Krzysztof Chmiel

Involutional Block Cipher for Limited Resources

We propose a scalable block cipher which is an involutional SPN. We use one S-box which is an involution and a bit permutation which also is an involution. As a result we received a totally involutional cipher. It means that we use the same network, and especially the same S-box and the same permutation P in the encryption and decryption data processing. PP-1 is a symmetric block cipher designed for platforms with very limited resources, especially with restricted amount of memory needed to store its components.

Scalable PP-1 block cipher

Scalable PP-1 block cipher A totally involutional, highly scalable PP-1 cipher is proposed, evaluated and discussed. Having very low memory requirements and using only simple and fast arithmetic operations, the cipher is aimed at platforms with limited resources, e.g., smartcards. At the core of the ciphers processing is a carefully designed S-box. The paper discusses in detail all aspects of PP-1 cipher design including S-box construction, permutation and round key scheduling. The quality of the PP-1 cipher is also evaluated with respect to linear cryptanalysis and other attacks. PP-1s concurrent error detection is also discussed. Some processing speed test results are given and compared with those of other ciphers.

Linear approximation of arithmetic sum function

In the paper the results concerning the linear approximation of n-bit arithmetic sum function are presented. In particular, the computationally effective algorithms are formulated, to compute values of the approximation tables and the distribution of values in these tables as well as the algorithm to generate the list of effective approximations, ordered decreasingly by the approximation effectiveness measure.

On Differential and Linear Approximation of S-box Functions

In the paper the differential and the linear approximations of two classes of S-box functions are considered. The classes are the permutations and arbitrary functions with n binary inputs and m binary outputs, where 1 ≤ n=m ≤10. For randomly chosen functions from each of the classes, the distribution of the best nonzero approximations is investigated. The based on the definitions of differential and linear approximation algorithms to compute a single element of the approximation tables, are of exponential complexity. The presented in the paper fast algorithms compute the best nonzero approximations in at worst linear time for a single element, without memory needed for storage of the whole table.

On Intermediate Evaluation of Block Ciphers

In the paper an intermediate evaluation of block ciphers method is presented. As a criterion of quality, probability of the best nonzero linear approximation is taken. The main idea of the method is to restrict considerations to only two types of approximations: zero and nonzero. For a cipher graph G of zero-nonzero approximations is constructed. Algorithm SP calculates the shortest path of a specified length in graph G. This path determines the best zero-nonzero approximation of the cipher, that fulfils approximation conditions. The method is quite general but it is not independent of the structure of a cipher. In the paper the method is presented for DES.

On arithmetic subtraction linear approximation

In the paper two methods of linear approximation of n-bit arithmetic subtraction function are considered. In the first method, called the model of approximation of a single S-box, approximations are calculated for arbitrary m consecutive bits, where m ≤ n is limited by the size of so-called table of pairs TP, used during calculation. In the second method, called the model of exact composition of approximations, the subtraction approximations are calculated as a composition of k approximations of m-bit subtraction cells, where m ≤ n is limited by the size of the same table of pairs TP. In the first method, the set of nonzero approximations is limited to approximations in the range of m consecutive bits while in the second method is not limited. For n-bit arithmetic subtraction function however, the approximation probability can be calculated with use of the methods in time O(l) and O(k), respectively.

Fast Computation of Approximation Tables

In the paper are presented results, concerning the linear approximation of arbitrary function f with n binary inputs and m binary outputs. The based on the definition of linear approximation algorithm to compute a single value of the approximation table, is of exponential complexity O((n+m) · 2n).The presented in the paper fast algorithm computes the whole approximation table, in linear time O(n+m) for a single value.