Search

We consider the so-called Encrypted Davies-Meyer (EDM) construction, which turns a permutation P on {0,1}n into a function from {0,1}n to {0,1}n defined as P(P(x)⊕x). A similar construction using two independent permutations, namely P′(P(x)⊕x), was previously analyzed by Cogliati and Seurin (Advances in cryptology—CRYPTO 2016 (Proceedings, Part I). LNCS, vol 9814, pp. 121-149, 2016) who showed that when P and P′ are secret and random, then any black-box adversary needs at least roughly 22n/3 queries to distinguish the construction from a uniformly random function from {0,1}n to {0,1}n. In this paper, we focus on the single-permutation variant of the construction. Our main result is that the PRF-security of the single-permutation EDM construction is also (at least) roughly 22n/3, in the sense that any black-box adversary needs at least this number of queries to distinguish the construction from a uniformly random function. This yields the first PRP-to-PRF conversion method which uses a single permutation, does not shrink the original domain nor range of the permutation, and provides security beyond the birthday bound. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the family of quotients of internally quasicontinuous functions. Moreover, we study cardinal invariants related to quotients in the case of internally quasicontinuous functions and the complement of this family. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the family of quotients of internally quasicontinuous functions. Moreover, we study cardinal invariants related to quotients in the case of internally quasicontinuous functions and the complement of this family. [ABSTRACT FROM AUTHOR]

With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]