A Survey on known algorithms in solving generalization birthday problem (K-List)

Namaziesfanjani, Mina
A well known birthday paradox is one the most important problems in cryptographic applications. Incremental hash functions or digital signatures in public key cryptography and low-weight parity check equations of LFSRs in stream ciphers are examples of such applications which bene t from birthday problem theories to run their attacks. Wagner introduced and formulated the k-dimensional birthday problem and proposed an algorithm to solve the problem in O(k.m^ 1/log k ). The generalized birthday solutions used in some applications to break Knapsack based systems or collision nding in hash functions. The optimized birthday algorithms can solve Knapsack problems of dimension n which is believed to be NP-hard. Its equivalent problem is Subset Sum Problem nds the solution over Z/mZ. The main property for the classi cation of the problem is density. When density is small enough the problem reduces to shortest lattice vector problem and has a solution in polynomial time. Assigning a variable to each element of the lists, decoding them into a matrix and considering each row of the matrix as an equation lead us to have a multivariate polynomial system of equations and all solution of this type can be a solution for the k- list problem such as F4, F5, another strategy called eXtended Linearization (XL) and sl. We discuss the new approaches and methods proposed to reduce the complexity of the algorithms. For particular cases in over-determined systems, more equations than variables, regarding to have a single solutions Wolf and Thomea work to make a gradual decrease in the complexity of F5. Moreover, his group try to solve the problem by monomials of special degrees and linear equations for small lists. We observe and compare all suggested methods in this


A Randomness test based on postulate r-2 on the number of runs
Şeker, Okan; Doğanaksoy, Ali; Department of Cryptography (2014)
Random values are considered as an indispensable part of cryptography, since they are necessary for almost all cryptographic protocols. Most importantly, key generation is done by random values and key itself should behave like a random value. Randomness is tested by statistical tests and hence, security evaluation of a cryptographic algorithm deeply depends on statistical randomness tests. In this thesis we focus on randomness postulates of Solomon W. Golomb in particular, second postulate which is about r...
A new sure-success generalization of Grover iteration and its application to weight decision problem of Boolean functions
Uyanik, K.; Turgut, Sadi (Springer Science and Business Media LLC, 2013-11-01)
In two recent papers, a sure-success version of the Grover iteration has been applied to solve the weight decision problem of a Boolean function and it is shown that it is quadratically faster than any classical algorithm (Braunstein et al. in J Phys A Math Theor 40:8441, 2007; Choi and Braunstein in Quantum Inf Process 10:177, 2011). In this paper, a new approach is proposed to generalize the Grover's iteration so that it becomes exact and its application to the same problem is studied. The regime where a ...
A QCD Sum Rules Approach to Mixing of Hadrons
Alıyev, Tahmasıb; Özpineci, Altuğ (2010-06-24)
A method for the calculation of the hadronic mixing angles using QCD sum rules is proposed. This method is then applied to predict the mixing angle between the heavy cascade hyperons Xi(Q) and Xi'Q where Q = c or Q = b. It is obtained the theta(b) = 6.4 degrees +/- 1.8 degrees and theta(c) = 5.5 degrees +/- 1.8 degrees.
A probabilistic sparse skeleton based object detection
Altinoklu, Burak; Ulusoy, İlkay; Tarı, Zehra Sibel (Elsevier BV, 2016-11)
We present a Markov Random Field (MRF) based skeleton model for object shape and employ it in a probabilistic chamfer-matching framework for shape based object detection. Given an object category, shape hypotheses are generated from a set of sparse (coarse) skeletons guided by suitably defined unary and binary potentials at and between shape parts. The Markov framework assures that the generated samples properly reflect the observed or desired shape variability. As the model employs a sparsely sampled skele...
A Genetic Isometric Shape Correspondence Algorithm with Adaptive Sampling
Sahillioğlu, Yusuf (2018-11-01)
We exploit the permutation creation ability of genetic optimization to find the permutation of one point set that puts it into correspondence with another one. To this end, we provide a genetic algorithm for the 3D shape correspondence problem, which is the main contribution of this article. As another significant contribution, we present an adaptive sampling approach that relocates the matched points based on the currently available correspondence via an alternating optimization. The point sets to be match...
Citation Formats
M. Namaziesfanjani, “A Survey on known algorithms in solving generalization birthday problem (K-List),” M.S. - Master of Science, Middle East Technical University, 2013.