What is discrete logarithm? - Mathematics Stack Exchange
Dec 11, 2021 · The discrete Logarithm is just reversing this question, just like we did with real numbers - but this time, with objects that aren't necessarily numbers. For example, if ${a\cdot a = a^2 = b}$, then we can say for example ${\log_{a}(b)=2}$. The "discrete" simply refers to the fact we have finite objects, that can only take on certain fixed values.
What is the difference between discrete logarithm and natural …
The simplified idea of the discrete logarithm is to return only the Integers ($\mathbb{Z}$). In $\mathbb{R}$, we have $\log_2 5 = 2.321\ldots$. This is not interesting for us.
Best Known Attacks on Discrete Logarithm in Generic Groups
May 26, 2023 · The above statement also applies to the Elliptic Curve Discrete Logarithm problem, for curves with no known shortcuts/weaknesses. Actually, it is a good demonstration of the above points; for even characteristic curves (which allow for a cheap canonicalization), Van Oorschot is probably better - for large characteristic curves (which don't have ...
Why was the term "discrete" used in discrete logarithm?
Apr 15, 2019 · This is not a question of what is a discrete logarithm or why the discrete logarithm problem is an "intractable problem" given certain circumstances. I'm just trying to determine if there's some additional meaning to the term "discrete" as it's used in name discrete logarithm? The definition of "discrete" is "individually separate and distinct".
Why is the discrete logarithm problem assumed to be hard?
Jan 12, 2014 · This might be a quite stupid question: since a naive brute force algorithm to solve the discrete logarithm problem will only take O(n) time for a group G with order n, why is it assumed to be hard to
group theory - Primitive root and discrete logarithm
Jul 20, 2011 · See André's answer about the basics of the discrete logarithm. We have a (cyclic) group (the multiplicative group modulo a big prime is the original case, but other groups are possible, too), in which we can multiply, and thus also have exponentation with integer numbers (using the square-and-multiply method, for example).
number theory - How robust is discrete logarithm in $GF(2^n ...
"Normal" discrete logarithm based cryptosystems (DSA, Diffie-Hellman, ElGamal) work in the finite field of ...
diffie hellman - Discrete Logarithm: What does it mean to find the ...
Dec 6, 2019 · Pollard's rho for discrete logarithm. The space complexity of baby-step/giant-step can be reduced down to the point of becoming a non-issue, by using collision search rather than a table. See wikipedia's Pollard's rho for the discrete logarithm. The time complexity remains similar to that in baby-step/giant-step.
Discrete Logarithm Problem - Mathematics Stack Exchange
Jan 30, 2015 · Question: Discrete Logarithm Problem: Let $g$ be a primitive root for $F_{p}$. Suppose that $x = a$ and $x = b$ are both integer solutions to the congruence $g^{x ...
group theory - Why is the discrete logarithm problem hard ...
Apr 2, 2022 · We do have some partial proofs, for example, that in the "black-box" model, a discrete log on a prime-order group is hard. On the other hand, the assumptions that makes is known to be false for finite-fields, and so that's less useful than one would hope.