Aris Tentes

Commitments and efficient zero-knowledge proofs from learning parity with noise

We construct a perfectly binding string commitment scheme whose security is based on the learning parity with noise (LPN) assumption, or equivalently, the hardness of decoding random linear codes. Our scheme not only allows for a simple and efficient zero-knowledge proof of knowledge for committed values (essentially a Σ-protocol), but also for such proofs showing any kind of relation amongst committed values, i.e., proving that messages m0,…,mu, are such that m0=C(m1,…,mu) for any circuit C. To get soundness which is exponentially small in a security parameter t, and when the zero-knowledge property relies on the LPN problem with secrets of length l, our 3 round protocol has communication complexity

Hardness preserving constructions of pseudorandom functions

{\mathcal O}(t|C|\ell\log(\ell))

On the Connection between Interval Size Functions and Path Counting

and computational complexity of

Efficient Network-Based Enforcement of Data Access Rights

{\mathcal O}(t|C|\ell)

On the instantiability of hash-and-sign RSA signatures

bit operations. The hidden constants are small, and the computation consists mostly of computing inner products of bit-vectors.

Coin flipping of any constant bias implies one-way functions

We show a hardness-preserving construction of a PRF from any length doubling PRG which improves upon known constructions whenever we can put a non-trivial upper bound q on the number of queries to the PRF. Our construction requires only O(logq) invocations to the underlying PRG with each query. In comparison, the number of invocations by the best previous hardness-preserving construction (GGM using Levins trick) is logarithmic in the hardness of the PRG. For example, starting from an exponentially secure PRG {0,1}n ↦{0,1}2n, we get a PRF which is exponentially secure if queried at most q = exp(√n) times and where each invocation of the PRF requires Θ(√n) queries to the underlying PRG. This is much less than the Θ(n) required by known constructions.

On the (In)Security of RSA Signatures.

We investigate the complexity of hard counting problems that belong to the class #P but have easy decision version; several well-known problems such as # Perfect Matchings , # DNFSat share this property. We focus on classes of such problems which emerged through two disparate approaches: one taken by Hemaspaandra et al. [1] who defined classes of functions that count the size of intervals of ordered strings, and one followed by Kiayias et al. [2] who defined the class TotP, consisting of functions that count the total number of paths of NP computations. We provide inclusion and separation relations between TotP and interval size counting classes, by means of new classes that we define in this work. Our results imply that many known #P-complete problems with easy decision are contained in the classes defined in [1]--but are unlikely to be complete for these classes under certain types of reductions. We also define a new class of interval size functions which strictly contains FP and is strictly contained in TotP under reasonable complexity-theoretic assumptions. We show that this new class contains some hard counting problems.

On the connection between interval size functions and path counting

Today, databases, especially those serving/connected to the Internet need strong protection against data leakage stemming from misconfiguration, as well as from attacks, such as SQL injection.