In the (preprocessing) Decisional Diffie-Hellman (DDH) problem, we are given a cyclic group G with a generator g and a prime order N, and want to prepare some advice of S, such that we can efficiently distinguish (gx,gy,gxy) from (gx,gy,gz) in time T for uniformly and independently chosen x,y,z from [N]. This is a central cryptographic problem whose computational hardness underpins many widely deployed schemes such as the Diffie–Hellman key exchange protocol.

In the past few years, we have seen multiple attacks on one-dimensional databases that support range queries. These attacks achieve full database reconstruction by exploiting access pattern leakage along with known query distribution or search pattern leakage. We are the first to go beyond one dimension, exploring this threat in two dimensions. We unveil an intrinsic limitation of reconstruction attacks by showing that there can be an exponential number of distinct databases that produce equivalent leakage. Next, we present a full database reconstruction attack. Our algorithm runs in polynomial time and returns a poly-size encoding of all databases consistent with the given leakage profile. We implement our algorithm and observe real-world databases that admit a large number of equivalent databases, which aligns with our theoretical results.

Breach in password databases has been a frequent phenomena in the software industry. Often these breaches go undetected for years. Sometimes, even the companies involved are not aware of the breach. Even after they are detected, publicizing such attacks might not always be in the best interest of the companies. This calls for a strong breach detection mechanism. Juels et al. (in ACM-CCS 2013) suggest a method called ‘Honeywords’, for detecting password database breaches. Their idea is to generate multiple fake passwords, called honeywords and store them along with the real password. Any login attempt with honeywords is identified as a compromise of the password database, since legitimate users are not expected to know the honeywords corresponding to their passwords. The key components of their idea are (i) generation of honeywords, (ii) typo-safety measures for preventing false alarms, (iii) alarm policy upon detection, and (iv) testing robustness of the system against various attacks. In this work, we analyze the limitations of existing honeyword generation techniques. We propose a new attack model called ‘Multiple System Intersection attack considering Input’. We show that the ‘Paired Distance Protocol’ proposed by Chakraborty et al., is not secure in this attack model. We also propose new and more practical honeyword generation techniques and call them the ‘evolving-password model’, the ‘user-profile model’, and the ‘append-secret model’. These techniques achieve ‘approximate flatness’, implying that the honeywords generated using these techniques are indistinguishable from passwords with high probability. Our proposed techniques overcome most of the risks and limitations associated with existing techniques. We prove flatness of our ‘evolving-password model’ technique through experimental analysis. We provide a comparison of our proposed models with the existing ones under various attack models to justify our claims.