Cube Testers and Key Recovery Attacks On Reduced-Round MD6 and Trivium

CRYPTO 2008 saw the introduction of the hash function MD6 and of cube attacks, a type of algebraic attack applicable to cryptographic functions having a low-degree algebraic normal form over GF(2). This paper applies cube attacks to reduced round MD6, finding the full 128-bit key of a 14-round MD6 with complexity 2^22 (which takes less than a minute on a single PC). This is the best key recovery attack announced so far for MD6. We then introduce a new class of attacks called cube testers, based on efficient property-testing algorithms, and apply them to MD6 and to the stream cipher Trivium. Unlike the standard cube attacks, cube testers detect nonrandom behavior rather than performing key extraction, but they can also attack cryptographic schemes described by nonrandom polynomials of relatively high degree. Applied to MD6, cube testers detect nonrandomness over 18 rounds in 2^17 complexity; applied to a slightly modified version of the MD6 compression function, they can distinguish 66 rounds from random in 2^24 complexity. Cube testers give distinguishers on Trivium reduced to 790 rounds from random with 2^30 complexity and detect nonrandomness over 885 rounds in 2^27, improving on the original 767-round cube attack

A 32‐society investigation of the influence of perceived economic inequality on social class stereotyping

There is a growing body of work suggesting that social class stereotypes are amplified when people perceive higher levels of economic inequality—that is, the wealthy are perceived as more competent and assertive and the poor as more incompetent and unassertive. The present study tested this prediction in 32 societies and also examines the role of wealth-based categorization in explaining this relationship. We found that people who perceived higher economic inequality were indeed more likely to consider wealth as a meaningful basis for categorization. Unexpectedly, however, higher levels of perceived inequality were associated with perceiving the wealthy as less competent and assertive and the poor as more competent and assertive. Unpacking this further, exploratory analyses showed that the observed tendency to stereotype the wealthy negatively only emerged in societies with lower social mobility and democracy and higher corruption. This points to the importance of understanding how socio-structural features that co-occur with economic inequality may shape perceptions of the wealthy and the poor.info:eu-repo/semantics/publishedVersio

Efficient and Provable White-Box Primitives

International audienceIn recent years there have been several attempts to build white-box block ciphers whose implementations aim to be incompress-ible. This includes the weak white-box ASASA construction by Bouil-laguet, Biryukov and Khovratovich from Asiacrypt 2014, and the recent space-hard construction by Bogdanov and Isobe from CCS 2015. In this article we propose the first constructions aiming at the same goal while offering provable security guarantees. Moreover we propose concrete instantiations of our constructions, which prove to be quite efficient and competitive with prior work. Thus provable security comes with a surprisingly low overhead

FPL: White-Box Secure Block Cipher Using Parallel Table Look-Ups

In this work, we propose a new table-based block cipher structure, dubbed $\mathsf{FPL}$, that can be used to build white-box secure block ciphers. Our construction is a balanced Feistel cipher, where the input to each round function determines multiple indices for the underlying table via a probe function, and the sum of the values from the table becomes the output of the round function. We identify the properties of the probe function that make the resulting block cipher white-box secure in terms of weak and strong space hardness against known-space and non-adaptive chosen-space attacks. Our construction, enjoying rigorous provable security without relying on any ideal primitive, provides flexibility to the block size and the table size, and permits parallel table look-ups. We also propose a concrete instantiation of $\mathsf{FPL}$, dubbed $\mathsf{FPL}_{\mathsf{AES}}$, using (round-reduced) $\mathsf{AES}$ for the underlying table and probe functions. Our implementation shows that $\mathsf{FPL}_{\mathsf{AES}}$ provides stronger security without significant loss of efficiency, compared to existing schemes including $\mathsf{SPACE}$, $\mathsf{WhiteBlock}$ and $\mathsf{WEM}$

Exponentiating in Pairing Groups

We study exponentiations in pairing groups for the most common security levels and show that, although the Weierstrass model is preferable for pairing computation, it can be worthwhile to map to alternative curve representations for the non-pairing group operations in protocols

Risky Traitor Tracing and New Differential Privacy Negative Results

In this work we seek to construct collusion-resistant traitor tracing systems with small ciphertexts from standard assumptions that also move toward practical efficiency. In our approach we will hold steadfast to the principle of collusion resistance, but relax the requirement on catching a traitor from a successful decoding algorithm. We define a $f$-risky traitor tracing system as one where the probability of identifying a traitor is $f(\lambda,n)$ times the probability a successful box is produced. We then go on to show how to build such systems from prime order bilinear groups with assumptions close to those used in prior works. Our core system achieves, for any $k > 0$, $f(\lambda,n) \approx \frac{k}{n + k - 1}$ where ciphertexts consists of $(k + 4)$ group elements and decryption requires $(k + 3)$ pairing operations. At first glance the utility of such a system might seem questionable since the $f$ we achieve for short ciphertexts is relatively small. Indeed an attacker in such a system can more likely than not get away with producing a decoding box. However, we believe this approach to be viable for four reasons: 1. A risky traitor tracing system will provide deterrence against risk averse attackers. In some settings the consequences of being caught might bear a high cost and an attacker will have to weigh his utility of producing a decryption $D$ box against the expected cost of being caught. 2. Consider a broadcast system where we want to support low overhead broadcast encrypted communications, but will periodically allow for a more expensive key refresh operation. We refer to an adversary produced algorithm that maintains the ability to decrypt across key refreshes as a persistent decoder. We show how if we employ a risky traitor tracing systems in this setting, even for a small $f$, we can amplify the chances of catching such a ``persistent decoder\u27\u27 to be negligibly close to 1. 3. In certain resource constrained settings risky traitor tracing provides a best tracing effort where there are no other collusion-resistant alternatives. For instance, suppose we had to support 100K users over a radio link that had just 10KB of additional resources for extra ciphertext overhead. None of the existing $\sqrt N$ bilinear map systems can fit in these constraints. On the other hand a risky traitor tracing system provides a spectrum of tracing probability versus overhead tradeoffs and can be configured to at least give some deterrence in this setting. 4. Finally, we can capture impossibility results for differential privacy from $\frac{1}{n}$-risky traitor tracing. Since our ciphertexts are short ($O(\lambda)$), we get the negative result which matches what one would get plugging in the obfuscation based tracing system Boneh-Zhandry (CRYPTO 2014) solution into the prior impossibility result of Dwork et al. (STOC 2009)

Attacks and Countermeasures for White-box Designs

In traditional symmetric cryptography, the adversary has access only to the inputs and outputs of a cryptographic primitive. In the white-box model the adversary is given full access to the implementation. He can use both static and dynamic analysis as well as fault analysis in order to break the cryptosystem, e.g. to extract the embedded secret key. Implementations secure in such model have many applications in industry. However, creating such implementations turns out to be a very challenging if not an impossible task. Recently, Bos et al. proposed a generic attack on white-box primitives called differential computation analysis (DCA). This attack was applied to many white-box implementations both from academia and industry. The attack comes from the area of side-channel analysis and the most common method protecting against such attacks is masking, which in turn is a form of secret sharing. In this paper we present multiple generic attacks against masked white-box implementations. We use the term “masking” in a very broad sense. As a result, we deduce new constraints that any secure white-box implementation must satisfy. Based on the new constraints, we develop a general method for protecting white-box implementations. We split the protection into two independent components: value hiding and structure hiding. Value hiding must pro- vide protection against passive DCA-style attacks that rely on analysis of computation traces. Structure hiding must provide protection against circuit analysis attacks. In this paper we focus on developing the value hiding component. It includes protection against the DCA attack by Bos et al. and protection against a new attack called algebraic attack. We present a provably secure first-order protection against the new al- gebraic attack. The protection is based on small gadgets implementing secure masked XOR and AND operations. Furthermore, we give a proof of compositional security allowing to freely combine secure gadgets. We derive concrete security bounds for circuits built using our construction