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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Pohlig-Hellman Algorithm: Adding up the solution via CRT

I have a question about the Pohlig-Hellman Algorithm for the discrete log problem. I understand the concept, but doing the exact calculations I get confused at one point; to illustrate, let's look at ...
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Pohlig-Hellman exponentiation block cipher

Let $G$ be a group of order $n$ and let $e,d$ be integers such that $ed\equiv 1 \pmod{n}$. Then the exponentiation maps $x \mapsto x^e$ and $y \mapsto y^d$ are inverse maps on $G$. These maps give us ...
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How to protect from Silver–Pohlig–Hellman algorithm

I read that Silver–Pohlig–Hellman algorithm solves the discrete logarithm with prime module $p$ in $O(\log^2(p))$ if $p-1$ is a smooth number. This seems pretty fatal for cryptography, since it is a ...
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Security of Pohlig-Hellman exponentation cipher?

I am looking into implementing Pohlig-Hellman exponentation cipher and I would like to know how secure that algorithm is? I am guessing it's security relates greatly to the prime number used in it. ...
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iterated discrete log problem

Consider the following problem: given $g_1 \ldots g_i,h_1 \ldots h_i \in G$, $\forall i$ find $x_i$ such that $g_i^{x_i}=h_i$ For $i=1$ this is the discrete log problem and is assumed to to have ...
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Is there a public key semantically secure cryptosystem for which one can prove in zero knowledge the equivalence of two plaintexts?

If Alice encrypts two messages $a$ and $b$, such that $x=E(a)$, $y=E(b)$. Can Alice prove (without revealing $a$, $b$ or the private key) that $a = b$? Obviously the proof must not be too long and it ...
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What's the main difference between Pohlig-Hellman and RSA?

Both Pohlig-Hellman and RSA perform encryption and decryption by exponentiation modulo some integer ($p$ prime for PH, $n$ composite for RSA). They both use a key $e$ as the exponent to encrypt a ...
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Software implementation of a commutative cipher?

I've got an application (detailed below) that calls for the use of a cipher that is commutative. I've been doing some googling & reading, and there are two algorithms that seem to get mentioned ...
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Applications of Group Ciphers

I've been reading a paper [1], and I've ran across something called a "Group Cipher", which is similar to homomorphic encryption, with an important difference. In homomorphic encryption we have an ...