A Systematic Analysis of the Juniper Dual EC Incident

In December 2015, Juniper Networks announced that unknown attackers had added unauthorized code to ScreenOS, the operating system for their NetScreen VPN routers. This code created two vulnerabilities: an authentication bypass that enabled remote administrative access, and a second vulnerability that allowed passive decryption of VPN traffic. Reverse engineering of ScreenOS binaries revealed that the first of these vulnerabilities was a conventional back door in the SSH password checker. The second is far more intriguing: a change to the Q parameter used by the Dual EC pseudorandom number generator. It is widely known that Dual EC has the unfortunate property that an attacker with the ability to choose Q can, from a small sample of the generator\u27s output, predict all future outputs. In a 2013 public statement, Juniper noted the use of Dual EC but claimed that ScreenOS included countermeasures that neutralized this form of attack. In this work, we report the results of a thorough independent analysis of the ScreenOS randomness subsystem, as well as its interaction with the IKE VPN key establishment protocol. Due to apparent flaws in the code, Juniper\u27s countermeasures against a Dual EC attack are never executed. Moreover, by comparing sequential versions of ScreenOS, we identify a cluster of additional changes that were introduced concurrently with the inclusion of Dual EC in a single 2008 release. Taken as a whole, these changes render the ScreenOS system vulnerable to passive exploitation by an attacker who selects Q. We demonstrate this by installing our own parameters, and showing that it is possible to passively decrypt a single IKE handshake and its associated VPN traffic in isolation without observing any other network traffic

Verified Correctness and Security of mbedTLS HMAC-DRBG

We have formalized the functional specification of HMAC-DRBG (NIST 800-90A), and we have proved its cryptographic security--that its output is pseudorandom--using a hybrid game-based proof. We have also proved that the mbedTLS implementation (C program) correctly implements this functional specification. That proof composes with an existing C compiler correctness proof to guarantee, end-to-end, that the machine language program gives strong pseudorandomness. All proofs (hybrid games, C program verification, compiler, and their composition) are machine-checked in the Coq proof assistant. Our proofs are modular: the hybrid game proof holds on any implementation of HMAC-DRBG that satisfies our functional specification. Therefore, our functional specification can serve as a high-assurance reference.Comment: Appearing in CCS '1

Unifying Kleptographic Attacks

We present two simple backdoors that can be implemented into Maurer\u27s unified zero-knowledge protocol. Thus, we show that a high level abstraction can replace individual backdoors embedded into protocols for proving knowledge of a discrete logarithm (e.g. the Schnorr and Girault protocols), protocols for proving knowledge of an $e^{th}$-root (e.g. the Fiat-Shamir and Guillou-Quisquater protocols), protocols for proving knowledge of a discrete logarithm representation (e.g. the Okamoto protocol) and protocols for proving knowledge of an $e^{th}$-root representation

Data Structures Meet Cryptography: 3SUM with Preprocessing

This paper shows several connections between data structure problems and cryptography against preprocessing attacks. Our results span data structure upper bounds, cryptographic applications, and data structure lower bounds, as summarized next. First, we apply Fiat--Naor inversion, a technique with cryptographic origins, to obtain a data structure upper bound. In particular, our technique yields a suite of algorithms with space $S$ and (online) time $T$ for a preprocessing version of the $N$-input 3SUM problem where $S^3\cdot T = \widetilde{O}(N^6)$. This disproves a strong conjecture (Goldstein et al., WADS 2017) that there is no data structure that solves this problem for $S=N^{2-\delta}$ and $T = N^{1-\delta}$ for any constant $\delta>0$. Secondly, we show equivalence between lower bounds for a broad class of (static) data structure problems and one-way functions in the random oracle model that resist a very strong form of preprocessing attack. Concretely, given a random function $F: [N] \to [N]$ (accessed as an oracle) we show how to compile it into a function $G^F: [N^2] \to [N^2]$ which resists $S$-bit preprocessing attacks that run in query time $T$ where $ST=O(N^{2-\varepsilon})$ (assuming a corresponding data structure lower bound on 3SUM). In contrast, a classical result of Hellman tells us that $F$ itself can be more easily inverted, say with $N^{2/3}$-bit preprocessing in $N^{2/3}$ time. We also show that much stronger lower bounds follow from the hardness of kSUM. Our results can be equivalently interpreted as security against adversaries that are very non-uniform, or have large auxiliary input, or as security in the face of a powerfully backdoored random oracle. Thirdly, we give non-adaptive lower bounds for 3SUM and a range of geometric problems which match the best known lower bounds for static data structure problems

Subliminal Hash Channels

Due to their nature, subliminal channels are mostly regarded as being malicious, but due to recent legislation efforts users\u27 perception might change. Such channels can be used to subvert digital signature protocols without degrading the security of the underlying primitive. Thus, it is natural to find countermeasures and devise subliminal-free signatures. In this paper we discuss state-of-the-art countermeasures and introduce a generic method to bypass them

DiSSECT: Distinguisher of Standard & Simulated Elliptic Curves via Traits

It can be tricky to trust elliptic curves standardized in a non-transparent way. To rectify this, we propose a systematic methodology for analyzing curves and statistically comparing them to the expected values of a large number of generic curves with the aim of identifying any deviations in the standard curves. For this purpose, we put together the largest publicly available database of standard curves. To identify unexpected properties of standard generation methods and curves, we simulate over 250 000 curves by mimicking the generation process of four standards. We compute 22 different properties of curves and analyze them with automated methods to pinpoint deviations in standard curves, pointing to possible weaknesses

Threshold Kleptographic Attacks on Discrete Logarithm Based Signatures

In an $\ell$ out of $n$ threshold scheme, $\ell$ out of $n$ members must cooperate to recover a secret. A kleptographic attack is a backdoor which can be implemented in an algorithm and further used to retrieve a user\u27s secret key. We combine the notions of threshold scheme and kleptographic attack to construct the first $\ell$ out of $n$ threshold kleptographic attack on discrete logarithm based digital signatures and prove its security in the standard and random oracle models