# Tagged Questions

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### Solving an equation for rational modulus 1

I want to solve an system of equations of the form $$\prod_{i=1}^n x_i^{M_{i,k}}=1 \qquad k=1,\ldots,n$$ with complex $x_i$ with constraint $|x_i|=1$ and $M_{i,k}$ integers. This is basically a ...
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### Why is Mathematica getting this modular root wrong?

First, note that $4^{96}\equiv96\ (mod\ 100)$. Mathematica claims that PowerMod[96, 1/96, 100] has no integer solutions. Even more obviously wrong, I get ...
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### Converting an expression to modular arithmetic automatically

I have the expression $\frac{1}{15} \left(-(-1)^n-5\times 2^{n+2}+3\times 2^{2 n+1}+15\right)$ which I want to calculate mod m for a very large n. My current method is to ask for this exression in ...
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### Polynomial GCD over a ring (with composite characteristic)

I'd like to implement the "Franklin-Reiter Related Message Attack" (see section 4.3 of Boneh's paper). As part of the implementation, I require to compute the GCD of two polynomials over ...
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### Solving for $d$ in $x= E^d mod(n)$

With regards to Public Key Cryptography, I have been tasked with the problem of attacking some information given in an assignment and discovered a private key used to digitally sign a message. Known: ...
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### Solving a system of linear equations modulo n

I have a system of linear equations $$a+b+c \equiv 31 \pmod{54}$$ $$4a+2b+c \equiv 3 \pmod{54}$$ $$9a+3b+c \equiv 11 \pmod{54}$$ What should I input (I'm using ...