The notion of a quantum random walk has emerged as an important element in the development of efficient quantum algorithms. In particular, it makes a dramatic appearance in the most efficient knownâ€¦ (More)

Recent results of Kaplan et al., building on previous work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems are completely broken when exposedâ€¦ (More)

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the securityâ€¦ (More)

We study the hidden subgroup problem (HSP) over groups of the form Gn where G is a group of constant size. While these groups are structurally simpler than the symmetric groups Sn, for which solvingâ€¦ (More)

The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifoldâ€¦ (More)

The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of aâ€¦ (More)

Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerousâ€¦ (More)

In encryption, non-malleability is a highly desirable property: it ensures that adversaries cannot manipulate the plaintext by acting on the ciphertext. In [5], Ambainis et al. gave a definition ofâ€¦ (More)

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group Bn for every n â‰¥ 2. If we view such an operator as aâ€¦ (More)

Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerfulâ€¦ (More)