HAVAL is a hash function proposed by Zheng et al.in 1992,including 3-,4-and 5-pass versions.We improve pseudo-preimage and preimage attacks on 3-pass HAVAL at the complexity of 2 172 and 2 209.6,respectively,as compared to the previous best known results:2 192 and 2 225 by Sasaki et al.in 2008.We extend the skip interval for partial-patching and apply the initial structure technique to find the better message chunks,and combine the indirect-partial-matching,partial-fixing and multi-neutral-word partial-fixing techniques to improve the attacks based on the meet-in-the-middle method.These are the best pseudo-preimage and preimage attacks on 3-pass HAVAL.
Keccak is one of the five hash functions selected for the final round of the SHA-3 competition,and its inner primitive is a permutation called Keccak-f.In this paper,we observe that for the inverse of the only nonlinear transformation in Keccak-f,the algebraic degree of any output coordinate and the one of the product of any two output coordinates are both 3,which is 2 less than its size of 5.Combining this observation with a proposition on the upper bound of the degree of iterated permutations,we improve the zero-sum distinguisher for the Keccak-f permutation with full 24 rounds by lowering the size of the zero-sum partition from 21590 to 21575.
This paper presents a DNA algorithm based on linear self-assembly which gives the result of the modular subtraction operation of two nonnegative integers.For two n-bit nonnegative integers A and B,the algorithm gives the result of A-B mod 2 n.An extended borrow tag which indicates the relation of the minuend and the subtrahend is included in the resulting strand so that the pre-classification based on A>B or B>A is not required before the experiment.From the resulting strand,we can draw the information of operation result,operands,borrow,and the tag of the relation between the minuend and the subtrahend.The algorithm takes advantage of the parallelism characteristic of DNA computing:while given two sets of operands (one the minuend set and the other subtrahend set),the modular subtraction operation of these two sets can be achieved by a parallel processing procedure.The feasibility of the algorithm is based on a known experiment.The algorithm is of spontaneous characteristic which prevents the scale of the experimental procedures from growing with the length of the operands.As for the length of the operands n,there are O(n) kinds of strands required in the experiment,and the biochemical experimental procedures can be accomplished in constant number of steps.
