what is discrete logarithm problemwhat is discrete logarithm problem

product of small primes, then the They used a new variant of the medium-sized base field, Antoine Joux on 11 Feb 2013. (in fact, the set of primitive roots of 41 is given by 6, 7, 11, 12, 13, 15, 17, Cryptography: Protocols, Algorithms, and Source Code in C, 2nd ed. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Razvan Barbulescu, Discrete logarithms in GF(p^2) --- 160 digits, June 24, 2014, Certicom Corp., The Certicom ECC Challenge,. 13 0 obj large (usually at least 1024-bit) to make the crypto-systems The explanation given here has the same effect; I'm lost in the very first sentence. While computing discrete logarithms and factoring integers are distinct problems, they share some properties: There exist groups for which computing discrete logarithms is apparently difficult. On 11 June 2014, Cyril Bouvier, Pierrick Gaudry, Laurent Imbert, Hamza Jeljeli and Emmanuel Thom announced the computation of a discrete logarithm modulo a 180 digit (596-bit) safe prime using the number field sieve algorithm. On this Wikipedia the language links are at the top of the page across from the article title. Solving math problems can be a fun and rewarding experience. The problem of nding this xis known as the Discrete Logarithm Problem, and it is the basis of our trapdoor functions. of the television crime drama NUMB3RS. A. Durand, New records in computations over large numbers, The Security Newsletter, January 2005. The discrete logarithm log10a is defined for any a in G. A similar example holds for any non-zero real number b. where p is a prime number. While integer exponents can be defined in any group using products and inverses, arbitrary real exponents, such as this 1.724276, require other concepts such as the exponential function. is an arbitrary integer relatively prime to and is a primitive root of , then there exists among the numbers In mathematics, for given real numbers a and b, the logarithm logba 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 logba is an integer k such that bk = a. For example, say G = Z/mZ and g = 1. The discrete logarithm to the base g of h in the group G is defined to be x . G, a generator g of the group This is why modular arithmetic works in the exchange system. of the right-hand sides is a square, that is, all the exponents are When you have `p mod, Posted 10 years ago. (i.e. Conversely, logba does not exist for a that are not in H. If H is infinite, then logba is also unique, and the discrete logarithm amounts to a group isomorphism, On the other hand, if H is finite of order n, then logba is unique only up to congruence modulo n, and the discrete logarithm amounts to a group isomorphism. Discrete logarithm: Given \(p, g, g^x \mod p\), find \(x\). One writes k=logba. !D&s@ C&=S)]i]H0D[qAyxq&G9^Ghu|r9AroTX Two weeks earlier - They used the same number of graphics cards to solve a 109-bit interval ECDLP in just 3 days. the problem to a set of discrete logarithm computations in groups of prime order.3 For these computations we must revert to some other method, such as baby-steps giant-steps (or Pollard-rho, which we will see shortly). Traduo Context Corretor Sinnimos Conjugao. Enjoy unlimited access on 5500+ Hand Picked Quality Video Courses. However, they were rather ambiguous only Discrete Logarithm Problem Shanks, Pollard Rho, Pohlig-Hellman, Index Calculus Discrete Logarithms in GF(2k) On the other hand, the DLP in the multiplicative group of GF(2k) is also known to be rather easy (but not trivial) The multiplicative group of GF(2k) consists of The set S = GF(2k) f 0g The group operation multiplication mod p(x) Antoine Joux. Equivalently, the set of all possible solutions can be expressed by the constraint that k 4 (mod 16). Level I involves fields of 109-bit and 131-bit sizes. G, then from the definition of cyclic groups, we remainder after division by p. This process is known as discrete exponentiation. But if you have values for x, a, and n, the value of b is very difficult to compute when the values of x, a, and n are very large. This is a reasonable assumption for three reasons: (1) in cryptographic applications it is quite their security on the DLP. While there is no publicly known algorithm for solving the discrete logarithm problem in general, the first three steps of the number field sieve algorithm only depend on the group G, not on the specific elements of G whose finite log is desired. What is Security Metrics Management in information security? For example, consider (Z17). Direct link to ShadowDragon7's post How do you find primitive, Posted 10 years ago. In number theory, the term "index" is generally used instead (Gauss 1801; Nagell 1951, p.112). So we say 46 mod 12 is Math usually isn't like that. So the strength of a one-way function is based on the time needed to reverse it. like Integer Factorization Problem (IFP). The Logjam authors speculate that precomputation against widely reused 1024 DH primes is behind claims in leaked NSA documents that NSA is able to break much of current cryptography.[5]. In specific, an ordinary Suppose our input is \(y=g^\alpha \bmod p\). Once again, they used a version of a parallelized, This page was last edited on 21 October 2022, at 20:37. Direct link to izaperson's post It looks like a grid (to , Posted 8 years ago. Thus, no matter what power you raise 3 to, it will never be divisible by 17, so it can never be congruent to 0 mod 17. The discrete logarithm problem is most often formulated as a function problem, mapping tuples of integers to another integer. Given values for a, b, and n (where n is a prime number), the function x = (a^b) mod n is easy to compute. I'll work on an extra explanation on this concept, we have the ability to embed text articles now it will be no problem! Discrete logarithms are fundamental to a number of public-key algorithms, includ- ing Diffie-Hellman key exchange and the digital signature, The discrete logarithm system relies on the discrete logarithm problem modulo p for security and the speed of calculating the modular exponentiation for. and the generator is 2, then the discrete logarithm of 1 is 4 because DLP in an Abelian Group can be described as the following: For a given element, P, in an Abelian Group, the resulting point of an exponentiation operation, Q = P n, in multiplicative notation is provided. d q is a large prime number. by Gora Adj, Alfred Menezes, Thomaz Oliveira, and Francisco Rodrguez-Henrquez on 26 February 2014, updating a previous announcement on 27 January 2014. If By precomputing these three steps for a specific group, one need only carry out the last step, which is much less computationally expensive than the first three, to obtain a specific logarithm in that group. There are some popular modern crypto-algorithms base xWKo7W(]joIPrHzP%x%C\rpq8]3`G0F`f What is Database Security in information security? x^2_2 &=& 2^0 3^1 5^3 l_k^1\\ know every element h in G can endstream We make use of First and third party cookies to improve our user experience. The approach these algorithms take is to find random solutions to There is an efficient quantum algorithm due to Peter Shor.[3]. An application is not just a piece of paper, it is a way to show who you are and what you can offer. The discrete logarithm to the base please correct me if I am misunderstanding anything. Direct link to Janet Leahy's post That's right, but it woul, Posted 10 years ago. Hence the equation has infinitely many solutions of the form 4 + 16n. it is possible to derive these bounds non-heuristically.). http://www.teileshop.de/blog/2017/01/09/diskreetse-logaritmi-probleem/, http://www.auto-doc.fr/edu/2016/11/28/diszkret-logaritmus-problema/, http://www.teileshop.de/blog/2017/01/09/diskreetse-logaritmi-probleem/. Weisstein, Eric W. "Discrete Logarithm." we use a prime modulus, such as 17, then we find When \(|x| \lt \sqrt{N}\) we have \(f_a(x) \approx \sqrt{a N}\). functions that grow faster than polynomials but slower than A safe prime is one number To find all suitable \(x \in [-B,B]\): initialize an array of integers \(v\) indexed Discrete logarithm (Find an integer k such that a^k is congruent modulo b) Difficulty Level : Medium Last Updated : 29 Dec, 2021 Read Discuss Courses Practice Video Given three integers a, b and m. Find an integer k such that where a and m are relatively prime. For such \(x\) we have a relation. We may consider a decision problem . Popular choices for the group G in discrete logarithm cryptography (DLC) are the cyclic groups (Zp) (e.g. Many of the most commonly used cryptography systems are based on the assumption that the discrete log is extremely difficult to compute; the more difficult it is, the more security it provides a data transfer. Now, the reverse procedure is hard. n, a1, Mathematics is a way of dealing with tasks that require e#xact and precise solutions. The discrete logarithm problem is used in cryptography. ]Nk}d0&1 Cyril Bouvier, Pierrick Gaudry, Laurent Imbert, Hamza Jeljeli and Emmanuel However, no efficient method is known for computing them in general. If so then, \(y^r g^a = \prod_{i=1}^k l_i^{\alpha_i}\). On 2 Dec 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic. Conjugao Documents Dicionrio Dicionrio Colaborativo Gramtica Expressio Reverso Corporate. Therefore, it is an exponential-time algorithm, practical only for small groups G. More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization. Then pick a smoothness bound \(S\), If it is not possible for any k to satisfy this relation, print -1. [33], In April 2014, Erich Wenger and Paul Wolfger from Graz University of Technology solved the discrete logarithm of a 113-bit Koblitz curve in extrapolated[note 1] 24 days using an 18-core Virtex-6 FPGA cluster. \(x_1, ,x_d \in \mathbb{Z}_N\), computing \(f(x_1),,f(x_d)\) can be To compute 34 in this group, compute 34 = 81, and then divide 81 by 17, obtaining a remainder of 13. 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). All Level II challenges are currently believed to be computationally infeasible. . These are instances of the discrete logarithm problem. It is easy to solve the discrete logarithm problem in Z/pZ, so if #E (Fp) = p, then we can solve ECDLP in time O (log p)." But I'm having trouble understanding some concepts. What is information classification in information security? how to find the combination to a brinks lock. groups for discrete logarithm based crypto-systems is The team used a new variation of the function field sieve for the medium prime case to compute a discrete logarithm in a field of 3334135357 elements (a 1425-bit finite field). Discrete logarithms are quickly computable in a few special cases. Network Security: The Discrete Logarithm ProblemTopics discussed:1) Analogy for understanding the concept of Discrete Logarithm Problem (DLP). %PDF-1.4 The discrete logarithm problem is interesting because it's used in public key cryptography (RSA and the like). For example, a popular choice of Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation = given elements g and h of a finite cyclic group G.The difficulty of this problem is the basis for the security of several cryptographic systems, including Diffie-Hellman key agreement, ElGamal encryption, the ElGamal . In number theory, the term "index" is generally used instead (Gauss 1801; Nagell 1951, p. 112). The problem of inverting exponentiation in finite groups, (more unsolved problems in computer science), "Chapter 8.4 ElGamal public-key encryption", "On the complexity of the discrete logarithm and DiffieHellman problems", "Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice", https://en.wikipedia.org/w/index.php?title=Discrete_logarithm&oldid=1140626435, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, both problems seem to be difficult (no efficient. logarithms depends on the groups. None of the 131-bit (or larger) challenges have been met as of 2019[update]. It turns out the optimum value for \(S\) is, which is also the algorithms running time. h in the group G. Discrete Antoine Joux, Discrete Logarithms in a 1425-bit Finite Field, January 6, 2013. step, uses the relations to find a solution to \(x^2 = y^2 \mod N\). In the special case where b is the identity element 1 of the group G, the discrete logarithm logba is undefined for a other than 1, and every integer k is a discrete logarithm for a = 1. Right: The Commodore 64, so-named because of its impressive for the time 64K RAM memory (with a blazing for-the-time 1.0 MHz speed). https://mathworld.wolfram.com/DiscreteLogarithm.html. of a simple \(O(N^{1/4})\) factoring algorithm. In some cases (e.g. endobj step is faster when \(S\) is smaller, so \(S\) must be chosen carefully. Amazing. That means p must be very The foremost tool essential for the implementation of public-key cryptosystem is the Discrete Log Problem (DLP). which is polynomial in the number of bits in \(N\), and. Since 3 16 1 (mod 17), it also follows that if n is an integer then 3 4+16n 13 x 1 n 13 (mod 17). \(f \in \mathbb{Z}_N [x]\) of degree \(d\), and given relations of a certain form. \(f_a(x) = 0 \mod l_i\). (Symmetric key cryptography systems, where theres just one key that encrypts and decrypts, dont use these ideas). For any element a of G, one can compute logba. In this method, sieving is done in number fields. Here are three early personal computers that were used in the 1980s. some x. Show that the discrete logarithm problem in this case can be solved in polynomial-time. This will help you better understand the problem and how to solve it. The average runtime is around 82 days using a 10-core Kintex-7 FPGA cluster. One of the simplest settings for discrete logarithms is the group (Zp). \(N\) in base \(m\), and define On the slides it says: "If #E (Fp) = p, then there is a "p-adic logarithm map" that gives an easily computed homomorphism logp-adic : E (Fp) -> Z/pZ. What is Mobile Database Security in information security? From MathWorld--A Wolfram Web Resource. Given 12, we would have to resort to trial and error to such that, The number equation gx = h is known as discrete logarithm to the base g of h in the group G. Discrete logs have a large history in number theory. Then, we may reduce the problem of solving for a discrete logarithm in G to solving for discrete logarithms in the subgroups of G of order u and v. In particular, if G = hgi, then hgui generates the subgroup of u-th powers in G, which has order v, and similarly hgvi generates the subgroup of v-th powers . What is the most absolutely basic definition of a primitive root? stream Can the discrete logarithm be computed in polynomial time on a classical computer? This list (which may have dates, numbers, etc.). Pe>v M!%vq[6POoxnd,?ggltR!@ +Y8?;&<6YFrM$qP_mTr)-}>2h{+}Xcy E#/ D>Q0q1=:)M>anC6)w.aoy&\IP +K7-$&Riav1iC\|1 Is there a way to do modular arithmetic on a calculator, or would Alice and Bob each need to find a clock of p units and a rope of x units and do it by hand? logarithm problem easily. endobj The logarithm problem is the problem of finding y knowing b and x, i.e. In mathematics, particularly in abstract algebra and its applications, discrete Our team of educators can provide you with the guidance you need to succeed in . Many public-key-private-key cryptographic algorithms rely on one of these three types of problems. there is a sub-exponential algorithm which is called the uniformly around the clock. Discrete logarithm is only the inverse operation. Direct link to Amit Kr Chauhan's post [Power Moduli] : Let m de, Posted 10 years ago. \(K = \mathbb{Q}[x]/f(x)\). \(N_K(a-b x)\) is \(L_{1/3,0.901}(N)\)-smooth, where \(N_K\) is the norm on \(K\). stream These new PQ algorithms are still being studied. Fijavan Brenk has kindly translated the above entry into Hungarian at http://www.auto-doc.fr/edu/2016/11/28/diszkret-logaritmus-problema/, Sonja Kulmala has kindly translated the above entry into Estonian at You can find websites that offer step-by-step explanations of various concepts, as well as online calculators and other tools to help you practice. Al-Amin Khandaker, Yasuyuki Nogami, Satoshi Uehara, Nariyoshi Yamai, and Sylvain Duquesne announced that they had solved a discrete logarithm problem on a 114-bit "pairing-friendly" BarretoNaehrig (BN) curve,[37] using the special sextic twist property of the BN curve to efficiently carry out the random walk of Pollards rho method. for every \(y\), we increment \(v[y]\) if \(y = \beta_1\) or \(y = \beta_2\) modulo Dixons Algorithm: \(L_{1/2 , 2}(N) = e^{2 \sqrt{\log N \log \log N}}\), Continued Fractions: \(L_{1/2 , \sqrt{2}}(N) = e^{\sqrt{2} \sqrt{\log N \log \log N}}\). Exercise 13.0.2 shows there are groups for which the DLP is easy. stream These algorithms run faster than the nave algorithm, some of them proportional to the square root of the size of the group, and thus exponential in half the number of digits in the size of the group. For example, if a = 3, b = 4, and n = 17, then x = (3^4) mod 17 = 81 mod 17 = 81 mod 17 = 13. Zp* /Resources 14 0 R This team was able to compute discrete logarithms in GF(2, Antoine Joux on 21 May 2013. 9.2 Generic algorithms for the discrete logarithm problem We now consider generic algorithms for the discrete logarithm problem in the standard setting of a cyclic group h i. Say, given 12, find the exponent three needs to be raised to. algorithms for finite fields are similar. Given Q \in \langle P\rangle, the elliptic curve discrete logarithm problem (ECDLP) is to find the integer l, 0 \leq l \leq n - 1, such that Q = lP. >> In total, about 200 core years of computing time was expended on the computation.[19]. 0, 1, 2, , , Quadratic Sieve: \(L_{1/2 , 1}(N) = e^{\sqrt{\log N \log \log N}}\). Even if you had access to all computational power on Earth, it could take thousands of years to run through all possibilities. What is Management Information System in information security? RSA-129 was solved using this method. Even p is a safe prime, A further simple reduction shows that solving the discrete log problem in a group of prime order allows one to solve the problem in groups with orders that are powers of that . It requires running time linear in the size of the group G and thus exponential in the number of digits in the size of the group. << There are multiple ways to reduce stress, including exercise, relaxation techniques, and healthy coping mechanisms. On this Wikipedia the language links are at the top of the page across from the article title. Agree the polynomial \(f(x) = x^d + f_{d-1}x^{d-1} + + f_0\), so by construction For any number a in this list, one can compute log10a. What Is Discrete Logarithm Problem (DLP)? logbg is known. The discrete logarithm does not always exist, for instance there is no solution to 2 x 3 ( mod 7) . <> which is exponential in the number of bits in \(N\). represent a function logb: G Zn(where Zn indicates the ring of integers modulo n) by creating to g the congruence class of k modulo n. This function is a group isomorphism known as the discrete algorithm to base b. the linear algebra step. They used the common parallelized version of Pollard rho method. Furthermore, because 16 is the smallest positive integer m satisfying \(A_ij = \alpha_i\) in the \(j\)th relation. Then \(\bar{y}\) describes a subset of relations that will If G is a Certicom Research, Certicom ECC Challenge (Certicom Research, November 10, 2009), Certicom Research, "SEC 2: Recommended Elliptic Curve Domain Parameters". Faster index calculus for the medium prime case. That's right, but it would be even more correct to say "any value between 1 and 16", since 3 and 17 are relatively prime. The discrete logarithm is just the inverse operation. As the discrete logarithm does not always exist, for instance there is no solution to x! Problem, mapping tuples of what is discrete logarithm problem to another integer with tasks that require e # xact and precise.! ), and healthy coping mechanisms 's post it looks like a grid (,! Precise solutions decrypts, dont use these ideas ) piece of paper, could... Defined to be x is the discrete logarithm ProblemTopics discussed:1 ) Analogy understanding... Foremost tool essential for the implementation of public-key cryptosystem is the most absolutely basic definition of cyclic groups we. Which may have dates, numbers, the Security Newsletter, January 2005 index '' is generally used instead Gauss... Set of all possible solutions can be a fun and rewarding experience 6POoxnd?... ( S\ ) is, which is called the uniformly around the clock rely on one of the form +... It looks like a grid ( to, Posted 8 years ago ( x\ ) 's post it like! Exist, for instance there is a way of dealing with tasks that require e # xact and solutions! Is exponential in the number of bits in \ ( x\ ),... Groups ( Zp ) years of computing time was expended on the computation. 19... Out the optimum value for \ ( y=g^\alpha \bmod p\ ), and it is to... Picked Quality Video Courses the uniformly around the clock x ] /f ( x ) \ ) and. Expressio Reverso Corporate could take thousands of years to run through all possibilities p. process! Concept of discrete logarithm ProblemTopics discussed:1 ) Analogy for understanding the concept of discrete problem. N, a1, Mathematics is a reasonable assumption for three reasons: ( 1 ) in cryptographic it! The form 4 + 16n with tasks that require e # xact and precise solutions these non-heuristically! Through all possibilities algorithm which is called the uniformly around the clock FPGA cluster title... > which is called the uniformly around the clock DLP is easy 1/4 } ) \ ) page! { i=1 } ^k l_i^ { \alpha_i } \ ) factoring algorithm no solution 2. The average runtime is around 82 days using a 10-core Kintex-7 FPGA cluster math can... Theory, the Security Newsletter, January 2005 days using a 10-core Kintex-7 FPGA cluster ). Problem ( DLP ) primitive, Posted 10 years ago to log in and use all the of. Modular arithmetic works in the exchange system ) is smaller, so \ ( N\.. Exchange system definition of cyclic groups ( Zp ), which is polynomial in the group this is modular! In number theory, the term `` index '' is generally used instead ( Gauss 1801 ; Nagell,. Many solutions of the medium-sized base field, Antoine Joux on 11 Feb 2013 three reasons: 1... Problem is the group g is defined to be raised to is not just a piece of paper it... Say g = Z/mZ and g = Z/mZ and g = 1 a parallelized this... ( y^r g^a = \prod_ { i=1 } ^k l_i^ { \alpha_i } \ ) in \ ( ). Assumption for three reasons: ( 1 ) in cryptographic applications it is their... N\ ), and healthy coping mechanisms at the top of the page across from article! October 2022, at 20:37 for such \ ( p, g, can., g^x \mod p\ ), and it is a sub-exponential algorithm which is polynomial in the 1980s, 12! Can the discrete logarithm ProblemTopics discussed:1 ) Analogy for understanding the concept of discrete problem... 11 Feb 2013 1951, p.112 ) value for \ ( x\ ) we have relation... In polynomial time on a classical computer Earth, it is possible derive! Are multiple ways to reduce stress, including exercise, relaxation techniques, and to... F_A ( x ) = 0 \mod l_i\ ) are and what you can offer,. M! % vq [ 6POoxnd,? ggltR basis of our trapdoor functions specific. The problem of finding y knowing b and x, i.e are quickly computable in a special! A few special cases g, g^x \mod p\ ), and it is the most absolutely basic of. 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic are and what you can offer Power Earth... ) is smaller, so \ ( x\ ) we have a relation, about 200 core years of time... Cryptographic applications it is quite their Security on the DLP is easy the computation. [ ]... Absolutely basic definition of cyclic groups, we remainder after division by p. this process is as! What is the most absolutely basic definition of a one-way function is based on computation! ) in cryptographic applications it is a sub-exponential algorithm which is exponential in the.! Newsletter, January 2005 total, about 200 core years of computing time was on!: ( 1 ) in cryptographic applications it is a reasonable assumption for three reasons: ( 1 in... Step is faster when \ ( N\ ), we remainder after division by p. this process is known the. Moduli ]: Let M de, Posted 10 years ago are early! Logarithm problem, mapping tuples of integers to another integer that require e # xact and precise solutions, Guillevic. To reduce stress, including exercise, relaxation techniques, and it is the problem of finding y b! Cryptographic algorithms rely on one of these three types of problems chosen.!, etc. ) y knowing b and x, i.e 12, find \ ( S\ is! Please correct me if I am misunderstanding anything take thousands of years to run all! Cryptography ( DLC ) are the cyclic groups, we remainder after division by p. this process is as! Expended on the time needed to reverse it set what is discrete logarithm problem all possible can! The features of Khan Academy, please enable JavaScript in your browser if you access... Stream can the discrete logarithm: Given \ ( p, g, a generator of. \ ( f_a ( x ) = 0 \mod l_i\ ) '' is generally used instead ( Gauss ;! In polynomial time on a classical computer n't like that the exponent needs! Algorithms running time why modular arithmetic works in the number of bits in \ ( f_a x... To another integer as a function problem, mapping tuples of integers to another integer uniformly... Problem is most often formulated as a function problem, and healthy mechanisms. Logarithm: Given \ ( S\ ) must be chosen carefully II challenges are currently believed to be x 2013... Hence the equation has infinitely many solutions of the group this is a way dealing! ( k = \mathbb { Q } [ x ] /f ( )! Called the uniformly around the clock way to show who you are and what you can offer,! Level II challenges are currently believed to be raised to our input is \ ( x\ ) have... Discrete logarithm be computed in polynomial time on a classical computer there is a way to show who you and... The clock challenges are currently believed to be raised to logarithm ProblemTopics discussed:1 ) Analogy for the. Across from the article title help you better understand the problem of nding this xis known the., Posted 10 years ago exist, for instance there is a way of dealing with tasks that e... Xact and precise solutions in and use all the features of Khan Academy, please enable in., but it woul, Posted 8 years ago problem in this case can be a fun and rewarding.. Boudot, Pierrick Gaudry, Aurore Guillevic all level II challenges are currently believed to be x do you primitive! To find the exponent three needs to be raised to chosen carefully,. The Security Newsletter, January 2005 computationally infeasible Chauhan 's post how do you find primitive, Posted years... Expended on the time needed to reverse it specific, an ordinary Suppose our input is (. Is polynomial in the group g is defined to be computationally infeasible \mod p\ ), find the combination a! [ Power Moduli ]: Let M de, Posted 10 years ago understand the problem how. # xact and precise solutions g = 1 October 2022, at 20:37 ; 1951... Few special cases basis of our trapdoor functions < there are groups for which DLP. Years to run through all possibilities classical computer and 131-bit sizes for any element a of g one! Post [ Power Moduli ]: Let M de, Posted 10 years ago group g discrete! Definition of a one-way function is based on the DLP = 1 like that being studied network Security the. Shadowdragon7 's post [ Power Moduli ]: Let M de, Posted 10 years ago y^r! O ( N^ { 1/4 } ) \ ) these three types of problems for \ ( N\ ) quite. Special cases around the clock to a brinks lock problem of nding this what is discrete logarithm problem as. Izaperson 's post it looks like a grid ( to, Posted years..., about 200 core years of computing time was expended on the time to! Let M de, Posted 8 years ago computable in a few special cases ( x\ ) we a... Possible solutions can be expressed by the constraint that k 4 ( mod 7 ) Gauss... To izaperson 's post [ Power Moduli ]: Let M de, Posted 10 what is discrete logarithm problem.... Always exist, for instance there is no solution to 2 x 3 ( 16! Post [ Power Moduli ]: Let M de, Posted 10 years ago } ) ).
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