Discrete logarithm wikipedia

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WebMar 24, 2024 · The term "discrete logarithm" is most commonly used in cryptography, although the term "generalized multiplicative order" is sometimes used as well (Schneier 1996, p. 501). In number theory, the term "index" is generally used instead (Gauss 1801; Nagell 1951, p. 112).

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WebMAT 5123. Introduction to Cryptography. (3-0) 3 Credit Hours. Prerequisite: MAT 4213. Congruences and residue class rings, Fermat’s Little Theorem, the Euler phi-function, the Chinese Remainder Theorem, complexity, symmetric-key cryptosystems, cyclic groups, primitive roots, discrete logarithms, one-way functions, public-key cryptosystems ... WebDefinition [ edit] An (imaginary) hyperelliptic curve of genus over a field is given by the equation where is a polynomial of degree not larger than and is a monic polynomial of degree . From this definition it follows that elliptic curves are hyperelliptic curves of genus 1. In hyperelliptic curve cryptography is often a finite field. homeless shelters in cleveland ohio area

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WebIn mathematics, for given real numbers a and b, the logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that bk = a. In number theory, the more commonly used term is index: we can write x = indr a for rx ≡ a if r is a primitive root of m … WebApr 23, 2024 · discrete-logarithm modular-arithmetic group-theory Share Improve this question Follow asked Apr 23, 2024 at 7:32 user58013 Ad 1: you probably want to restrict g to be a group generator. For arbitrary g the claim is clearly not true. Just take, e.g., p = 5 and g = 4. – dkaeae Apr 23, 2024 at 9:22 1 WebDiscrete logarithm From Wikipedia the free encyclopedia In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm log b a is an integer k such that bk = a. hinder band hits

What is discrete logarithm? - Mathematics Stack Exchange

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WebThe discrete logarithm is used to replace the cumbersome multiplication (and raising to an integer power) of the field with more familiar integer arithmetic. Exactly like the old-timers used logarithm tables to replace the error-prone multiplication with the easier addition. WebThe decisional Diffie–Hellman (DDH) assumptionis a computational hardness assumptionabout a certain problem involving discrete logarithmsin cyclic groups. It is used as the basis to prove the security of many cryptographicprotocols, most notably the ElGamaland Cramer–Shoup cryptosystems. Definition[edit] hinder band lips of an angelWebIt is closely related to the discrete logarithm. Wikipedia lists several algorithms that are faster than going through all the powers of ten, which is relevant if you're dealing with very large numbers (hundreds of digits). Share Cite Follow answered Mar 26, 2015 at 5:48 jcsahnwaldt Reinstate Monica 197 1 10 Add a comment 2 homeless shelters in colorado

"WebA discrete logarithm is just the inverse operation. For example, take the equation 3 k ≡12 (mod 23) for k. As shown above k=4 is a solution, but it is not the only solution. Since 3 22 ≡1 (mod 23), it also follows that if n is an integer, then 3 4+22n ≡12×1 n ≡12 (mod 23). " - Discrete logarithm wikipedia

Discrete logarithm wikipedia

algorithms - How hard is finding the discrete logarithm?

Web在整數中，離散對數（英語： Discrete logarithm ）是一種基於同餘運算和原根的一種對數運算。而在實數中對數的定義是指對於給定的和，有一個數，使得。相同地在任何群 G 中可為所有整數定義一個冪數為，而離散對數是指使得的整數。離散對數在一些特殊情況下可以快速計算。然而，通常沒有具非常效率的方法來計算它們。公鑰密碼學中 … WebJul 20, 2011 · More recently, and universally in Computer Science, the k is called the discrete logarithm of a (with respect to the primitive root g ). These "discrete logarithms" have formal properties much like ordinary logarithms. Note in particular that discrete logarithms are exponents, just like ordinary logarithms.

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WebStrong RSA assumption. In cryptography, the strong RSA assumption states that the RSA problem is intractable even when the solver is allowed to choose the public exponent e (for e ≥ 3). More specifically, given a modulus N of unknown factorization, and a ciphertext C, it is infeasible to find any pair ( M , e) such that C ≡ M e mod N . Webwhere denotes the sum over the variable's possible values. The choice of base for , the logarithm, varies for different applications.Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys".An equivalent definition of entropy is the expected value of the self-information …

WebFinding discrete logarithm with baby-step-giant-step algorithm Asked 8 years, 3 months ago Modified 7 years, 9 months ago Viewed 4k times 2 I am trying to use the Baby Step Giant Step algorithm to find discrete logarithm in: a x = B ( mod p) with using BSGS: x = i m + j a j = B a − i m where m = p Wikipedia says: WebAs is the case with the usual logarithm, L(x)/L(g) is, in a sense, the logarithm of x with base g. which is accomplished by (()) =. [further explanation needed] Security. The security of the entire message can be shown to be equivalent to factoring n.

WebApr 11, 2024 · Discrete mathematics is the study of mathematical structures that are countable or otherwise distinct and separable. Examples of structures that are discrete are combinations, graphs, and logical statements. Discrete structures can be finite or infinite. Discrete mathematics is in contrast to continuous mathematics, which deals with … WebThe 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 ⋅ 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.

WebApr 19, 2015 · The simplest discrete logarithm algorithm is exhaustive search: you try 1, 2, 3... as potential logarithm values until one matches (i.e. a.modPow (k, p).equals (x) for successive values of k ). This is highly inefficient, but you cannot have more simple than that. – Thomas Pornin Apr 26, 2011 at 21:50 Add a comment Your Answer Post Your …

WebNov 22, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site homeless shelters in compton californiaWebThe discrete logarithm is just the inverse operation. For example, consider the equation 3k≡ 13 (mod 17) for k. From the example above, one solution is k = 4, but it is not the only solution. Since 316≡ 1 (mod 17)—as follows from Fermat's little theorem—it also follows that if nis an integer then 34+16n≡ 34× (316)n≡ 13 × 1n≡ 13 (mod 17). hinder better than me tabWebIn code below I used help of Wikipedia to implement Pollard's Rho Discrete Logarithm and Elliptic Curve Point Multiplication. Code doesn't depend on any external modules, it uses just few built-in Python modules. There is a possibility to use gmpy2 module if you install it through python -m pip install gmpy2 and uncomment line #import gmpy2 in ... hinder band shirtWebThe discrete logarithm problem is most often formulated as a function problem, mapping tuples of integers to another integer. That formulation of the problem is incompatible with the complexity classes P, BPP, NP, and so forth which people prefer to consider, which concern only decision (yes/no) problems. homeless shelters in clinton county paWeb在整數中，離散對數（英語： Discrete logarithm ）是一種基於同餘運算和原根的一種對數運算。而在實數中對數的定義是指對於給定的和，有一個數，使得 = 。相同地在任何群 G中可為所有整數定義一個冪數為，而離散對數是指使得 = 的整數。離散對數在一些特殊情況下可以快速計算。 homeless shelters in columbus gaWebJun 6, 2024 · The discrete logarithm is an integer x satisfying the equation. a x ≡ b ( mod m) for given integers a , b and m . The discrete logarithm does not always exist, for instance there is no solution to 2 x ≡ 3 ( mod 7) . There is no simple condition to determine if the discrete logarithm exists. homeless shelters in columbus msWebThe ordinary discrete logarithm does not necessarily involve group-theoretic frame.--5.2.200.163 13:07, 11 November 2016 (UTC) You seem to be talking about a third class of logarithm problem, beyond discrete logarithms and the special case of modular logarithms. Can you give a concrete example? hinder better than me lyrics