Related papers: Collision-resistant hash-shuffles on the reals
Imagine handling collisions in a hash table by storing, in each cell, the bit-wise exclusive-or of the set of keys hashing there. This appears to be a terrible idea: For $\alpha n$ keys and $n$ buckets, where $\alpha$ is constant, we expect…
The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an…
Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an…
We propose a hash function based on arithmetic coding and public-key cryptography. The resistance of the hash function to second preimage attack, collision and differential cryptanalysis is based on the properties of arithmetic coding as a…
Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most…
Iterated hash functions process strings recursively, one character at a time. At each iteration, they compute a new hash value from the preceding hash value and the next character. We prove that iterated hashing can be pairwise independent,…
HighwayHash is a new pseudo-random function based on SIMD multiply and permute instructions for thorough and fast hashing. It is 5.2 times as fast as SipHash for 1 KiB inputs. An open-source implementation is available under a permissive…
We study randomness properties of graphs and hypergraphs generated by simple hash functions. Several hashing applications can be analyzed by studying the structure of $d$-uniform random ($d$-partite) hypergraphs obtained from a set $S$ of…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…
The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
Random hashing can provide guarantees regarding the performance of data structures such as hash tables---even in an adversarial setting. Many existing families of hash functions are universal: given two data objects, the probability that…
Secret sharing schemes create an effective method to safeguard a secret by dividing it among several participants. By using hash functions and the herding hashes technique, we first set up a (t+1, n) threshold scheme which is perfect and…
This text presents the proofs of the technical facts underlying theoretical justification of the convergence and performance of the novel algorithm for reactive navigation of differential drive wheeled robots in dynamic uncertain…
Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces. The basic idea is that similar objects should produce hash collisions with probability significantly…
We show how to construct pseudorandom permutations (PRPs) that remain secure even if the adversary can query the permutation, both in the forward and reverse directions, on a quantum superposition of inputs. Such quantum-secure PRPs have…
The characteristic function of row contractions and liftings of row contractions are complete invariants up to unitary equivalence for row contractions and liftings of row contractions, respectively. We provide alternate proofs for these…
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.