Geavanceerde Cryptografie voor Moderne Gegevensbeveiliging: Bewijsbaar Veilige en Efficiënte Symmetrische-Sleutel Modi van Uitbreidende Primitieven

This thesis explores and advances symmetric-key cryptography for modern data security by systematically investigating the design and application of expanding primitives -- cryptographic functions such as forkciphers, multi-forkciphers, and expanding pseudorandom functions that map fixed-length inputs to larger, structured outputs. We demonstrate that these primitives, when integrated into tailored modes of operation, enable enhanced security guarantees, including beyond-birthday-bound (BBB) security and improved robustness against nonce misuse and the release of unverified plaintexts (RUP), coupled with significant performance benefits. The core contributions include: 1. The formalization of the multiforkcipher and its use in the BBB-secure GCTR encryption family; 2. the introduction of the xor-related-tweakey security model and the Sonikku family of fast, BBB-secure message authentication codes; 3. the definition of the strong OAE-RUP security notion for online authenticated encryption with associated data (AEAD) schemes and the validation of SAEF mode under this notion; 4. the conceptualization of a secure IoT-to-Cloud computation framework (where IoT stands for Internet-of-Things) and the design of the Eevee AEAD family optimized for this transciphering scenario; and 5. the development of the DExt_f extended randomness extractor and the high-performance Skye key derivation function for source-aware key derivation in protocols such as end-to-end encrypted Signal messaging service. Through rigorous provable security analyses, often in the standard model, and concrete performance evaluations, this work provides a suite of novel, efficient, and provably secure cryptographic tools. These contributions deliver significant improvements for a wide range of applications, from secure messaging and IoT security to high-volume data encryption and secure multi-party computation, highlighting the transformative potential of expanding primitives in addressing contemporary cryptographic challenges.