On the security of symmetric-key cryptographic primitives

Topics: Symmetric-key cryptography, cryptanalysis and provable security

Title:

On the security of symmetric-key cryptographic primitives

Brief Project Description:

Block ciphers serve as foundational components in numerous cryptographic constructions, including authenticated encryption schemes and hash functions. Hash functions, in return, are building blocks in many cryptographic protocols such as digital signatures and zero-knowledge proofs. Established paradigms for block cipher designs encompass the generalized Feistel network, substitution-permutation network, and add-rotate-XOR (ARX) constructions. Similarly, standardized hash functions follow well-established designs like the Merkle-Damgard transformation and the sponge construction.

In the past, researchers have investigated the provable security guarantees provided by these classical design paradigms. However, further understanding of these designs in terms of how close to their ideal version they are in certain settings is yet to be explored. In this project, we will aim to understand these design paradigms under the notion of indifferentiability. This definitional notion allows us to reason how well a construction of a primitive models the ideal version of that primitive (under some assumptions). This goes beyond the typical security considerations of these primitives where the definitions test how they behave as a standalone object, whereas what may be needed in many instances is to understand how well these primitives behave when instantiated as an underlying component of a larger cryptographic protocol.

One of the aims of this project will be to contribute towards the understanding of such security for block cipher designs -- both through weakening previously made assumptions and through analysing newer constructions. In particular, we aim to understand whether certain block cipher constructions (with suitable underlying primitives) can behave as an ideal cipher.

Further, significant attention has turned toward building hash functions that are useful in specific contexts such as zero-knowledge proofs and post-quantum signature schemes. Another aim of this project will be to deepen our understanding of the security of these underlying hash functions that have been developed for such contexts. In particular, we aim to understand how well such a hash function construction can model a random oracle with appropriate underlying primitives.