# Questions tagged [pohlig-hellman]

In cryptography, Pohlig-Hellman is a symmetric cipher. In number theory, the Pohlig–Hellman algorithm sometimes is a special-purpose algorithm for computing discrete logarithms in a multiplicative group whose order is a smooth integer. The cipher builds upon the number theory algorithm.

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### Are the Baby-step/Giant-step, Pohlig–Hellman, Index Calculs, and NFS algorithms to compute a discrete log modulo n effective with a composite modulus?

I've read different posts about the effectiveness of Baby-step/Giant-step on computing DLP with a composite modulus. This one seems to indicate that Baby-step/Giant-step is for use with a prime ...
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### Parity of the order of a element

Given an element $g$ in a cyclic group $G$ of known order $m$ its easy to test if $m$ has even or odd order. In other words $\textrm{ord}(g) \pmod 2$ can be computed easily. In some cases where the ...
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### Cryptographically Secure Elliptic Curve

What are the properties a cryptographically secure Elliptic Curve must have? I have started to create a list and wanted to know if I forgot some important points, and if it is correct so far: A curve ...
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### Discrete logarithm problem - Pohlig Hellman $GF(2^p)$

I would like to ask how to modify Pohlig Hellman algorithm if I need to work with polynomials $GF(2^{60})$ I know how this algorithm works with numbers, but I am not able to imagine how to do some ...
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### Can Pohlig-Hellman encryption be done over elliptic curves?

Following a bunch of questions on the topic of Pohlig-Hellman encryption. I was wondering if this could be trivially adapted to be done over elliptic curves just like we create EC-DH instead of DH. ...
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### Implementing Pohlig-Hellman Exponentiation chiper

I need to use Pohlig-Hellman exponentiation cipher for reasons explained here. However, I can't seem to find an implementation of this cipher anywhere. It doesn't seem to be too difficult to implement ...
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### Is Pohlig-Hellman Cipher the only option?

I am looking for a cipher which would allow something like this: E(E(M, a), b) = E(M, ab), where a and b are encryption keys, and ab is a combination of the keys that is impractical to separate into a ...
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### Generalised DLPC

Been reading about Pohlig Hellman algo to solve DLP. But can't seem to get an example based on the following: So if modulus, n is composite (i.e. non-prime) and the base is NOT a generator of Zn. ...
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### Discrete logarithm weak group

I'm looking for weak groups in discrete logarithm, that $x$ can be extracted from $Y$ in polynomial time where $Y \equiv g^x \pmod{p}$ . I thought one way is to produce a prime $p$ that $p-1$ is an ...
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### Factors of the group order to secure against Pohlig-Hellman

I am looking into the security of Diffie-Hellman and the discrete log in general. To make sure an attacker can not use Pohlig-Hellman to solve the discrete log quickly we need to make sure that the ...
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