Linked Questions

10
votes
2answers
2k views

Why is this not a viable key exchange algorithm? [duplicate]

I was just wondering why this kind of algorithm can't be used instead of, say, Diffie-Hellman to exchange keys: Alice decides on a key she wishes to share with Bob. Alice generates a stream of bytes ...
4
votes
5answers
3k views

Why do we use groups, rings and fields in cryptography?

I'm a student of Masters in Cyber Security. I have a habit to understand things from their first principles (at the very beginning). Kindly use any simple mathematical example to answer because I have ...
13
votes
1answer
2k views

Trying to better understand the failure of the Index Calculus for ECDLP

So I'm going to give you guys my understanding and then if you would be so kind as to tell me where I'm off the mark (hopefully I'm not completely wrong). So basically the index calculus for the ...
4
votes
1answer
815 views

Elliptic Curve vs RSA key length comparison

I'm new to ECC. From this website (GlobalSign Elliptic Curve Cryptography) a 256 elliptic curve key pair provides as much security as a 3072 bit RSA key pair. My question is: how do experts come to ...
4
votes
1answer
357 views

Is double encryption really a bad idea? Are meet-in-the-middle attacks practical at all?

Meet-in-the-middle attacks are used to justify that attacks on ECC and double encryption will have complexity of $O(\sqrt{n})$ for ECC and $O(2^{n+1})$ for double encryption complexity instead of $O(n)...
2
votes
3answers
195 views

Can DNA computing to solve elliptic curve algorithms using this method

The authors of this paper: Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over $GF(2^n)$ proposed a novel algorithm based on DNA ...
0
votes
3answers
132 views

What is the discrete logarithm assumption and why it is not easy with Shank's baby-step/giant-step

When I read about the DLP, it seems that the assumption is that it is not generally possible to solve it in polynomial time. But I also read that there are several algorithms in $\mathcal{O}(\sqrt{n})$...
1
vote
1answer
168 views

EL Gamal Attack without a secret key

I have the following data where all the inputs are Big Integers, group size $p$, group generator $g$ public key of the receiver $y$ $c_1$ and $c_2$ Random Number as well I am trying to execute an ...
1
vote
1answer
62 views

By what modulo calculations with discrete logarithms are performed?

For odd prime $p$, I have been given a group $\mathbb{Z}_p^*$ of all invertible elements from $\mathbb{Z}_p$. Basically, $\mathbb{Z}_p^* = \{1,2,\ldots , p-1 \}$. I also have $a$ and $b$, which are ...
0
votes
1answer
78 views

Why is private key chosen to be less than chosen prime in diffie-hellman?

since the public key is calculated as Y=(alpha^private-key)mod(chosen prime) and alpha is a primitive root of prime, when Y becomes public then private key can be calculated easily right? since there ...
0
votes
1answer
95 views

Discrete logarithm with 2 solutions? A clarification request

I need some clarification on the discrete logarithm problem... When a friend and I were solving for the discrete logarithm problem of 9 = 2 ^ x mod 11, we got two ...
3
votes
0answers
90 views

How can the Number Field Sieve attack the discrete log in $\mathbb Z_p^*$ of DSA?

The Digital Signature Algorithm (DSA) uses $L$-bit prime $p$ and $N$-bit prime $q$ with $q| p-1$, i.e., $p = r\cdot q +1$ ( Schnorr group if $r>2$ and safe prime if $r=2$). In a way, the security ...
1
vote
1answer
57 views

Elliptic Curves and Finite Abelian Groups

One can note that, given an elliptic curve mod $p$, that the set of points together with the usual addition law gives a finite Abelian group. Now by the fundamental theorem of finite abelian groups, $$...
0
votes
1answer
57 views

Time complexity of DLP over Elliptic curve group

Consider NIST 192 elliptic curve group https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-186-draft.pdf. What is the time complexity of discrete log problem of it? Is it Pollard $\rho$ ...
1
vote
0answers
71 views

Converting a point in a finite field to its real (x, y) coordinate [closed]

Let curve $A: y^2 = x^3 + 7$ and curve $B: y^2 \equiv x^3 + 7 \pmod{p}$ Curve $B$ is secp256k1, assume the usual parameters for that curve. Let $k$ be any private key, and compute the corresponding ...

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