Anna Grocholewska-Czurylo

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.

Generating Bent Functions

In the paper a method of efficient generation of random bent functions is presented. Obtaining a random bent function is not a straight forward process, since the introduction of bent functions in the most of published works studied their construction and gave algorithms for their generation. Drawing such functions at random from a set of all the Boolean functions is not feasible for n-argument functions for n higher than 4. On the other hand, all the known algorithms for constructing bent functions have deterministic dependencies which introduce certain low complexity problems and significantly narrow the range of bent functions that can be generated with each algorithm (bent function class). We describe a new method of obtaining random bent functions without constraints described above. The algorithm for generating bent functions operates in the Algebraic Normal Form domain. This approach allows for generation of bent functions of arbitrary order and even some special nonlinear requirements as homogeneity.

Cryptographic properties of modified AES-like S-boxes

Using AES-like S-boxes (generated using finite field inversion) provides an excellent starting point for generating S-boxes with some specific design criteria dictated by the implemented cipher and still maintaining all the most commonly recognized cryptographic criteria to a large extent. This paper presents the results of statistical analysis of fulfilment of those basic cryptographic criteria by the modified AES-like S-boxes that do have neither equivalence nor cycles.

Evaluation of PP-1 Cipher Resistance against Differential and Linear Cryptanalysis in Comparison to a DES-like Cipher

In the paper we present an involutional block cipher PP-1, which is a scalable SPN. The cipher has very low memory requirements and uses only simple and fast arithmetic operations. The paper discusses in detail the PP-1 cipher design, including the S-box construction, the permutation and the round key scheduling. The quality of the PP-1 cipher is evaluated with respect to differential and linear cryptanalysis. Its quality is compared to the quality of a comparative algorithm with the same block length, as well as to the quality of the class of balanced Feistel ciphers, and in particular to DES quality.

Parameterized Hash Functions

In this paper we describe a family of highly parameterized hash functions. This parameterization results in great flexibility between performance and security of the algorithm. The three basic functions, HaF-256, HaF-512 and HaF-1024 constitute this hash function family. Lengths of message digests are 256, 512 and 1024 bits respectively. The paper discusses the details of functions structure. The method used to generate function S-box is also described in detail.

S-boxes Cryptographic Properties from a Statistical Angle

A new, strong S-box was required to be designed to be incorporated as the nonlinear element of the PP-2 block cipher designed recently at Poznan University of Technology. This paper presents statistical analysis of the cryptographic criteria characterizing a group of S-boxes generated by inverse mapping with random search elements. Statistical tests used in this research were not pure randomness checks but were related to the most important real cryptographic criteria like nonlinearity, SAC, collision avoidance.

Random Generation of S-Boxes for Block Ciphers

In the paper results of experiments in designing S-boxes and nonlinear Boolean functions as their components are presented. We discuss deterministic algorithms for the construction of bent functions and we formulate our algorithm for random generation of perfect nonlinear functions. We present results of experiments performed on S-boxes and we compare them with results obtained using deterministic methods.