# Where can I find the source of the Coppersmith method univariate in C with GMP library?

Could someone please tell me where I can find the source code of the Coppersmith method univariate written in C with the GMP library?

to be fair I will explain how I will use it for factoring

Let's take the example N=1763 of Factorization nr 88 Part I

$$P=27*b+1$$ ; $$p=65-8*b$$

$$Q=25*a+11$$ ; $$q=67-8*a$$

$$p^2=(65-8*b)^2=64*b^2-1040*b+4225$$

We find the integer delta $$D$$ of $$x*p+p^2$$

$$(27*x-1040)^2-4*64*(4225+x)=D^2$$

$$x=1/729*(28208-sqrt(729*D^2+795691264))$$

$$795691264=1763*451328$$

A partial factorization of $$451328$$ that is $$8$$ is the biggest problem with my approach

we replace $$D$$

$$28208-729*x-27*sqrt[(27*x-1040)^2-4*64*(4225+x)]=8*(67-8*a)$$

$$->$$

$$64*a^2+55344*a+11964681=729*W$$

$$55344+729*x=64*y$$ $$->$$ $$x=16$$

$$11964681+729*x=64*y$$ $$->$$ $$x=15$$

$$[64/64*a^2+(((55344+16*729)/64) mod (729))*a+(((11964681+15*729)/64) mod (729))] mod (729) = 0$$

$$(a^2+318*a+495) mod (729) = 0$$

Applying the Coppersmith univariate method

$$->$$ $$a=3$$ $$->$$ $$q=43$$

• @kelalaka not RSA attack Jan 26, 2022 at 14:28
• Ah, I see. github.com/defund/coppersmith, no easy to convert to C/GNU/GMP. May be you can benefit from NTL on your progress. Jan 26, 2022 at 14:54
• @kelalaka thank you! I will try to learn over the years Jan 26, 2022 at 15:46