Differential Analysis of Block Ciphers SIMON and SPECK

In this paper we continue the previous line of research on the analysis of the differential properties of the lightweight block ciphers Simon and Speck. We apply a recently proposed technique for automatic search for differential trails in ARX ciphers and improve the trails in Simon32 and Simon48 previously reported as best. We further extend the search technique for the case of differen- tials and improve the best previously reported differentials on Simon32, Simon48 and Simon64 by exploiting more effectively the strong differential effect of the cipher. We also present improved trails and differentials on Speck32, Speck48 and Speck64. Using these new results we improve the currently best known attacks on several versions of Simon and Speck. A second major contribution of the paper is a graph based algorithm (linear time) for the computation of the exact differential probability of the main building block of Simon: an AND operation preceded by two bitwise shift operations. This gives us a better insight into the differential property of the Simon round function and differential effect in the cipher. Our algorithm is general and works for any rotation constants. The presented techniques are generic and are therefore applicable to a broader class of ARX designs

Unaligned Rebound Attack: Application on Keccak

We analyze the internal permutations of Keccak, one of the NIST SHA-3 competition finalists, in regard to differential properties. By carefully studying the elements composing those permutations, we are able to derive most of the best known differential paths for up to 5 rounds. We use these differential paths in a rebound attack setting and adapt this powerful freedom degrees utilization in order to derive distinguishers for up to 8 rounds of the internal permutations of the submitted version of Keccak. The complexity of the 8 round distinguisher is $2^{491.47}$. Our results have been implemented and verified experimentally on a small version of Keccak. This is currently the best known differential attack against the internal permutations of Keccak

Constructing TI-Friendly Substitution Boxes Using Shift-Invariant Permutations

The threat posed by side channels requires ciphers that can be efficiently protected in both software and hardware against such attacks. In this paper, we proposed a novel Sbox construction based on iterations of shift-invariant quadratic permutations and linear diffusions. Owing to the selected quadratic permutations, all of our Sboxes enable uniform 3-share threshold implementations, which provide first order SCA protections without any fresh randomness. More importantly, because of the shift-invariant property, there are ample implementation trade-offs available, in software as well as hardware. We provide implementation results (software and hardware) for a four-bit and an eight-bit Sbox, which confirm that our constructions are competitive and can be easily adapted to various platforms as claimed. We have successfully verified their resistance to first order attacks based on real acquisitions. Because there are very few studies focusing on software-based threshold implementations, our software implementations might be of independent interest in this regard

The related-key analysis of feistel constructions

Lecture Notes in Computer Science, Volume 8540, 2015.It is well known that the classical three- and four-round Feistel constructions are provably secure under chosen-plaintext and chosen-ciphertext attacks, respectively. However, irrespective of the number of rounds, no Feistel construction can resist related-key attacks where the keys can be offset by a constant. In this paper we show that, under suitable reuse of round keys, security under related-key attacks can be provably attained. Our modification is substantially simpler and more efficient than alternatives obtained using generic transforms, namely the PRG transform of Bellare and Cash (CRYPTO 2010) and its random-oracle analogue outlined by Lucks (FSE 2004). Additionally we formalize Luck’s transform and show that it does not always work if related keys are derived in an oracle-dependent way, and then prove it sound under appropriate restrictions

Rotational-XOR Cryptanalysis of Simon-like Block Ciphers

Rotational-XOR cryptanalysis is a cryptanalytic method aimed at finding distinguishable statistical properties in ARX-C ciphers, i.e., ciphers that can be described only using modular addition, cyclic rotation, XOR, and the injection of constants. In this paper we extend RX-cryptanalysis to AND-RX ciphers, a similar design paradigm where the modular addition is replaced by vectorial bitwise AND; such ciphers include the block cipher families Simon and Simeck. We analyse the propagation of RX-differences through AND-RX rounds and develop closed form formula for their expected probability. Finally, we formulate an SMT model for searching RX-characteristics in simon and simeck. Evaluating our model we find RX-distinguishers of up to 20, 27, and 35 rounds with respective probabilities of $2^{-26}, 2^{-42}$, and $2^{-54}$ for versions of simeck with block sizes of 32, 48, and 64 bits, respectively, for large classes of weak keys in the related-key model. In most cases, these are the longest published distinguishers for the respective variants of simeck. Interestingly, when we apply the model to the block cipher simon, the best distinguisher we are able to find covers 11 rounds of SIMON32 with probability $2^{-24}$. To explain the gap between simon and simeck in terms of the number of distinguished rounds we study the impact of the key schedule and the specific rotation amounts of the round function on the propagation of RX-characteristics in Simon-like ciphers

Improved Differential-Linear Attacks with Applications to ARX Ciphers

We present several improvements to the framework of differential-linear attacks with a special focus on ARX ciphers. As a demonstration of their impact, we apply them to Chaskey and ChaCha and we are able to significantly improve upon the best attacks published so far

Fast Message Franking: From Invisible Salamanders to Encryptment

Message franking enables cryptographically verifiable reporting of abusive content in end-to-end encrypted messaging. Grubbs, Lu, and Ristenpart recently formalized the needed underlying primitive, what they call compactly committing authenticated encryption (AE), and analyzed the security of a number of approaches. But all known secure schemes are still slow compared to the fastest standard AE schemes. For this reason Facebook Messenger uses AES-GCM for franking of attachments such as images or videos. We show how to break Facebook’s attachment franking scheme: a malicious user can send an objectionable image to a recipient but that recipient cannot report it as abuse. The core problem stems from use of fast but non-committing AE, and so we build the fastest compactly committing AE schemes to date. To do so we introduce a new primitive, called encryptment, which captures the essential properties needed. We prove that, unfortunately, schemes with performance profile similar to AES-GCM won’t work. Instead, we show how to efficiently transform Merkle-Damgärd-style hash functions into secure encryptments, and how to efficiently build compactly committing AE from encryptment. Ultimately our main construction allows franking using just a single computation of SHA-256 or SHA-3. Encryptment proves useful for a variety of other applications, such as remotely keyed AE and concealments, and our results imply the first single-pass schemes in these settings as well

Algebraic Cryptanalysis of STARK-Friendly Designs:Application to MARVELlous and MiMC

The block cipher Jarvis and the hash function Friday, both members of the MARVELlous family of cryptographic primitives, are among the first proposed solutions to the problem of designing symmetric-key algorithms suitable for transparent, post-quantum secure zero-knowledge proof systems such as ZK-STARKs. In this paper we describe an algebraic cryptanalysis of Jarvis and Friday and show that the proposed number of rounds is not sufficient to provide adequate security. In Jarvis, the round function is obtained by combining a finite field inversion, a full-degree affine permutation polynomial and a key addition. Yet we show that even though the high degree of the affine polynomial may prevent some algebraic attacks (as claimed by the designers), the particular algebraic properties of the round function make both Jarvis and Friday vulnerable to Gröbner basis attacks. We also consider MiMC, a block cipher similar in structure to Jarvis. However, this cipher proves to be resistant against our proposed attack strategy. Still, our successful cryptanalysis of Jarvis and Friday does illustrate that block cipher designs for “algebraic platforms” such as STARKs, FHE or MPC may be particularly vulnerable to algebraic attacks

An Algebraic Attack on Ciphers with Low-Degree Round Functions: Application to Full MiMC

Item does not contain fulltextAdvances in Cryptology – ASIACRYPT 202