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Détails du magazine
Format
Magazine
eISSN
1338-9750
Première publication
12 Nov 2012
Période de publication
3 fois par an
Langues
Anglais

Chercher

Volume 70 (2017): Edition 1 (September 2017)

Détails du magazine
Format
Magazine
eISSN
1338-9750
Première publication
12 Nov 2012
Période de publication
3 fois par an
Langues
Anglais

Chercher

11 Articles
Accès libre

Wolfenbüttel, a Minor German Duchy But a Major Center of Cryptology in the Early Modern Period

Publié en ligne: 23 Mar 2018
Pages: 1 - 40

Résumé

Abstract

This paper highlights cryptographic activities from 1540 to about 1680 at the small duchy-Brunswick-Lüneburg in northern Germany, not too far from Hanover (see Fig. 1, p. 2). The analysis shall proceed chronologically and present some relevant examples from the 16th century before focusing on the most important German cryptological author of his time, Duke August the Younger (1579-1666).

Mots clés

  • cryptology
  • Duke August the Younger of Brunswick-Wolfenbüttel
  • Francis Bacon
  • Shakespeare

MSC 2010

  • 01A45
  • 94A60
Accès libre

Application and Misapplication of the Czechoslovak STP Cipher During WWII

Publié en ligne: 23 Mar 2018
Pages: 41 - 91

Résumé

Abstract

Lieutenant colonel Karol Cigáň (1921-2005), head of the cryptographic unit of the Czechoslovak Ministry of National Defence in the period 1949-1958 was after discharging from this position in Prague relocated to an insignificant and substandard command position at a district military administration in Slovakia. His cryptographic experience was of no use in his new position. To profit from his previous experience as a high qualified cryptographer he started to study the accessible literature and archive materials about the usage of the Czechoslovak cipher systems during the WWII. The result of this his activity were some manuscripts where he deciphered and analyzed some Czechoslovak military wireless telegrams. His critical analysis and his conclusions did not meet an understanding or a positive response of historians and were nor accepted for publication. He had no other chance as to send them to archives. Unfortunately only one (in two copies) and a collection of small notes survived. The aim of this paper is to make decisive technical parts of manuscript [K. Cigáň: Impacts of the decryption of the cipher system of the Czechoslovak Ministry of Defence in London from the years 1940-1945 on the resistance movement. Archive of the Slovak National Uprising, Banská Bystrica, Slovakia, Document collection (Fond) V, manuscript no. S36/90, 46 pp.] about the usage of the socalled STP cipher accessible. Thereby we complement the paper [Š. Porubský: STP cipher of the Czechoslovak in-exile Ministry of Defence in London during WWII, in: Proc. of EuroHCC’17, 3rd European Historical Ciphers Colloq., Smolenice Castle, Slovakia, 2017 (J. von zur Gathen et al., eds.), Slovak Univ. of Technology in Bratislava, 2017, pp. 47-66] where the part of this manuscript containing Cigáň’s method for solving STP cipher which he calls “mathematical” is published. To put Cigáň’s analysis and comment into their historical framework we briefly outline the history of Czechoslovak military intelligence activities with emphasis on their cryptological component.

Mots clés

  • STP cipher
  • Josef Růžek
  • Karol Cigáň
  • František Moravec
  • Czechoslovak military cryptography
  • World War II

MSC 2010

  • Primary: 01A60
  • Secondary: 01A70
  • 01A85
Accès libre

Optimization of the High Nonlinear S-Boxes Generation Method

Publié en ligne: 23 Mar 2018
Pages: 93 - 105

Résumé

Abstract

The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear Substitutions for Symmetric Encryption Algorithms. The thesis for the scholarly degree of candidate of technical sciences, speciality 05.13.21 - - Information security systems, Kharkiv National University of Radioelectronics, Kharkiv, 2014. (In Russian)] requires consecutive applications of several criteria for each formed substitution. This paper presents an improvement of the considered method by the appropriate selection of the criteria application order which decreases the required computational power for S-box generation. The proposed modification allows generation of a byte substitution with nonlinearity 104, algebraic immunity 3 and 8-uniformity within approximately 30 minutes of a single PC running time.

Mots clés

  • S-box
  • nonlinearity
  • algebraic immunity
  • vectorial Boolean function

MSC 2010

  • 94A60
  • 68P25
Accès libre

On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications

Publié en ligne: 23 Mar 2018
Pages: 107 - 117

Résumé

Abstract

Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.

Mots clés

  • Multivariate cryptography
  • stable transformations
  • key exchange protocols
  • shifted multivariate ElGamal algorithm
  • desynchronisation diagram

MSC 2010

  • Primary 11T71
  • Secondary 11Rxx
Accès libre

Generalized Key Substitution Attacks on Message Recovery Signatures

Publié en ligne: 23 Mar 2018
Pages: 119 - 138

Résumé

Abstract

The generalized key substitution attacks were proposed as a generalization of the key substitution attacks to examine the security of the signature schemes adopted in ISO/IEC (1st CD) 14888-3, which standardizes appendix- -type signature schemes based on the discrete logarithm problem. This paper examines the message recovery signature schemes based on the discrete logarithm problem, adopted in ISO/IEC 9796-3:2006, and shows that all but one scheme are vulnerable to the generalized key substitution attacks.

Mots clés

  • message recovery signature
  • discrete logarithm
  • generalized key substitution attacks

MSC 2010

  • 94A60
Accès libre

Improvement on Bit Diffusion Analysis of π-Cipher

Publié en ligne: 23 Mar 2018
Pages: 139 - 149

Résumé

Abstract

π-Cipher, designed by Gligoroski et al., is a second round candidate of the CAESAR competition. The designers analyzed the bit diffusion of the cipher by examining the * operation and 1 round π-function. We improve this analysis by applying Strict Avalanche Criterion (SAC) test to * operation and reduced round versions of π-function for π 16-Cipher. We found out that * operation fails SAC test whereas all versions of π-function for π 16-Cipher pass the test.

Mots clés

  • The CAESAR competition
  • π-Cipher
  • bit diffusion analysis
  • Strict Avalanche Criterion (SSAC) test

MSC 2010

  • 00A69
  • 94A60
  • 94A62
  • 60K35
  • 49J55
Accès libre

Key Exchange Over Particular Algebraic Closure Ring

Publié en ligne: 23 Mar 2018
Pages: 151 - 162

Résumé

Abstract

In this paper, we propose a new method of Diffie-Hellman key exchange based on a non-commutative integral closure ring. The key idea of our proposal is that for a given non-commutative ring, we can define the secret key and take it as a common key to encrypt and decrypt the transmitted messages. By doing, we define a new non-commutative structure over the integral closure OL of sextic extension L, namely L is an extension of ℚ of degree 6 in the form ℚ(α, β), which is a rational quadratic and monogenic extension over a non-pure and monogenic cubic subfield K = ℚ(β).

Mots clés

  • integral basis
  • key exchange
  • fully homomorphic cryptosystems
  • cryptography

MSC 2010

  • Primary 11T71
  • Secondary 11Rxx
Accès libre

Connecting the Complexity of MQ- and Code-Based Cryptosystems

Publié en ligne: 23 Mar 2018
Pages: 163 - 177

Résumé

Abstract

We study the connection between the MQ problem and the de­coding problem, through the intermediate MRHS representation. The main goal of this study is to explicitly bound the complexity of solving MQ systems with decoding tools. The main observation is that although the MQ problem over GF(2) can be efficiently transformed to syndrome decoding, the existing general decoding methods are not suitable to solve the system as efficiently as expected from the MQ representation.

Mots clés

  • decoding problem
  • MQ problem
  • MEHS

MSC 2010

  • 94A60
  • 68P25
  • 06E30
Accès libre

Evolutionary Computation in Cryptanalysis of Classical Ciphers

Publié en ligne: 23 Mar 2018
Pages: 179 - 197

Résumé

Abstract

Evolutionary computation has represented a very popular way of problem solving in the recent years. This approach is also capable of effectively solving historical cipher in a fully automated way. This paper deals with empirical cryptanalysis of a monoalphabetic substitution using a genetic algorithm (GA) and a parallel genetic algorithm (PGA). The key ingredient of our contribution is the parameter analysis of GA and PGA. We focus on how these parameters affect the success rate of solving the monoalphabetic substitution.

Mots clés

  • historical ciphers
  • grid
  • MPI
  • genetic algorithm
  • parallel genetic algorithm

MSC 2010

  • 94A60
  • 68P25
Accès libre

Power Series with Inverse Binomial Coefficients and Harmonic Numbers

Publié en ligne: 23 Mar 2018
Pages: 199 - 206

Résumé

Abstract

In this note we compute the generating function for the numbers terms of elementary functions and dilogarithms.

Mots clés

  • central binomial coefficients
  • reciprocals of binomial coefficients
  • harmonic numbers
  • generating functions
  • Euler series transformation
  • binomial identities

MSC 2010

  • 05A15
  • 11B05
Accès libre

On the Diophantine Equation 11 + 2X+2 + (7)3Y = Z2

Publié en ligne: 23 Mar 2018
Pages: 207 - 209

Résumé

Abstract

In this note, we investigate solutions of the Diophantine equation 11 + 2x+2 + (7)3y = z2 (x, y, z) ∈ℕ3

Mots clés

  • exponential Diophantine equations

MSC 2010

  • 11D61
11 Articles
Accès libre

Wolfenbüttel, a Minor German Duchy But a Major Center of Cryptology in the Early Modern Period

Publié en ligne: 23 Mar 2018
Pages: 1 - 40

Résumé

Abstract

This paper highlights cryptographic activities from 1540 to about 1680 at the small duchy-Brunswick-Lüneburg in northern Germany, not too far from Hanover (see Fig. 1, p. 2). The analysis shall proceed chronologically and present some relevant examples from the 16th century before focusing on the most important German cryptological author of his time, Duke August the Younger (1579-1666).

Mots clés

  • cryptology
  • Duke August the Younger of Brunswick-Wolfenbüttel
  • Francis Bacon
  • Shakespeare

MSC 2010

  • 01A45
  • 94A60
Accès libre

Application and Misapplication of the Czechoslovak STP Cipher During WWII

Publié en ligne: 23 Mar 2018
Pages: 41 - 91

Résumé

Abstract

Lieutenant colonel Karol Cigáň (1921-2005), head of the cryptographic unit of the Czechoslovak Ministry of National Defence in the period 1949-1958 was after discharging from this position in Prague relocated to an insignificant and substandard command position at a district military administration in Slovakia. His cryptographic experience was of no use in his new position. To profit from his previous experience as a high qualified cryptographer he started to study the accessible literature and archive materials about the usage of the Czechoslovak cipher systems during the WWII. The result of this his activity were some manuscripts where he deciphered and analyzed some Czechoslovak military wireless telegrams. His critical analysis and his conclusions did not meet an understanding or a positive response of historians and were nor accepted for publication. He had no other chance as to send them to archives. Unfortunately only one (in two copies) and a collection of small notes survived. The aim of this paper is to make decisive technical parts of manuscript [K. Cigáň: Impacts of the decryption of the cipher system of the Czechoslovak Ministry of Defence in London from the years 1940-1945 on the resistance movement. Archive of the Slovak National Uprising, Banská Bystrica, Slovakia, Document collection (Fond) V, manuscript no. S36/90, 46 pp.] about the usage of the socalled STP cipher accessible. Thereby we complement the paper [Š. Porubský: STP cipher of the Czechoslovak in-exile Ministry of Defence in London during WWII, in: Proc. of EuroHCC’17, 3rd European Historical Ciphers Colloq., Smolenice Castle, Slovakia, 2017 (J. von zur Gathen et al., eds.), Slovak Univ. of Technology in Bratislava, 2017, pp. 47-66] where the part of this manuscript containing Cigáň’s method for solving STP cipher which he calls “mathematical” is published. To put Cigáň’s analysis and comment into their historical framework we briefly outline the history of Czechoslovak military intelligence activities with emphasis on their cryptological component.

Mots clés

  • STP cipher
  • Josef Růžek
  • Karol Cigáň
  • František Moravec
  • Czechoslovak military cryptography
  • World War II

MSC 2010

  • Primary: 01A60
  • Secondary: 01A70
  • 01A85
Accès libre

Optimization of the High Nonlinear S-Boxes Generation Method

Publié en ligne: 23 Mar 2018
Pages: 93 - 105

Résumé

Abstract

The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear Substitutions for Symmetric Encryption Algorithms. The thesis for the scholarly degree of candidate of technical sciences, speciality 05.13.21 - - Information security systems, Kharkiv National University of Radioelectronics, Kharkiv, 2014. (In Russian)] requires consecutive applications of several criteria for each formed substitution. This paper presents an improvement of the considered method by the appropriate selection of the criteria application order which decreases the required computational power for S-box generation. The proposed modification allows generation of a byte substitution with nonlinearity 104, algebraic immunity 3 and 8-uniformity within approximately 30 minutes of a single PC running time.

Mots clés

  • S-box
  • nonlinearity
  • algebraic immunity
  • vectorial Boolean function

MSC 2010

  • 94A60
  • 68P25
Accès libre

On the Families of Stable Multivariate Transformations of Large Order and Their Cryptographical Applications

Publié en ligne: 23 Mar 2018
Pages: 107 - 117

Résumé

Abstract

Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces Kn over general commutative ring K of with n increasing order can be used in the key exchange protocols and El Gamal multivariate cryptosystems related to them. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via conjugations of two polynomials of kind gk and g−1 given by key holder (Alice) or giving them as elements of different transformation groups. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity.

Mots clés

  • Multivariate cryptography
  • stable transformations
  • key exchange protocols
  • shifted multivariate ElGamal algorithm
  • desynchronisation diagram

MSC 2010

  • Primary 11T71
  • Secondary 11Rxx
Accès libre

Generalized Key Substitution Attacks on Message Recovery Signatures

Publié en ligne: 23 Mar 2018
Pages: 119 - 138

Résumé

Abstract

The generalized key substitution attacks were proposed as a generalization of the key substitution attacks to examine the security of the signature schemes adopted in ISO/IEC (1st CD) 14888-3, which standardizes appendix- -type signature schemes based on the discrete logarithm problem. This paper examines the message recovery signature schemes based on the discrete logarithm problem, adopted in ISO/IEC 9796-3:2006, and shows that all but one scheme are vulnerable to the generalized key substitution attacks.

Mots clés

  • message recovery signature
  • discrete logarithm
  • generalized key substitution attacks

MSC 2010

  • 94A60
Accès libre

Improvement on Bit Diffusion Analysis of π-Cipher

Publié en ligne: 23 Mar 2018
Pages: 139 - 149

Résumé

Abstract

π-Cipher, designed by Gligoroski et al., is a second round candidate of the CAESAR competition. The designers analyzed the bit diffusion of the cipher by examining the * operation and 1 round π-function. We improve this analysis by applying Strict Avalanche Criterion (SAC) test to * operation and reduced round versions of π-function for π 16-Cipher. We found out that * operation fails SAC test whereas all versions of π-function for π 16-Cipher pass the test.

Mots clés

  • The CAESAR competition
  • π-Cipher
  • bit diffusion analysis
  • Strict Avalanche Criterion (SSAC) test

MSC 2010

  • 00A69
  • 94A60
  • 94A62
  • 60K35
  • 49J55
Accès libre

Key Exchange Over Particular Algebraic Closure Ring

Publié en ligne: 23 Mar 2018
Pages: 151 - 162

Résumé

Abstract

In this paper, we propose a new method of Diffie-Hellman key exchange based on a non-commutative integral closure ring. The key idea of our proposal is that for a given non-commutative ring, we can define the secret key and take it as a common key to encrypt and decrypt the transmitted messages. By doing, we define a new non-commutative structure over the integral closure OL of sextic extension L, namely L is an extension of ℚ of degree 6 in the form ℚ(α, β), which is a rational quadratic and monogenic extension over a non-pure and monogenic cubic subfield K = ℚ(β).

Mots clés

  • integral basis
  • key exchange
  • fully homomorphic cryptosystems
  • cryptography

MSC 2010

  • Primary 11T71
  • Secondary 11Rxx
Accès libre

Connecting the Complexity of MQ- and Code-Based Cryptosystems

Publié en ligne: 23 Mar 2018
Pages: 163 - 177

Résumé

Abstract

We study the connection between the MQ problem and the de­coding problem, through the intermediate MRHS representation. The main goal of this study is to explicitly bound the complexity of solving MQ systems with decoding tools. The main observation is that although the MQ problem over GF(2) can be efficiently transformed to syndrome decoding, the existing general decoding methods are not suitable to solve the system as efficiently as expected from the MQ representation.

Mots clés

  • decoding problem
  • MQ problem
  • MEHS

MSC 2010

  • 94A60
  • 68P25
  • 06E30
Accès libre

Evolutionary Computation in Cryptanalysis of Classical Ciphers

Publié en ligne: 23 Mar 2018
Pages: 179 - 197

Résumé

Abstract

Evolutionary computation has represented a very popular way of problem solving in the recent years. This approach is also capable of effectively solving historical cipher in a fully automated way. This paper deals with empirical cryptanalysis of a monoalphabetic substitution using a genetic algorithm (GA) and a parallel genetic algorithm (PGA). The key ingredient of our contribution is the parameter analysis of GA and PGA. We focus on how these parameters affect the success rate of solving the monoalphabetic substitution.

Mots clés

  • historical ciphers
  • grid
  • MPI
  • genetic algorithm
  • parallel genetic algorithm

MSC 2010

  • 94A60
  • 68P25
Accès libre

Power Series with Inverse Binomial Coefficients and Harmonic Numbers

Publié en ligne: 23 Mar 2018
Pages: 199 - 206

Résumé

Abstract

In this note we compute the generating function for the numbers terms of elementary functions and dilogarithms.

Mots clés

  • central binomial coefficients
  • reciprocals of binomial coefficients
  • harmonic numbers
  • generating functions
  • Euler series transformation
  • binomial identities

MSC 2010

  • 05A15
  • 11B05
Accès libre

On the Diophantine Equation 11 + 2X+2 + (7)3Y = Z2

Publié en ligne: 23 Mar 2018
Pages: 207 - 209

Résumé

Abstract

In this note, we investigate solutions of the Diophantine equation 11 + 2x+2 + (7)3y = z2 (x, y, z) ∈ℕ3

Mots clés

  • exponential Diophantine equations

MSC 2010

  • 11D61

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