International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Christian Rechberger

Affiliation: TU Graz

Publications

Year
Venue
Title
2019
EUROCRYPT
Linear Equivalence of Block Ciphers with Partial Non-Linear Layers: Application to LowMC
$$\textsc {LowMC}$$LOWMC is a block cipher family designed in 2015 by Albrecht et al. It is optimized for practical instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. $$\textsc {LowMC}$$LOWMC is used in the $$\textsc {Picnic}$$PICNIC signature scheme, submitted to NIST’s post-quantum standardization project and is a substantial building block in other novel post-quantum cryptosystems. Many $$\textsc {LowMC}$$LOWMC instances use a relatively recent design strategy (initiated by Gérard et al. at CHES 2013) of applying the non-linear layer to only a part of the state in each round, where the shortage of non-linear operations is partially compensated by heavy linear algebra. Since the high linear algebra complexity has been a bottleneck in several applications, one of the open questions raised by the designers was to reduce it, without introducing additional non-linear operations (or compromising security).In this paper, we consider $$\textsc {LowMC}$$LOWMC instances with block size n, partial non-linear layers of size $$s \le n$$s≤n and r encryption rounds. We redesign LowMC’s linear components in a way that preserves its specification, yet improves LowMC’s performance in essentially every aspect. Most of our optimizations are applicable to all SP-networks with partial non-linear layers and shed new light on this relatively new design methodology.Our main result shows that when $$s < n$$s<n, each $$\textsc {LowMC}$$LOWMC instance belongs to a large class of equivalent instances that differ in their linear layers. We then select a representative instance from this class for which encryption (and decryption) can be implemented much more efficiently than for an arbitrary instance. This yields a new encryption algorithm that is equivalent to the standard one, but reduces the evaluation time and storage of the linear layers from $$r \cdot n^2$$r·n2 bits to about $$r \cdot n^2 - (r-1)(n-s)^2$$r·n2-(r-1)(n-s)2. Additionally, we reduce the size of LowMC’s round keys and constants and optimize its key schedule and instance generation algorithms. All of these optimizations give substantial improvements for small s and a reasonable choice of r. Finally, we formalize the notion of linear equivalence of block ciphers and prove the optimality of some of our results.Comprehensive benchmarking of our optimizations in various $$\textsc {LowMC}$$LOWMC applications (such as $$\textsc {Picnic}$$PICNIC) reveals improvements by factors that typically range between 2x and 40x in runtime and memory consumption.
2018
CRYPTO
Rasta: A Cipher with Low ANDdepth and Few ANDs per Bit 📺
Recent developments in multi party computation (MPC) and fully homomorphic encryption (FHE) promoted the design and analysis of symmetric cryptographic schemes that minimize multiplications in one way or another. In this paper, we propose with Rastaa design strategy for symmetric encryption that has ANDdepth d and at the same time only needs d ANDs per encrypted bit. Even for very low values of d between 2 and 6 we can give strong evidence that attacks may not exist. This contributes to a better understanding of the limits of what concrete symmetric-key constructions can theoretically achieve with respect to AND-related metrics, and is to the best of our knowledge the first attempt that minimizes both metrics simultaneously. Furthermore, we can give evidence that for choices of d between 4 and 6 the resulting implementation properties may well be competitive by testing our construction in the use-case of removing the large ciphertext-expansion when using the BGV scheme.
2018
TOSC
Cryptanalysis of Low-Data Instances of Full LowMCv2 📺
Christian Rechberger Hadi Soleimany Tyge Tiessen
LowMC is a family of block ciphers designed for a low multiplicative complexity. The specification allows a large variety of instantiations, differing in block size, key size, number of S-boxes applied per round and allowed data complexity. The number of rounds deemed secure is determined by evaluating a number of attack vectors and taking the number of rounds still secure against the best of these. In this paper, we demonstrate that the attacks considered by the designers of LowMC in the version 2 of the round-formular were not sufficient to fend off all possible attacks. In the case of instantiations of LowMC with one of the most useful settings, namely with few applied S-boxes per round and only low allowable data complexities, efficient attacks based on difference enumeration techniques can be constructed. We show that it is most effective to consider tuples of differences instead of simple differences, both to increase the range of the distinguishers and to enable key recovery attacks. All applications for LowMC we are aware of, including signature schemes like Picnic and more recent (ring/group) signature schemes have used version 3 of the roundformular for LowMC, which takes our attack already into account.
2017
EUROCRYPT
2016
ASIACRYPT
2016
TOSC
Haraka v2 - Efficient Short-Input Hashing for Post-Quantum Applications
Recently, many efficient cryptographic hash function design strategies have been explored, not least because of the SHA-3 competition. These designs are, almost exclusively, geared towards high performance on long inputs. However, various applications exist where the performance on short (fixed length) inputs matters more. Such hash functions are the bottleneck in hash-based signature schemes like SPHINCS or XMSS, which is currently under standardization. Secure functions specifically designed for such applications are scarce. We attend to this gap by proposing two short-input hash functions (or rather simply compression functions). By utilizing AES instructions on modern CPUs, our proposals are the fastest on such platforms, reaching throughputs below one cycle per hashed byte even for short inputs, while still having a very low latency of less than 60 cycles. Under the hood, this results comes with several innovations. First, we study whether the number of rounds for our hash functions can be reduced, if only second-preimage resistance (and not collision resistance) is required. The conclusion is: only a little. Second, since their inception, AES-like designs allow for supportive security arguments by means of counting and bounding the number of active S-boxes. However, this ignores powerful attack vectors using truncated differentials, including the powerful rebound attacks. We develop a general tool-based method to include arguments against attack vectors using truncated differentials.
2016
TOSC
Subspace Trail Cryptanalysis and its Applications to AES
Lorenzo Grassi Christian Rechberger Sondre Rønjom
We introduce subspace trail cryptanalysis, a generalization of invariant subspace cryptanalysis. With this more generic treatment of subspaces we do no longer rely on specific choices of round constants or subkeys, and the resulting method is as such a potentially more powerful attack vector. Interestingly, subspace trail cryptanalysis in fact includes techniques based on impossible or truncated differentials and integrals as special cases. Choosing AES-128 as the perhaps most studied cipher, we describe distinguishers up to 5-round AES with a single unknown key. We report (and practically verify) competitive key-recovery attacks with very low data-complexity on 2, 3 and 4 rounds of AES. Additionally, we consider AES with a secret S-Box and we present a (generic) technique that allows to directly recover the secret key without finding any information about the secret S-Box. This approach allows to use e.g. truncated differential, impossible differential and integral attacks to find the secret key. Moreover, this technique works also for other AES-like constructions, if some very common conditions on the S-Box and on the MixColumns matrix (or its inverse) hold. As a consequence, such attacks allow to better highlight the security impact of linear mappings inside an AES-like block cipher. Finally, we show that our impossible differential attack on 5 rounds of AES with secret S-Box can be turned into a distinguisher for AES in the same setting as the one recently proposed by Sun, Liu, Guo, Qu and Rijmen at CRYPTO 2016
2015
JOFC
2015
EPRINT
2015
EPRINT
2015
EPRINT
2015
FSE
2015
EUROCRYPT
2014
JOFC
2012
EUROCRYPT
2012
ASIACRYPT
2012
FSE
2011
ASIACRYPT
2010
EPRINT
The Rebound Attack and Subspace Distinguishers: Application to Whirlpool
We introduce the rebound attack as a variant of differential cryptanalysis on hash functions and apply it to the hash function Whirlpool, standardized by ISO/IEC. We give attacks on reduced variants of the Whirlpool hash function and the Whirlpool compression function. Next, we introduce the subspace problems as generalizations of near-collision resistance. Finally, we present distinguishers based on the rebound attack, that apply to the full compression function of Whirlpool and the underlying block cipher $W$.
2010
ASIACRYPT
2010
ASIACRYPT
2010
EPRINT
Advanced Meet-in-the-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-2
Jian Guo San Ling Christian Rechberger Huaxiong Wang
We revisit narrow-pipe designs that are in practical use, and their security against preimage attacks. Our results are the best known preimage attacks on Tiger, MD4, and reduced SHA-2, with the result on Tiger being the first cryptanalytic shortcut attack on the full hash function. Our attacks runs in time $2^{188.8}$ for finding preimages, and $2^{188.2}$ for second-preimages. Both have memory requirement of order $2^{8}$, which is much less than in any other recent preimage attacks on reduced Tiger. Using pre-computation techniques, the time complexity for finding a new preimage or second-preimage for MD4 can now be as low as $2^{78.4}$ and $2^{69.4}$ MD4 computations, respectively. The second-preimage attack works for all messages longer than 2 blocks. To obtain these results, we extend the meet-in-the-middle framework recently developed by Aoki and Sasaki in a series of papers. In addition to various algorithm-specific techniques, we use a number of conceptually new ideas that are applicable to a larger class of constructions. Among them are (1) incorporating multi-target scenarios into the MITM framework, leading to faster preimages from pseudo-preimages, (2) a simple precomputation technique that allows for finding new preimages at the cost of a single pseudo-preimage, and (3) probabilistic initial structures, compared with deterministic ones, to enable more neutral words, and hence to reduce the attack time complexity. All the techniques developed await application to other hash functions. To illustrate this, we give as another example improved preimage attacks on SHA-2 members.
2009
ASIACRYPT
2009
ASIACRYPT
2009
EUROCRYPT
2009
FSE
2008
FSE
2008
FSE
2008
EPRINT
Analysis of Step-Reduced SHA-256
This is the first article analyzing the security of SHA-256 against fast collision search which considers the recent attacks by Wang et al. We show the limits of applying techniques known so far to SHA-256. Next we introduce a new type of perturbation vector which circumvents the identified limits. This new technique is then applied to the unmodified SHA-256. Exploiting the combination of Boolean functions and modular addition together with the newly developed technique allows us to derive collision-producing characteristics for step-reduced SHA-256, which was not possible before. Although our results do not threaten the security of SHA-256, we show that the low probability of a single local collision may give rise to a false sense of security.
2008
EPRINT
Collisions and other Non-Random Properties for Step-Reduced SHA-256
We study the security of step-reduced but otherwise unmodified SHA-256. We show the first collision attacks on SHA-256 reduced to 23 and 24 steps with complexities $2^{18}$ and $2^{28.5}$, respectively. We give example colliding message pairs for 23-step and 24-step SHA-256. The best previous, recently obtained result was a collision attack for up to 22 steps. We extend our attacks to 23 and 24-step reduced SHA-512 with respective complexities of $2^{44.9}$ and $2^{53.0}$. Additionally, we show non-random behaviour of the SHA-256 compression function in the form of free-start near-collisions for up to 31 steps, which is 6 more steps than the recently obtained non-random behaviour in the form of a free-start near-collision. Even though this represents a step forwards in terms of cryptanalytic techniques, the results do not threaten the security of applications using SHA-256.
2008
CRYPTO
2008
CRYPTO
2007
FSE
2007
EPRINT
New Features of Latin Dances: Analysis of Salsa, ChaCha, and Rumba
The stream cipher Salsa20 was introduced by Bernstein in 2005 as a candidate in the eSTREAM project, accompanied by the reduced versions Salsa20/8 and Salsa20/12. ChaCha is a variant of Salsa20 aiming at bringing better diffusion for similar performance. Variants of Salsa20 with up to 7 rounds (instead of 20) have been broken by differential cryptanalysis, while ChaCha has not been analyzed yet. In this paper, we introduce a novel method for differential cryptanalysis of Salsa20 and ChaCha, inspired by correlation attacks and related to the notion of neutral bits. This is the first application of neutral bits in stream cipher cryptanalysis, and it allows us to present the first break of Salsa20/8, to bring faster attacks on the 7-round variant, and to break 6- and 7-round ChaCha. In a second part, we analyze the compression function Rumba, constructed as the XOR of four Salsa20 instances, and returning a 512-bit output. We find collision and preimage attacks for two simplified variants, then we discuss differential attacks on the original version, and exploit a high-probability differential to reduce complexity of collision search from 2^(256) to 2^(79) for 3-round Rumba. We give examples of collisions over three rounds for a version without feedforward, and near-collisions of weight 16 for three rounds of the original compression function, and of weight 129 for four rounds.
2006
ASIACRYPT
2006
FSE
2006
FSE
2006
EPRINT
On Authentication with HMAC and Non-Random Properties
Christian Rechberger Vincent Rijmen
MAC algorithms can provide cryptographically secure authentication services. One of the most popular algorithms in commercial applications is HMAC based on the hash functions MD5 or SHA-1. In the light of new collision search methods for members of the MD4 family including SHA-1, the security of HMAC based on these hash functions is reconsidered. We present a new method to recover both the inner- and the outer key used in HMAC when instantiated with a concrete hash function by observing text/MAC pairs. In addition to collisions, also other non-random properties of the hash function are used in this new attack. Among the examples of the proposed method, the first theoretical full key recovery attack on NMAC-MD5 is presented. Other examples are distinguishing, forgery and partial or full key recovery attacks on NMAC/HMAC-SHA-1 with a reduced number of steps (up to 61 out of 80). This information about the new, reduced security margin serves as an input to the selection of algorithms for authentication purposes.
2005
EPRINT
Smashing SMASH
Norbert Pramstaller Christian Rechberger Vincent Rijmen
We present a collision attack on the recently proposed hash function SMASH. The attack uses negligible resources and we conjecture that it works for all hash functions built following the design method of SMASH.

Program Committees

CHES 2019
Eurocrypt 2019
Crypto 2016
FSE 2016
Eurocrypt 2015
Asiacrypt 2014
FSE 2014
FSE 2013
Crypto 2013
Asiacrypt 2012
Asiacrypt 2011
FSE 2011
FSE 2010
FSE 2009
Eurocrypt 2009