# Tagged Questions

In cryptography, a discrete logarithm is the number of times a generator of a group must be multiplied by itself to produce a known number. By choosing certain groups, the task of finding a discrete logarithm can be made intractable.

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### What does Shor's algorithm tell us about the complexity class of RSA and the DLP?

If quantum computers operate in BQP and (using Shor's algorithm) they are able to factor large integers and break the discrete log problem, what does that tell us about the complexity class of these ...
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### Is it possible to determine or estimate the period for Blum-Micali PRG?

The Blum-Micali is a cryptographically secure pseudorandom number generator. The construction (from wikipedia): Let $p$ be an odd prime, and let $g$ be a primitive root modulo $p$. Let $x_0$ be a ...
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### Are analog quantum computers a threat to RSA and DLP?

We already know that D-WAVE's "quantum computers" can't really run the Shor's algorithm, because the way they're built doesn't qualify them as universal quantum computers. Now researchers actually ...
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### Fixed primes in discrete logarithm

The discrete logarithm problem is to find $z$ when the inputs are $g,h,p$ where $g^z\bmod p$. Supposing if you fix $p$ then does the problem become any easier to attacks and is there a $(\log p)^c$ ...
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### Using Shor's algorithm to solve the discrete logarithm problem

I have read about Shor's algorithm and my understanding is that it can be used to factor large numbers efficiently. Can Shor's algorithm, though, be used to solve this problem: Find the number $e$ ...
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### How robust is discrete logarithm in $GF(2^n)$?

"Normal" discrete logarithm based cryptosystems (DSA, Diffie-Hellman, ElGamal) work in the finite field of integers modulo a big prime $p$. However, there exist other finite fields out there, in ...
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### Are there security issues with discrete logarithm keys not being uniformly distributed?

Generally, algorithms based on discrete logarithm specify that private keys are chosen as scalars between 1 and the order of the group (denoted $q$ here). For instance IEEE P1363 and FIPS 186-3 both ...
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### How does the Number Field Sieve find the target number for Diffie-Hellman?

I have read some papers relating to the Number Field Sieve, but I could not figure out how this algorithm helps in Logjam, or even what is meant by the number field. What is this? What is meant by ...
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### Why $p-1$ needs large factors in discrete logarithm?

In discrete logarithm over cyclic group $\Bbb Z_p$ where $p$ is a prime or $p=q^n$ a prime power it is desired that $p-1$ needs to have large factors except for $2$. What is the consequence even if ...
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### Are there asymmetric cryptographic algorithms that are not based on integer factorization and discrete logarithm?

In the computer security class (in which cryptography is a big chapter) that I took, I remembered the professor said about current asymmetric cryptography algorithms are based on integer factorization ...
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### How to calculate the exponent in modular exponentiation?

I have a problem when calculating power in modular, $a^b \bmod c = d$. where we can know values of $a$, $c$ and d, but we don't know values of $b$. example : $29^b \bmod 1024 = 365$. So, how can I ...
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### The difficulty of computing discrete logs

I understand that in Diffie-Hellman it should be hard to compute $a$ given $g$ and $g^a$. In computational Diffie-Hellman, it appears to be hard to compute $(g^{ab})$ from $g^a$ and $g^b$. As for ...
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### Zero knowledge-proof for discrete log that is not honest-verifier

Take a cyclic group of prime order. The Schnorr-protocol for proving knowledge of the discrete logarithm of some group element is honest-verifier zero-knowledge, meaning that if the verifier chooses ...
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### Sigma protocol: witness hiding

I am working on an assignment and I am stuck with the last part of proving witness hiding for the protocol. I have previously proved it is witness indistinguishable, and it has q (primer number ...
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### Why is “multiplying” $g^x$ and $g^y$ not possible?

The computational Diffie-Hellman problem states that for a cyclic group $G$ of order $p$ and a generator $g$, it is hard to find the value $g^{xy}$ given only $g^x$ and $g^y$ (but easy if either $x$ ...
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### How secure is this logarithmic encryption algorithm?

How secure would the following logarithmic encryption algorithm be when tested under the same conditions as high end encryption algorithms (AES, RSA etc...). Note: For smaller text the text will be ...
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### Calculating the discrete logarithm

I'm given a prime number $p = 1217$ I'm also given the following equations:  40 \equiv \log2 \pmod{64} \\ 63 \equiv \log3 \pmod{64} \\ 13 \equiv \log5 \pmod{64} \\ 13 \equiv \log2 \pmod{19} \\ 10 \...
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### Software timing attack using Kocher method

What's the minimum number of random sample points needed in Kocher's timing attack, so that we can determine enough valid measurements of $A_{i,r}$ and $D_{i,r}$? I'm working from this paper: Volker ...
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### Is the Discrete logarithm problem suitable for this pairing scheme?

Let $Ans$ be the product of two pairings : $e(g,h)^{k} \times e(g,h)^{r}=Ans$ If everybody knows only $[g,h,e(g,h)^{k}]$ but $[r,Ans]$ is not known. In the discrete logarithm problem, the user knows ...
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### Discrete logarithm problem is easy in a cyclic group of order a power of two

Let $G=\langle g\rangle$ be a cyclic group of order $2^{k}$ and let $h\in G$. I have read that it is easy to find $\log _{g} h$, but I haven't been able to figure out how. Do you know why this can be ...
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### How to prove knowledge of discrete logarithm in a product?

Definitions Suppose I have two large safe primes $p$ and $q$, and a composite number $N=pq$. I have $G$, a large cyclic subgroup of $\mathbb{Z}^{*}_{N}$; $g$ and $h$ are generators of $G$. I commit ...
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### Discrete Logarithm problem with inverse

Let $\mathbb G$ be a cyclic group of order $q$. The Discrete Logarithm Problem (DLP) is, given $g, g^x \in \mathbb G$, to compute $x \in \mathbb Z_q$. I'm interested to know if there is a known ...
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### State level “Weak Diffie-Hellman” working for SRP too?

I've read about the "Weak Diffie-Hellman" attack (paper, website), where a resourceful entity like a state can pre-compute values for known primes to aid solving the discrete logarithm problem for ...
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### Reuse of a DH / ECDH public key

I was wondering whether it is safe to use the same DH or ECDH key pair in more than one key agreement, particularly if these public keys are in a public registry. These public keys could be used by ...
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### Perfect zero knowledge for the Schnorr protocol?

Can somebody explain (or point to a reference) why the Schnorr protocol cannot be proved zero knowledge?
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### Is it possible to generate backdoored DH parameters?

I know it has been already asked and answered whether it's possible to generate weak DH parameters. But "recentely" we experienced the Logjam attack, which makes use of the pre-computation ...
Having a large set of ECC public keys $P_i = n_iB$ on a fixed curve $E$ over a prime field, is there a way to determine if coefficients $n_i$ were generated using a bad PRNG? In other words, can a ...
Assuming a randomize encoding scheme that takes as input a secret key $\mathsf{sk} \in \mathbb{Z}_p$ for a large prime number $p$. Then the algorithm outputs $g^{\mathsf{sk}x}, x \in \mathbb{Z}_p^*$. ...