## CryptoDB

### Magnus Daum

#### Publications

Year
Venue
Title
2005
FSE
2005
EPRINT
T-functions were introduced by Klimov and Shamir in a series of papers during the last few years. They are of great interest for cryptography as they may provide some new building blocks which can be used to construct efficient and secure schemes, for example block ciphers, stream ciphers or hash functions. In the present paper, we define the narrowness of a T-function and study how this property affects the strength of a T-function as a cryptographic primitive. We define a new data strucure, called a solution graph, that enables solving systems of equations given by T-functions. The efficiency of the algorithms which we propose for solution graphs depends significantly on the narrowness of the involved T-functions. Thus the subclass of T-functions with small narrowness appears to be weak and should be avoided in cryptographic schemes. Furthermore, we present some extensions to the methods of using solution graphs, which make it possible to apply these algorithms also to more general systems of equations, which may appear, for example, in the cryptanalysis of hash functions.
2003
PKC
2002
EPRINT
Quartz is a signature scheme based on an HFEv- trapdoor function published at Eurocrypt 1996. In this paper we study "inversion" attacks for Quartz, i.e. attacks that solve the system of multivariate equations used in Quartz. We do not cover some special attacks that forge signatures without inversion. We are interested in methods to invert the HFEv- trapdoor function or at least to distinguish it from a random system of the same size. There are 4 types of attacks known on HFE: Shamir-Kipnis, Shamir-Kipnis-Courtois, Courtois, and attacks related to Gr\"{o}bner bases such as the F5/2 attack by Jean Charles Faug\`{e}re. No attack has been published so far on HFEv- and it was believed to be more secure than HFE. In this paper we show that even modified HFE systems can be successfully attacked. It seems that the complexity of the attack increases by at least a factor of $q^{tot}$ with $tot$ being the total number of perturbations in HFE. From this and all the other known attacks we will estimate what is the complexity of the best "inversion" attack for Quartz.

#### Coauthors

Nicolas Courtois (2)
Patrick Felke (2)