conscious that this sort of information is very delicate.For that i not made public how i can show with out invisible information,how can k1 and k2 are associated via (4),(5) and (6).However as you anticipate with a little bit of considering you are able to do,too.If somebody may give me the reply in personal,please do.
