Algorithmically Distinguishing Irreducible Characters of the Symmetric Group

Suppose that $\chi_\lambda$ and $\chi_\mu$ are distinct irreducible characters of the symmetric group $S_n$. We give an algorithm that, in time polynomial in $n$, constructs $\pi\in S_n$ such that $\chi_\lambda(\pi)$ is provably different from $\chi_\mu(\pi)$. In fact, we show a little more. Suppose $f = \chi_\lambda$ for some irreducible character $\chi_\lambda$ of $S_n$, but we do not know $\lambda$, and we are given only oracle access to $f$. We give an algorithm that determines $\lambda$, using a number of queries to $f$ that is polynomial in $n$. Each query can be computed in time polynomial in $n$ by someone who knows $\lambda$.

Values of rational functions in small subgroups of finite fields and the identity testing problem from powers

Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a finite field [Formula: see text] considered as a linear space over a subfield [Formula: see text]. We apply this to the recently introduced algorithmic problem of identity testing of “hidden” polynomials [Formula: see text] and [Formula: see text] over a high degree extension of a finite field, given oracle access to [Formula: see text] and [Formula: see text].

Why Attackers Lose: Design and Security Analysis of Arbitrarily Large XOR Arbiter PUFs

In a novel analysis, we show that arbitrarily many Arbiter PUFs can be combined into a stable XOR Arbiter PUF. To the best of our knowledge, this design cannot be modeled by any known oracle access attack in polynomial time.Using majority vote of Arbiter Chain responses, our analysis shows that with a polynomial number of votes the XOR Arbiter PUF stability of almost all challenges can be boosted exponentially close to 1; that is, the stability gain through majority voting can exceed the stability loss introduced by large XORs for a feasible number of votes. Hence, our proposal enables the designer to increase the attacker's effort exponentially while still maintaining polynomial design effort for all known oracle access modeling attacks. This is the first result that relates PUF design to this traditional cryptographic design principle.

Quantum conditional query complexity

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain highly efficient quantum algorithms for identity testing, equivalence testing and uniformity testing of probability distributions; (b) study the power of these oracles for testing properties of boolean functions, and obtain an algorithm for checking whether an n-input m-output boolean function is balanced or e-far from balanced; and (c) give an algorithm, requiring O˜(n/e) queries, for testing whether an n-dimensional quantum state is maximally mixed or not.

Using Simon's algorithm to attack symmetric-key cryptographic primitives

We present new connections between quantum information and the field of classical cryptography. In particular, we provide examples where Simon’s algorithm can be used to show insecurity of commonly used cryptographic symmetric-key primitives. Specifically, these examples consist of a quantum distinguisher for the 3-round Feistel network and a forgery attack on CBC-MAC which forges a tag for a chosen-prefix message querying only other messages (of the same length). We assume that an adversary has quantum-oracle access to the respective classical primitives. Similar results have been achieved recently in independent work by Kaplan et al. [KLLNP16]. Our findings shed new light on the post-quantum security of cryptographic schemes and underline that classical security proofs of cryptographic constructions need to be revisited in light of quantum attackers.

General Design and Implementation of Heterogeneous Data Conversion Tools

We will undertake an in-depth analysis of the data conversion,and take a detailed study of thoughts and realization methods of data conversion. On the basis of methods above-mentioned,we design and implement the sofeware of the data conversion between the heterogeneous databases of MS SQL Server,Oracle,Access,Excel.