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J. Math. Cryptol. 4 (2010), 239–270 DOI 10.1515/JMC.2010.010 © de Gruyter 2010 Multicollision attacks and generalized iterated hash functions Juha Kortelainen, Kimmo Halunen and Tuomas Kortelainen Communicated by Douglas R. Stinson Abstract. We apply combinatorics on words to develop an approach to multicollisions in generalized iterated hash functions. Our work is based on the discoveries of A. Joux and on generalizations provided by M. Nandi and D. Stinson as well as J. Hoch and A. Shamir. We wish to unify the existing diverse notation in the field, bring basic

1 Introduction Hash functions are an essential part of many cryptographic schemes, principally as tools of message authentication and modification detection. In [ 1 ] and [ 2 ] Gilles Zémor introduced the idea of building hash functions from Cayley graphs of large girth. The remarkable property of these Cayley graph hash functions, known as the small modifications property , is that any small modification of a message necessarily changes its hash value. This idea was popularized by a later construction due to Tillich and Zémor [ 3 ]. Recalling that {0, 1

References 1 I. Anshel, M. Anshel, D. Goldfeld and S. Lemieux, Key agreement, the algebraic eraser™, and lightweight cryptography, Algebraic Methods in Cryptography, Contemp. Math. 418, American Mathematical Society, Providence (2006), 1–34. Anshel I. Anshel M. Goldfeld D. Lemieux S. Key agreement, the algebraic eraser™, and lightweight cryptography Algebraic Methods in Cryptography Contemp. Math. 418 American Mathematical Society Providence 2006 1 34 2 I. Anshel and D. Goldfeld, Cryptographic hash function, US Patent number 8,972,715, March 3, 2015. Anshel I

Abstract.

We propose a new simple and efficient family of hash functions based on matrix-vector multiplications with a competitive software implementation. The hash design combines a hard mathematical problem based on solving a system of linear equations with special-random requirements and the fast computation of the convolution product algorithm. Such a mixing was often unrealizable. For security, the one-way and collision resistant criteria are based on the fact that inverting the compression function for random values is infeasible in reasonable time. In a subsequent result, we conjecture a general framework for producing secure matrix multiplication hash functions.

c© de Gruyter 2009 J. Math. Crypt. 3 (2009), 69–87 DOI 10.1515 / JMC.2009.004 Hash function requirements for Schnorr signatures Gregory Neven, Nigel P. Smart, and Bogdan Warinschi Communicated by Alfred Menezes Abstract. We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group representations such as those which occur in elliptic curve groups. We also show, via an argument in the generic group model, that these conditions are suffi- cient. Our hash function security requirements are variants of

References [1] AUMASSON, J.-R: Cryptanalysis of a hash function based on norm form equations, Cryptologia 33 (2009), 1-4. [2] BÉRCZES, A.-FOLLÁTH, J.-PETHŐ, A.: On a family of preimage-resistant functions, Tatra Mt. Math. Publ. 47 (2010), 1-13. [3] BÉRCZES, A.-JÁRÁSI, L: An application of index forms in cryptography, Period. Math. Hungar. 58 (2008), 35-45. [4] BÉRCZES, A.-KÖDMÖN, J.-PETHŐ, A.: A one-way function based on norm form equations, Period. Math. Hungar. 49 (2004), 1-13. [5] BUCHMANN, J.-PAULUS, S.: A one-way function based on ideal arithmetic

DE GRUYTER OLDENBOURG it – Information Technology 2015; 57(6): 347–356 Special Issue Harald Baier* Towards automated preprocessing of bulk data in digital forensic investigations using hash functions DOI 10.1515/itit-2015-0023 Received June 1, 2015; revised October 10, 2015; accepted October 12, 2015 Abstract:Handling bulk data (e. g. some terabytes of data) is a issue in contemporary digital forensics. Separating rel- evant data structures from irrelevant ones resembles find- ing the needle in the haystack. The article at hand presents and assesses automatic

1 Introduction A hash function H : { 0 , 1 } * → { 0 , 1 } n {H:\{0,1\}^{*}\to\{0,1\}^{n}} maps an input message m of arbitrary length to a fixed-length hash value h = H ⁢ ( m ) {h=H(m)} of size n . If such a function satisfies additional requirements, it can be used for cryptographic applications, for example in digital signatures, ID based cryptography, and randomization of plaintexts in probabilistic cryptosystems. The primary properties that a hash function H should possess are the following: • Computation of H ⁢ ( x ) {H(x)} should be fast and

References [1] DÉNES, J. - KEEDWELL, A. D.: Latin Squares and their Applications , Acad. Press, New York, 1974. [2] DVORSKÝ, J. - OCHODKOVÁ, E. - SNÁŠEL, V.: Hash function based on quasigroups , in: Proc. of Mikulášska kryptobesídka, Praha, 2001, pp. 27-36. (In Czech) [3] DVORSKÝ, J. - OCHODKOVÁ, E. - SNÁŠEL, V.: Hash functions based on largequasigroups , in: Proc. of Velikonoční kryptologie, Brno, 2002, pp. 1-8. (In Czech) [4] GLIGOROSKI, D. - MARKOVSKI, S. - KNAPSKOG, S. J.: The stream cipherEdon80 , in: New Stream Cipher Designs: The eSTREAM Finalists

1 Introduction After a cautious start with Couveignes’ unpublished note [ 1 ] from 1997 and Stolbunov’s master thesis [ 2 ] from 2004, the area of isogeny-based cryptography took a more visible turn in 2006 when Charles, Goren and Lauter [ 3 ] showed how to construct collision-resistant hash functions from deterministic walks in isogeny graphs of supersingular elliptic curves over finite fields. Five years later Jao and De Feo applied similar ideas to the design of a key exchange protocol [ 4 , 5 ] now known as SIDH, after which isogenies became a very active