# Tagged Questions

If two numbers $b$ and $c$ have the property that their difference $b-c$ is integrally divisible by a number $m$ (i.e., $(b-c)/m$ is an integer), then $b$ and $c$ are said to be "congruent modulo $m$."

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### Inverting RSA using an oracle

Say you are given an efficient deterministic algorithm 'I' that can invert the RSA function on 1% of the points in $Z^*_{N}$. That is to say that if y $\in$ $Z^*_{N}$ is a "good" point for 'I', then ...
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### Safe elliptic curve point addition using projective coordinates: How do I tell if the points are the same?

I am trying to implement elliptic curve point addition in hardware for NIST p256 and p384 curves. I have noticed the following issue with the suggested NIST routines: Consider routine 2.2.7 of http://...
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### Crack linear congruential generator knowing every other word in sequence

I need to crack one of the example of linear congruential generator. I have $X_{n+1} = (a \cdot X_n + b) \bmod m$ and I know every other word in the output sequence: ..., 3158, ..., 1888, ..., 1285,...
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### Find a polynomial time algorithm for the following problem

Let $p$ be a prime number and let $c \in \mathbb{Z}_p$ and $e \in (\mathbb{Z}/(p-1))^{\ast}$. Put $c \equiv_p m^e$. Find a polynomial time algorithm that given $p$, $e$, and $c$ will compute $m$. I ...
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### Significance of 3mod4 in squares and square roots mod n?

Why do most literature while discussing squares or square root modulo a prime P, consider P to be congruent to 3 mod 4?
I am trying to solve congruences of the form $$J_A \cdot a^e\equiv 1 \pmod n$$ where $n=pq$ for $p,q$ prime and $\gcd(e,\varphi(n))=\gcd(J_A,n)=1$ Solve for $a\in \mathbb{Z}$, in terms of $n,J_A$ ...