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1

Using SAT Solvers to Finding Short Cycles in Cryptographic Algorithms

Dudzic Władysław, Kanciak Krzysztof

International Journal of Electronics and Telecommunications

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2020

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Vol. 66, No. 3

443--448

EN

A desirable property of iterated cryptographic algorithms, such as stream ciphers or pseudo-random generators, is the lack of short cycles. Many of the previously mentioned algorithms are based on the use of linear feedback shift registers (LFSR) and nonlinear feedback shift registers (NLFSR) and their combination. It is currently known how to construct LFSR to generate a bit sequence with a maximum period, but there is no such knowledge in the case of NLFSR. The latter would be useful in cryptography application (to have a few taps and relatively low algebraic degree). In this article, we propose a simple method based on the generation of algebraic equations to describe iterated cryptographic algorithms and find their solutions using an SAT solver to exclude short cycles in algorithms such as stream ciphers or nonlinear feedback shift register (NLFSR). Thanks to the use of AIG graphs, it is also possible to fully automate our algorithm, and the results of its operation are comparable to the results obtained by manual generation of equations. We present also the results of experiments in which we successfully found short cycles in the NLFSRs used in Grain-80, Grain-128 and Grain-128a stream ciphers and also in stream ciphers Bivium and Trivium (without constants used in the initialization step).

2

Phase-shift Fault Analysis of Grain v1

Hromada V., Pethö T.

International Journal of Electronics and Telecommunications

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2018

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Vol. 64, No. 2

131--136

EN

This paper deals with the phase-shift fault analysis of stream cipher Grain v1. We assume that the attacker is able to desynchronize the linear and nonlinear registers of the cipher during the keystream generation phase by either forcing one of the registers to clock one more time, while the other register is not clocked, or by preventing one of the registers from clocking, while the other register is clocked. Using this technique, we are able to obtain the full inner state of the cipher in reasonable time (under 12 hours on a single PC) by using 150 bits of unfaulted keystream, 600 bits of faulted keystreams and by correctly guessing 28 bits of the linear register.

3

Badania własności liczb pierwszych i wielomianów nieprzywiedlnych pod kątem zastosowania w telekomunikacji

Paszkiewicz A.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2012

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z. 181

3--175

PL

Praca stanowi obliczeniowe studium dwóch podstawowych obiektów matematycznych: liczb pierwszych i wielomianów nieprzywiedlnych pod kątem zastosowań w telekomunikacji. Oba z wymienionych obiektów pełnią podobną, podstawową rolę w teorii ciał skończonych, teorii kodowania i kryptografii. Duża część rozprawy obejmuje oryginalne wyniki autora dotyczące najmniejszych niereszt kwadratowych, najmniejszych pierwiastków pierwotnych modulo liczba pierwsza lub potęga liczby pierwszej oraz wybranych własności wielomianów nieprzywiedlnych. Autor pokazuje, jak można je wykorzystać do projektowania generatorów pseudolosowych i szyfrów. Jednym z przykładów zastosowań przywiedzionych w rozprawie jest modyfikacja algorytmu A5/1 wykorzystywanego w komunikacji GSM w celu poprawy jego mocy kryptograficznej.

EN

This dissertation is a numerical study of two basic mathematical objects, prime numbers and irreducible polynomials, in terms of telecommunications applications. The above-mentioned objects play a similar, basic role in finite fields theory, coding theory and cryptography. A large part of the dissertation contains author's original results, concerning the least quadratic non-residues, least primitive roots of a prime or a prime power, as well as some selected properties of irreducible polynomials. The author shows how the theory can be applied in designing pseudorandom generators and stream ciphers. An example is presented - how to modify the A5/1 encryption algorithm, used in GSM communication, to improve its cryptographic strength.

4

Szyfry strumieniowe na przykładzie algorytmów A5/1 i Rabbit

Poznański R.

Elektronika : konstrukcje, technologie, zastosowania

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2011

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Vol. 52, nr 6

129-131

PL

W artykule przedstawiono budowę i zasadę działania szyfrów strumieniowych. Zostały omówione dwa przykładowe szyfry strumieniowe, A5/1 oraz Rabbit.

EN

In this paper was presented construction and way how stream ciphers work. There are two examples of stream ciphers discussed, A5/1 and Rabbit.

5

Generating quasigroups for cryptographic applications

Kościelny Cz.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 4

559-569

EN

A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of order 256, suitable for a fast software encryption of messages written down in the universal ASCII code. That is exactly what this paper provides: fast and easy ways of generating quasigroups of order up to 256 and a little more.

6

Cascade parallel k-nets of shift registers

Grodzki Z.

Demonstratio Mathematica

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2001

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Vol. 34, nr 1

205-216

EN

A new class CPRNk, of cascade parallel k-nets of shift registers (briefly k-nets) is introduced. A characterization of the k-nets by means of their sets of state sequences is given. In particular the periodicity problem of state sequences is studied. Two subclasses CPNRn/k, n = 1,2, of CPNTR1/k are distinguished. The main attention is devoted to the class CPNR1/k whose elements can be described by the transition graphs. In the last section the other classes of parallel k-nets are introduced.

7

Implementacja szyfru strumieniowego WAKE w architekturach programowalnych

Gliwa R.

Biuletyn Wojskowej Akademii Technicznej

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2001

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Vol. 50, nr 1

91-109

PL

Artykuł zawiera opis implementacji szyfru strumieniowego WAKE w układach programowalnych z wykorzystaniem systemu MAX+PLUS II firmy ALTERA. Przedstawiono opis algorytmu, sposób implementacji sprzętowej, dokonano analizy i weryfikacji symulacyjnej układu.

EN

This paper comprises the description of stream cipher WAKE and its implementation using ALTERA programmable logic devices of the family MAX+PLUS II. There is described the way of hardware implementation. There are presented the results of analysis and verification of the algorithm simulation.

8

A Quasigroup-Based Public-Key Cryptosystem

Kościelny Cz., Mullen G. L.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 4

955-963

EN

A public-key cryptosystem, using generalized quasigroup-based streamciphers is presented. It is shown that such a cryptosystem allows one to transmit securely both a cryptogram and a secret portion of the enciphering key using the same insecure channel. The system is illustrated by means of a simple, but non-trivial, example.

9

On some class of stream ciphers

Grodzki Z., Janowski K.

Biuletyn Wojskowej Akademii Technicznej

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1999

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Vol. 48, nr 10

97-110

EN

The aim of this paper is to build a class SCk of stream ciphers based linear maximal hift-registers. The sequences generated by a proposed class are pseudo-random according to postulates given in Federal Information Processing Standards Publications 140-1, 1994, Announcing the Standard for Security Requirements for Cryptographic Modules. In this paper a construction of a SCk class based on four shift-registers is described and a listing of a program implementing a chosen stream cipher sck epsilon SCk is given. Tests specified in FIPS 140-1 are recalled and examples of their results for sck are presented. At the end some open problems are put forward.

PL

Celem niniejszej pracy jest określenie nowej klasy SCk szyfrów strumieniowych w oparciu o maksymalne liniowe rejestry przesuwające. Ciągi generowane przez sieci klasy SCk są pseudolosowe zgodnie z postulatami zgodnie z postulatami podanymi w FIPS Pub 140-1, 1994 (Federal Information Processing Standards Publications 140-1, 1994, Announcing the Standard for Security Requirements for Cryptographic Modules). Zamieszczono wydruk programu w języku C implementującego wybrane szyfry należące do tej klasy.