Boolean functions with optimal stability of their cryptographic indicators under restriction of the inputs

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-Short summary-Encrypting data is essential for ensuring the security of our electronic communications. The main tool for evaluating the security of a symmetric cipher is to examine its resistance to the currently known attack techniques. The ciphers in use are built from smaller components, one of them being a cryptographic Boolean function. Its resistance to known attacks is quantified by cryptographic indicators. We investigate a type of property of Boolean functions which was very little studied before, despite its relevance to actual attacks. Namely, for several cryptographic indicators, we determine how they change when the inputs are maliciously manipulated by an attacker by restricting them to certain types of inputs. Ideally, the cryptographic indicators should be stable, i.e. not change much. We aim to answer questions like: What are the optimal values that can be achieved for the stability of the indicators? How many optimal functions are there? How to construct such functions? How to test if proposed or existing functions (from currently used ciphers) are optimal or close to optimal from this point is view?-Extended summary-Electronic communications are an essential part of everyday life for individuals and for society (e.g. online shopping, banking, e-government). Encrypting the data is a core technique for achieving security of these communications. Two types of cryptography are used: symmetric cryptography (used for the vast majority of the transmitted data) and public-key cryptography (used mainly for key exchange and digital signatures).In symmetric cryptography, the sender encrypts and the receiver decrypts using the same key; it is crucial that the key is kept secret. The symmetric ciphers such as AES (the main current standard), as well as the ciphers used in mobile phones, are built out of several smaller components. Each individual component, as well as the overall system, must satisfy certain cryptographic requirements which makes them resistant to the currently known attack techniques. This project looks at one such component, namely cryptographic Boolean functions, and several indicators that have been developed over time to quantify their resistance to the known cryptographic attacks.Attacks on symmetric ciphers go beyond intercepting encrypted data and attempting to determine the original data. In chosen plaintext attacks, the attacker manipulates the data before encryption in the hope that the corresponding encrypted data will reveal useful information about the key.One simple but effective way to manipulate the input is to only consider inputs that conform to a given pattern, eg. setting the first byte of the data to zero, or setting the first byte to the same value as the second. These examples belong to the more general class of affine subspaces, which we are focusing on in this project.Boolean functions should not only have good values of their cryptographic indicators, but also preserve these good values when subjected to the malicious manipulation of the inputs mentioned above. We will consider several cryptographic and see how they are affected by restriction to affine spaces. For each of these indicators, we will study functions which are optimal from the point of view of maintaining good values of the indicators, understand their mathematical properties, determine how many such functions exist and devise methods of constructing them. We will also examine existing ciphers and determine their behaviour from this point of view.The theoretical results will be published in research journals and conferences. The new functions that we will construct, and the values of the newly introduced parameters computed for existing benchmark functions, will be made publicly available.The new functions and properties studied in the project will contribute to ensuring that new ciphers designed in the future, as well as the protocols based on them, will be less vulnerable to attacks.