Research article a novel multireceiver signcryption scheme with complete anonymity liaojun pang1,2, xuxia yan1, huiyang zhao1, yufei hu1, huixian li3 1 state key lab. Diffie hellman is a way of generating a shared secret between two people in such a way that the secret cant be seen by observing the communication. Add rogaways recent exposition on the necessity of ethicality for cr dec 15, 2015. The basic tools for relating the complexities of various problems are polynomial reductions and transformations. Diffie hellman key exchange and the discrete log problem by christof paar. In this research, we try to bring out the challenges and some best solutions that may solve the problems. What i had was not pdf file nor book chapter, just a webpage. The diffie hellman problemsthe diffie hellman problems are formulated for an abelian group. Cherepnev ma 1996 on the connection between the discrete logarithms and the diffiehellman problem. Spdh a secure plain diffiehellman algorithm dtu orbit. Brewers conjecture and the feasibility of consistent. The bit security or hardcore bits of diffie hellman problem in arbitrary finite cyclic group is a longstanding open problem in cryptography.
Lately ive been reading about the diffie hellman keyexchange methods, and specifically about the computational diffie hellman assumption vs. Public key exchange using matrices over group rings. In this pap er w e surv ey the recen applications of ddh as w ell kno wn results regarding its. Cryptography stack exchange is a question and answer site for software developers, mathematicians and others interested in cryptography. Can you give me a summary of cryptographic hardness. The cdh assumption states that, given for a randomly chosen. In this paper we survey the recent applications of ddh as well as known results regarding its security. The discrete logarithm problem dlp, the computational diffie. Usually easy to convert to decision problem if we know how to solve the decision problem, then we can usually solve the original problem.
Proceedings of the ieee, 67, privacy and authentication. E be an undirected graph with n vertices and m edges. Offline epayment system using proxy blind signature scheme. Decision problems for which there is a polytime certifier. We survey the recent applications of ddh as well as known results regarding its security. The decisional diffie hellman ddh assumption is a computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. Im extremely new to crypto, and very much inexperienced. Several pseudopolynomial, polynomial, and strongly polynomial al. For example, they enable encrypting a message, but reversing the encryption is difficult. By definition, there exists a polytime algorithm as that solves x. Provably secure authenticated group diffiehellman key. Proving decision problems npcomplete npcompleteness is a useful concept for showing the di culty of a computational problem, by showing that the existence of a polynomialtime algorithm for the problem would imply that p np. The diffie hellman problem dhp is a mathematical problem first proposed by whitfield diffie and martin hellman in the context of cryptography. The xdh assumption holds that there exist certain subgroups of elliptic curves which have useful properties for cryptography.
The computational diffie hellman assumption is a computational hardness assumption about the diffiehellman problem. Second, it is proved that the diffiehellman problem and the dis. Prathiba abstract mobile cloud computing is an evolving technology which is still unclear to many security problems and ensuring the security of data storage in cloud servers is one of the most challenging task. C program files the weather channel fw desktop weather adware. Finitememory algorithms for estimating the mean of a. Hodgeslehmann confidence intervals for a shift in location. Rp354 10 4 2009 6 21 54 pm software distribution service 3. Distortion maps allow one to solve the decision diffie hellman problem on subgroups of points on the elliptic curve. It is tempting to try to develop a variation on diffie hellman that could be used as a digital signature. It enables one to construct efficient cryptographic systems with strong security properties. The external diffie hellman xdh assumption is a computational hardness assumption used in elliptic curve cryptography.
The decisiondiffiehellman problem ddh is a central computational problem in cryptography. Solving largescale realworld telecommunication problems. Diffiehellmansleuteluitwisselingsprotocol wikipedia. We define an algorithm that calculates the discrete logarithm in the group, given, a parameter that determines the size of. May 24, 2006 the decision diffie hellman assumption ddh is a gold mine. Answer false diff 1 keywords categorical random variable topics. The goal of most web services today is to be as available as the network on which they run. The decision diffiehellman assumption ddh is a gold mine.
Given additive and multiplicative cyclic group s of the same prime order. Let g be a cyclic group of prime order r written additively. If cryptanalysis is impossible so that a cryptanalyst cannot. It is known that the weil and tate pairings can be used to solve many ddh problems on elliptic curves. Easy decision diffie hellman groups volume 7 steven d. Decision problems for which there is an exponentialtime algorithm. Decision problems princeton university computer science. The proxy blind signature scheme is demonstrated as secure under discrete logarithm problem, decision bilinear diffie hellman scheme and the chosentarget computational diffie hellman. Show that if every vertex has degree at least n2, the graph is connected. This hypothesis suggests that, in the in is difficult to calculate in b00 let generator polylinear display. The cdh assumption involves the problem of computing the discrete logarithm in cyclic groups.
However, we are able to show that the twin diffie hellman problem remains hard, even in the presence of a decision oracle that recognizes solutions to the problem this is a feature not enjoyed. Pdf the ndiffiehellman problem and its applications. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Here is one that is simpler than dsa and that does not require a secret random number in addition to the private key. On the existence of distortion maps on ordinary elliptic. To implement diffie hellman, the two end users alice and bob, while communicating over a channel they know to be private, mutually agree on positive whole numbers p and q, such that p is a prime.
There are a couple variations on the diffie hellman problem in cryptography. The decision di ehellman problem stanford university. Solved it is tempting to try to develop a variation on. A novel multireceiver signcryption scheme with complete. A secure and efficient identitybased proxy signcryption. It enables one to construct e cien t cryptographic systems with strong securit y prop erties. The decision diffie hellman problem ddh is a central computational problem in cryptography. Efidpsccs model depends on the following hard diffie hellman problems. On the complexity of the discrete logarithm and diffiehellman. Hodgeslehmann confidence intervals for a shift in location using sas procedure sql ann olmsted, dept. A can learn any information about the agreed value and often also ensure a and b that their. We offer a public key exchange protocol in the spirit of diffie hellman, but we use small matrices over a group ring of a small symmetric group as the. However, because the diffiehellman decision problem is difficult, a more. The ddh problem is to distinguish the two distributions in g4.
The computational diffie hellman cdh assumption is the assumption that a certain computational problem within a cyclic group is hard. Npcompleteness and changing it for a decision problem. Boneh declared in 19, the decision diffiehellman assumption is a gold mine. The amount of calories contained in a pack of 12ounce cheese is an example of a discrete variable. However, until recently the effects of finite memory were never considered.
Publickey cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys. Xdh assumption crypto wiki fandom powered by wikia. First introduced in 22, the protocol is almost exactly the same as the basic one. Boek maken downloaden als pdf printvriendelijke versie. An introduction to intractable problems, nphardness, and heuristics will also be given. Proposition a machine that solves decision diffie hellman problems mod p can be from sit 281 at deakin. The decision diffie hellman assumption ddh is a gold mine. The above formulation is referred to as asymmetric xdh.
In the diffiehellman algorithm the public key is used on both. Smoothed analysis of the successive shortest path algorithm tobias brunsch y kamiel cornelissen z bodo manthey x heiko r oglin abstract the minimumcost ow problem is a classic problem in combinatorial optimization with various applications. If so, are problems which ask for a solution harder than the equivalent decision problem. Problems 101 users a and b use the diffie hellman key. Beating the odds on the diffiehellman decision problem. The cdh problem illustrates the attack of an eavesdropper in the diffiehellman key exchange protocol to obtain the exchanged secret key. However, as of today, april 1st 2014, the researcher has proven sans rigor that p6np. Most importantly, decision problem is easier at least, not harder, so a lower bound on the decision problem is a lower bound on the associated searchoptimization problem 8. Supoose that you are given three numbers a, b, and c, and suppose that a and b are equal to. We say that a problem a reduces in poly nomial time to another problem b, denoted by a b, if and only if there is an algorithm for a which uses a subroutine for b, and each call to the subroutine for b counts as a single step, and the algorithm for a runs in polynomialtime. T is a partition of the vertices into two sets s and t such that s t v and s \t. The moral character of cryptographic work 2015 rogaway.
Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. An introduction to cryptography 399 any attempt by the eavesdropper either to decrypt a cryp togram c to get the plaintext p, or to encrypt an inauthentic plaintext p to get an acceptable cryptogram c, without ob taining the key k from the key channel is called cryptanalysis. Challenges of online exam, performances and problems for. The problem of estimating the mean p of a sequence of independent jj,o observations is a classic problem in statistics.
Our construction works in groups equipped with an efficient bilinear map, or, more generally, an algorithm for the decision diffie hellman problem. Jan 26, 20 the generalized discrete logarithm problem and security of diffie hellman. Dhies is a diffie hellman based scheme that combines a symmetric encryption method, a message authentication code, and a hash function, in addition to numbertheoretic operations, in a way which. Youre not sharing information during the key exchange, youre creating a key together. The security of our scheme depends on a new intractability assumption we call strong diffie hellman sdh, by analogy to the strong rsa assumption with which it shares many properties. In this paper we study generalizations of the diffiehellman problems recently used to construct cryptographic schemes for practical purposes. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. The design and implementation of datagram tls 2004 modadugu, rescorla. Proposition a machine that solves decision diffie hellman.
Public key encryption from diffiehellman elgamal variants with better security. Bdh is reducible to most of the older believedtobehard discretelog problems and dh problems, but there is no known reduction from any of those problems to bdh. My suspicion is that the answer to the first question is a resounding yes and that the answer to the second is a resounding no. The bilinear diffiehellman bdh intractability assumptionis required to establish the security of new weilpairing based cryptosystems. Polynomial representations of the diffiehellman mapping. Explanation of the decision diffie hellman ddh problem. Het diffiehellmansleuteluitwisselingsprotocol is een cryptografisch protocol, waarmee twee. To set up a common key, a and b proceed as follows.
This is particularly useful because you can use this technique to create an encryption key with someone, and then start. Rene descartes, philosophical writings of descartes, v. This post will explain both and give an example of where the former is hard and the latter easy. Methods designed to deal with this cryptographic problem ensure a resp. The knapsack problem is a problem in combinatorial optimization. Discrete logarithms and the diffie hellman exchange 3 diffie hellman key exchange alice and bob wish to agree on a common secret, a key, which for example can be used as the basis for exchanging messages using a cryptosystem requiring such a key. Lecture 8 public key cryptography diffie hellman and rsa 1 public key cryptography asymmetric cryptography invented.
The generalized discrete logarithm problem and security of. Decision problems for which there is a polytime algorithm. The amount of time a student spent studying for an exam will be measured on a ratio scale. The decisional diffie hellman problem ddh is intractable in. It is used as the basis to prove the security of many cryptographic protocols, most notably the elgamal and cramershoup cryptosystems. Smoothed analysis of the successive shortest path algorithm. Carmens decides to forecast auto sales by weighting the three weeks as follows. Notice that this is different from the diffie hellman problem described on. A stronger version of the assumption symmetric xdh, or sxdh holds if ddh.
This led me to consider a windows phone, but i was reluctant due to all the negative information regarding it. Are there decision problems which are decidable but not in np. The central idea is the construction of a mapping between two useful cryptographic groups which allows for new cryptographic schemes based on the reduction of one problem in one group to a di. The group in this paper is a concept for entities with similar roles. It is known that the weil and tate pairings can be used to solve. The participants choose numbers p and x, such that p is a large prime on the order of at least 300 decimal digits 1024 bits, p. We now show that there is a polynomial reduction from sat to 3sat. In this patent paper, a proxy blind signature scheme typed bilinear pairings is suggested. Secondly, even a long path in a decision tree typically involves only a small proportion of the possible attributes. The external diffie hellman xdh assumption is a mathematic assumption used in elliptic curve cryptography.
Two random samples are taken, with each group asked if they support a particular candidate. Specifically, xdh implies the existence of two distinct groups with the following properties. Authenticated keyexchange protocols allow two participants a and b, communicating over a public network and each holding an authentication means to exchange a shared secret value. Secure and energy efficient model with modified offloading.
The general system is a set of instructions, a piece of. Specifically im referencing dan bonehs paper on ddh problem. Since this problem is nphard, the problem with arbitrary weights is also nphard. The generalized discrete logarithm problem and security of diffie hellman. The group computational and the group decisional diffie hellman assumptions not only enable one to construct efficient pseudorandom functions but also to naturally extend. The computational diffiehellman cdh assumption is a computational hardness assumption about the diffiehellman problem. The training set of figure 1 uses 23 attributes to describe each case, but no. Encryption from standard diffie hellman assumptions twin hybrid elgamal encryption security from standard cdh problem in the rom simple and generic trick. First of all, since 3sat problem is also a sat problem, it is np. Jan 30, 2014 for slides, a problem set and more on learning cryptography, visit.
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