Getting SYMmetric CryPtography Out of its Comfort ZONe

Our lives are profoundly affected by the digitization of data, and the amount of sensitive data that is shared on cloud storage grows considerably every day.Whenever sensitive data is collected, manipulated, exchanged, analyzed, and retained, symmetric cryptography is used.The most commonly used and famous symmetric cryptography algorithms are AES and Keccak/SHA-3.Due to their importance, the entire research community focuses its attention on such schemes, with the result that the great majority of the symmetric primitives recently published resemble them.While positive at first glance, the limits of this approach and of the current state of the art are appearing in several contexts.First, the similarity of such schemes caused a performance flatness, with no substantial improvement recently achieved.Next, our understanding of their security has not fundamentally improved in the course of the last years, since their security arguments are still based on unverified and often false assumptions.Finally, and more importantly, the current bit-oriented schemes are *not* suitable for rising applications of practical importance such as Format Preserving Encryption, Multi-Party Computation, Fully Homomorphic Encryption, and Zero-Knowledge, which naturally operate over prime fields and/or integer rings.The only way we can overcome these fundamental problems is by considering non-standard innovative approaches for designing secure and efficient symmetric primitives.Within the SYMPZON project, I plan to reshape the whole process of designing symmetric primitives by- developing design strategies for defeating attacks against symmetric primitives that mainly operate over integer rings;- constructing new cryptographic components over integer rings that admit an efficient bit-representation.This will lead to revolutionary symmetric primitives dedicated to targeting the rising number of applications operating over rings, with unprecedent security arguments and performances.