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


On the efficiency of lattice-based cryptographic schemes on graphical processing unit
Yüce Tok, Zaliha; Akyıldız, Ersan; Akleylek, Sedat; Department of Cryptography (2016)
Lattice-based cryptography, a quantum-resistant public key alternative, has received a lot of attention due to the asymptotic efficiency. However, there is a bottleneck to get this advantage on practice: scheme-based arithmetic operations and platform-based implementations. In this thesis, we discuss computational aspects of lattice-based cryptographic schemes focused on NTRU and GLP in view of the time complexity on both CPUs and Graphical Processing Units (GPU). We focus on the optimization of polynomial ...
On statistical analysis of synchronous stream ciphers
Sönmez Turan, Meltem; Doğanaksoy, Ali; Department of Cryptography (2008)
Synchronous stream ciphers constitute an important class of symmetric ciphers. After the call of the eSTREAM project in 2004, 34 stream ciphers with different design approaches were proposed. In this thesis, we aim to provide a general framework to analyze stream ciphers statistically. Firstly, we consider stream ciphers as pseudo random number generators and study the quality of their output. We propose three randomness tests based on one dimensional random walks. Moreover, we theoretically and experimenta...
A New Algorithm for Residue Multiplication Modulo 2(521)-1
Ali, Shoukat; Cenk, Murat (2016-12-02)
We present a new algorithm for residue multiplication modulo the Mersenne prime p = 2(521) - 1 based on the Toeplitz matrix-vector product. For this modulus, our algorithm yields better result in terms of the total number of operations than the previously known best algorithm of Granger and Scott presented in Public Key Cryptography (PKC) 2015. We have implemented three versions of our algorithm to provide an extensive comparison - according to the best of our knowledge with respect to the well-known algori...
Basic cryptanalysis methods on block ciphers
Çelik, Dilek; Doğanaksoy, Ali; Department of Cryptography (2010)
Differential cryptanalysis and linear cryptanalysis are the first significant methods used to attack on block ciphers. These concepts compose the keystones for most of the attacks in recent years. Also, while designing a cipher, these attacks should be taken into consideration and the cipher should be created as secure against them. Although di fferential cryptanalysis and linear cryptanalysis are still important, they started to be ine cient due to the improvements in the technology. So, these attacks are ...
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 ...
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.