Cryptoanalysis by means of numerical methods

The transition to the electronic world raises increasing challenges for privacy, security, financial regulation, and intellectual property. Security in the electronic can be ensured only by using cryptographic operations like encryption, authentication and hashing. Due to the rapid evolutions in computing technology, old cryptography outdates quickly and new demands arise all the time. Hence the need for continuous evaluation of the security of existing techniques and creation of new cryptographic techniques. Symmetric algorithms are the workhorses of cryptography. There are no symmetric algorithms that come with a formal proof of security, hence continuous evaluation is a necessity. In the early 1990`s first Biham and Shamir, and later Matsui published two general techniques to cryptanalyze mainly symmetric, cryptographic algorithms. These techniques have been used with great success to break ---at least in an academic sense--- many existing ciphers, including the Data Encryption Standard (DES). For the next 10 years, researchers have been studying, applying and generalizing these cryptanalysis methods. Furthermore, several design strategies have been proposed in order to create ciphers that resist these attacks. Nowadays, mandatory requirements for new cipher proposals are that they are backed up by an analysis of the resistance of the proposed cipher against at least the basic forms of linear and differential cryptanalysis. Although there has been significant progress in the construction of symmetric cryptographic algorithms which can be proven to be secure against several types of attacks, general proofs of security can still not be given. Hence, this research field progresses by designing ciphers which are secure against known attacks and by subjecting them constantly to new methods of analysis. The primary goal of this project is to apply numerical solving methods in the cryptanalysis of symmetric cryptographic primitives. We will study whether numerical methods can be used with success to improve existing cryptanalytic attacks and as a new method for cryptanalysis in its own right. The target cryptographic algorithms of our analysis will be hash functions and stream ciphers. We anticipate that the application of numerical solvers may lead to new insights in the structure of the cryptographic algorithm under investigation. Finally, this research will lead to the definition of new design criteria, which improve resistance against this type of attacks.

The transition to the electronic world raises increasing challenges for privacy, security, financial regulation, and intellectual property. Security in the electronic can be ensured only by using cryptographic operations like encryption, authentication and hashing. Due to the rapid evolutions in computing technology, old cryptography outdates quickly and new demands arise all the time. Hence the need for continuous evaluation of the security of existing techniques and creation of new cryptographic techniques. Symmetric algorithms are the workhorses of cryptography. There are no symmetric algorithms that come with a formal proof of security, hence continuous evaluation is a necessity. In the early 1990`s first Biham and Shamir, and later Matsui published two general techniques to cryptanalyze mainly symmetric, cryptographic algorithms. These techniques have been used with great success to break - at least in an academic sense - many existing ciphers, including the Data Encryption Standard (DES). For the next 10 years, researchers have been studying, applying and generalizing these cryptanalysis methods. Furthermore, several design strategies have been proposed in order to create ciphers that resist these attacks. Nowadays, mandatory requirements for new cipher proposals are that they are backed up by an analysis of the resistance of the proposed cipher against at least the basic forms of linear and differential cryptanalysis. Although there has been significant progress in the construction of symmetric cryptographic algorithms which can be proven to be secure against several types of attacks, general proofs of security can still not be given. Hence, this research field progresses by designing ciphers which are secure against known attacks and by subjecting them constantly to new methods of analysis. The primary goal of this project is to apply numerical solving methods in the cryptanalysis of symmetric cryptographic primitives. We will study whether numerical methods can be used with success to improve existing cryptanalytic attacks and as a new method for cryptanalysis in its own right. The target cryptographic algorithms of our analysis will be hash functions and stream ciphers. We anticipate that the application of numerical solvers may lead to new insights in the structure of the cryptographic algorithm under investigation. Finally, this research will lead to the definition of new design criteria, which improve resistance against this type of attacks.