# Linked Questions

2answers
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### 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 ...
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 ...
1answer
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### 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 ...
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 ...
1answer
357 views

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 $O(n)... 3answers 195 views ### Can DNA computing to solve elliptic curve algorithms using this method The authors of this paper: Fast Parallel Molecular Algorithms for DNA-Based Computation: Solving the Elliptic Curve Discrete Logarithm Problem over$GF(2^n)$proposed a novel algorithm based on DNA ... 3answers 132 views ### What is the discrete logarithm assumption and why it is not easy with Shank's baby-step/giant-step When I read about the DLP, it seems that the assumption is that it is not generally possible to solve it in polynomial time. But I also read that there are several algorithms in$\mathcal{O}(\sqrt{n})$... 1answer 168 views ### EL Gamal Attack without a secret key I have the following data where all the inputs are Big Integers, group size$p$, group generator$g$public key of the receiver$yc_1$and$c_2$Random Number as well I am trying to execute an ... 1answer 62 views ### By what modulo calculations with discrete logarithms are performed? For odd prime$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$, which are ... 1answer 78 views ### Why is private key chosen to be less than chosen prime in diffie-hellman? since the public key is calculated as Y=(alpha^private-key)mod(chosen prime) and alpha is a primitive root of prime, when Y becomes public then private key can be calculated easily right? since there ... 1answer 95 views ### Discrete logarithm with 2 solutions? A clarification request I need some clarification on the discrete logarithm problem... When a friend and I were solving for the discrete logarithm problem of 9 = 2 ^ x mod 11, we got two ... 0answers 90 views ### How can the Number Field Sieve attack the discrete log in$\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$). In a way, the security ... 1answer 57 views ### Elliptic Curves and Finite Abelian Groups One can note that, given an elliptic curve mod$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,$$... 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$\rho$... 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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