# Tagged Questions

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### Does Zhang's result on primes makes RSA weaker?

I read from Finnish newspaper ( http://www.uusisuomi.fi/tiede-ja-ymparisto/72212-matemaattinen-ongelma-eli-2-300-vuotta-mies-subway-tiskin-takaa-ratkaisi#.VBwhYp09F2k.facebook ) the article of Zhang's ...
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### Finding a point on an elliptic curve

I have an elliptic curve with the equation $y^2 = x^3 + ax + b$ in modulo p, where p is prime. I also have a point G on that curve. How can I find another point that isn't a multiple of G? I ...
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### Affine cipher and shift cipher

I have the following question: $$An\;affine\;cipher\;with\;key\;K(0,b)\;is\;equivalent\;to\;a\;shift\;cipher\;explain\;why$$ I don't think this is true, and assume it is a typo, $K(1,b)$ I would ...
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### How do I compute Euler phi function efficiently for repeated prime factors?

In RSA decryption problems, you have to compute $\phi(n)$ and then sometimes $\phi(\phi(n))$ quickly. For example, I had to compute $\phi(2^5)$ for one particular problem and it seems to me (for ...
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### Determining if a number is an nth root

I am working on a proof that depends on if an adversary can determine if a number is an $nth$ power for some large prime $p$. My intuition tells me that for a sufficiently large value of $n$ this is ...
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### Confused about discrete logarithm question

For purposes of explaining the notation for those unfamiliar, if we fix a prime $q$, as well as $a,b$ nonzero integers $\mod{q}$, $L_a(b) = x$ is the solution to the equation $b = a^x \mod{p}$ We are ...
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### Figuring out RSA Encryption from 1 encrypted and decrypted message

Suppose that you have an encrypted message and a decrypted message (just one). M (the public key) and k (the exponent you raise each number to) are public. Does having one copy both version of a ...
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### How large do my $2$ primes need to be to “guarantee” a longevity of security for my RSA-encrypted plaintext?

I am currently attempting to learn RSA. Most of the literature I am using is at least a few years old, if not older. Given the advancements in computing and improvements in attacking RSA, I am wanting ...
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### Inverse Totient Function, given $n$ find all possible is for $\phi(i)=n$

I am trying to figure out easy understandable approach to given small number of $n$, list all possible is with proof, I read this paper but it is really beyond my level to fathom, attempt for ...
If $x \equiv 23 \bmod 317$ and $x \equiv 25 \bmod 331$, what is $x \bmod 104927$? What techniques are typically used to solve problems of this nature? It doesn't seem clear to me that it can be solved ...