Random Number In R Value , what is it actually, is it the same as Nonce in the blocks

Question

I wonder about the random number in R value ...

if i am right , the R value is First part of the script signature which is combined of two parts (r,s)

r = Gk (elliptic curve scalar multiplication) Or does the whole signature is the Gk ?? So r , is a multiplication of random number ( k ) times G (elliptic curve scalar multiplication )

while r = xcoordinate(R) , is just the first part of the ( r,s )

I read an article the most repeated R values in transactions is 0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63 while G is the Double of this point means that the random number is (1/2)

so R value Is simply is simply calculated by multiplying any number by G ???

and they do call it nonce , so is it the same nonce shown in blocks ? that is already public ? or it is another nonce ?

Answer 1

The nonce in a signature is different from the nonce used in the block header. These are unrelated to each other. They only share a name because the term nonce is a generic word that means "a number used only once."

A signature is composed of two numbers: R and s. R is the X coordinate of a random nonce k multiplied by the generator point G. It is the result of elliptic curve scalar multiplication with a point. k is a scalar, which means it is just a random integer modulo the n, the order of G.

The nonce k must be kept private. If it is known, then anyone can compute the private key used in the signature. Additionally, reusing the same k (which results in R being the same) with the same private key will allow the private key to be computed.