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Multivariate cryptography
Jančaříková, Irena ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
This thesis deals with multivariate cryptography. It includes specifically a description of the MQ problem and the proof of it's NP-completness. In the part of the MQ problem there is a description of a general pattern for the creation of the public part of asymetric cryptosystems based on the MQ problem. It this part the thesis describes the QMLE problem, which is important for the figure of the cryptosystem private key based on the MQ problem. Further, the thesis includes a description of the influence of the structure display, which appears in the QMLE problem, on time solution complexity of QMLE problem. The influence of time complexity has been detected by means of experimental measurement with programed algorithm. At the end of the thesis there is specified description of selected multivariety cryptosystems based on the MQ problem. Selected cryptosystems are provided with detailed description of encryption and decryption by means of selected cryptosystems and time estimations of these operations. The thesis includes estimations of memory requirements on saving of private and public key of the selected cryptosystems. Powered by TCPDF (www.tcpdf.org)
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MQ problem
Středa, Adolf ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
The aim of this thesis is to describe a general MQ Problem with a focus on its variant called HFE, outline several attacks on a basic scheme based on HFE and describe a new attack on HFEz, a cryptosystem based on special polynomials over finite fields with a modification, which discards a portion of the output from the initial transformation. This ensures a dependency on more variables while keeping the same size of the field. The attack starts with a translation of HFE into HFE with branches, followed by a branch separating algorithm described in [Fel06]. The separation algorithm uses the public key to derive an operation, which induces (with addition) a non-associative algebra. Utilising some properties of non-associative algebras, a matrix, which can separate variables into distinct sets according to branches, is calculated. This leads to stripping off the HFEz modification and thus allowing us to attack directly the HFE polynomial. Powered by TCPDF (www.tcpdf.org)
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MQ problem
Středa, Adolf ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
The aim of this thesis is to describe a general MQ Problem with a focus on its variant called HFE, outline several attacks on a basic scheme based on HFE and describe a new attack on HFEz, a cryptosystem based on special polynomials over finite fields with a modification, which discards a portion of the output from the initial transformation. This ensures a dependency on more variables while keeping the same size of the field. The attack starts with a translation of HFE into HFE with branches, followed by a branch separating algorithm described in [Fel06]. The separation algorithm uses the public key to derive an operation, which induces (with addition) a non-associative algebra. Utilising some properties of non-associative algebras, a matrix, which can separate variables into distinct sets according to branches, is calculated. This leads to stripping off the HFEz modification and thus allowing us to attack directly the HFE polynomial. Powered by TCPDF (www.tcpdf.org)
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Multivariate cryptography
Jančaříková, Irena ; Žemlička, Jan (advisor) ; Růžička, Pavel (referee)
This thesis deals with multivariate cryptography. It includes specifically a description of the MQ problem and the proof of it's NP-completness. In the part of the MQ problem there is a description of a general pattern for the creation of the public part of asymetric cryptosystems based on the MQ problem. It this part the thesis describes the QMLE problem, which is important for the figure of the cryptosystem private key based on the MQ problem. Further, the thesis includes a description of the influence of the structure display, which appears in the QMLE problem, on time solution complexity of QMLE problem. The influence of time complexity has been detected by means of experimental measurement with programed algorithm. At the end of the thesis there is specified description of selected multivariety cryptosystems based on the MQ problem. Selected cryptosystems are provided with detailed description of encryption and decryption by means of selected cryptosystems and time estimations of these operations. The thesis includes estimations of memory requirements on saving of private and public key of the selected cryptosystems. Powered by TCPDF (www.tcpdf.org)
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