## CryptoDB

### Thomas Johansson

#### Affiliation: Lund University

#### Publications

**Year**

**Venue**

**Title**

2020

JOFC

Solving LPN Using Covering Codes
Abstract

We present a new algorithm for solving the LPN problem. The algorithm has a similar form as some previous methods, but includes a new key step that makes use of approximations of random words to a nearest codeword in a linear code. It outperforms previous methods for many parameter choices. In particular, we can now solve the $$(512,\frac{1}{8})$$ ( 512 , 1 8 ) LPN instance with complexity less than $$2^{80}$$ 2 80 operations in expectation, indicating that cryptographic schemes like HB variants and LPN-C should increase their parameter size for 80-bit security.

2020

TOSC

Spectral analysis of ZUC-256
Abstract

In this paper we develop a number of generic techniques and algorithms in spectral analysis of large linear approximations for use in cryptanalysis. We apply the developed tools for cryptanalysis of ZUC-256 and give a distinguishing attack with complexity around 2236. Although the attack is only 220 times faster than exhaustive key search, the result indicates that ZUC-256 does not provide a source with full 256-bit entropy in the generated keystream, which would be expected from a 256-bit key. To the best of our knowledge, this is the first known academic attack on full ZUC-256 with a computational complexity that is below exhaustive key search.

2020

TOSC

Vectorized linear approximations for attacks on SNOW 3G
Abstract

SNOW 3G is a stream cipher designed in 2006 by ETSI/SAGE, serving in 3GPP as one of the standard algorithms for data confidentiality and integrity protection. It is also included in the 4G LTE standard. In this paper we derive vectorized linear approximations of the finite state machine in SNOW3G. In particular,we show one 24-bit approximation with a bias around 2−37 and one byte-oriented approximation with a bias around 2−40. We then use the approximations to launch attacks on SNOW 3G. The first approximation is used in a distinguishing attack resulting in an expected complexity of 2172 and the second one can be used in a standard fast correlation attack resulting in key recovery in an expected complexity of 2177. If the key length in SNOW 3G would be increased to 256 bits, the results show that there are then academic attacks on such a version faster than the exhaustive key search.

2019

TCHES

Error Amplification in Code-based Cryptography
📺
Abstract

Code-based cryptography is one of the main techniques enabling cryptographic primitives in a post-quantum scenario. In particular, the MDPC scheme is a basic scheme from which many other schemes have been derived. These schemes rely on iterative decoding in the decryption process and thus have a certain small probability p of having a decryption (decoding) error.In this paper we show a very fundamental and important property of code-based encryption schemes. Given one initial error pattern that fails to decode, the time needed to generate another message that fails to decode is strictly much less than 1/p. We show this by developing a method for fast generation of undecodable error patterns (error pattern chaining), which additionally proves that a measure of closeness in ciphertext space can be exploited through its strong linkage to the difficulty of decoding these messages. Furthermore, if side-channel information is also available (time to decode), then the initial error pattern no longer needs to be given since one can be easily generated in this case.These observations are fundamentally important because they show that a, say, 128- bit encryption scheme is not inherently safe from reaction attacks even if it employs a decoder with a failure rate of 2−128. In fact, unless explicit protective measures are taken, having a failure rate at all – of any magnitude – can pose a security problem because of the error amplification effect of our method.A key-recovery reaction attack was recently shown on the MDPC scheme as well as similar schemes, taking advantage of decoding errors in order to recover the secret key. It was also shown that knowing the number of iterations in the iterative decoding step, which could be received in a timing attack, would also enable and enhance such an attack. In this paper we apply our error pattern chaining method to show how to improve the performance of such reaction attacks in the CPA case. We show that after identifying a single decoding error (or a decoding step taking more time than expected in a timing attack), we can adaptively create new error patterns that have a much higher decoding error probability than for a random error. This leads to a significant improvement of the attack based on decoding errors in the CPA case and it also gives the strongest known attack on MDPC-like schemes, both with and without using side-channel information.

2019

PKC

Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes
Abstract

In this paper we investigate the impact of decryption failures on the chosen-ciphertext security of lattice-based primitives. We discuss a generic framework for secret key recovery based on decryption failures and present an attack on the NIST Post-Quantum Proposal ss-ntru-pke. Our framework is split in three parts: First, we use a technique to increase the failure rate of lattice-based schemes called failure boosting. Based on this technique we investigate the minimal effort for an adversary to obtain a failure in three cases: when he has access to a quantum computer, when he mounts a multi-target attack or when he can only perform a limited number of oracle queries. Secondly, we examine the amount of information that an adversary can derive from failing ciphertexts. Finally, these techniques are combined in an overall analysis of the security of lattice based schemes under a decryption failure attack. We show that an attacker could significantly reduce the security of lattice based schemes that have a relatively high failure rate. However, for most of the NIST Post-Quantum Proposals, the number of required oracle queries is above practical limits. Furthermore, a new generic weak-key (multi-target) model on lattice-based schemes, which can be viewed as a variant of the previous framework, is proposed. This model further takes into consideration the weak-key phenomenon that a small fraction of keys can have much larger decoding error probability for ciphertexts with certain key-related properties. We apply this model and present an attack in detail on the NIST Post-Quantum Proposal – ss-ntru-pke – with complexity below the claimed security level.

2019

TOSC

A new SNOW stream cipher called SNOW-V
Abstract

In this paper we are proposing a new member in the SNOW family of stream ciphers, called SNOW-V. The motivation is to meet an industry demand of very high speed encryption in a virtualized environment, something that can be expected to be relevant in a future 5G mobile communication system. We are revising the SNOW 3G architecture to be competitive in such a pure software environment, making use of both existing acceleration instructions for the AES encryption round function as well as the ability of modern CPUs to handle large vectors of integers (e.g. SIMD instructions). We have kept the general design from SNOW 3G, in terms of linear feedback shift register (LFSR) and Finite State Machine (FSM), but both entities are updated to better align with vectorized implementations. The LFSR part is new and operates 8 times the speed of the FSM. We have furthermore increased the total state size by using 128-bit registers in the FSM, we use the full AES encryption round function in the FSM update, and, finally, the initialization phase includes a masking with key bits at its end. The result is an algorithm generally much faster than AES-256 and with expected security not worse than AES-256.

2019

ASIACRYPT

A Novel CCA Attack Using Decryption Errors Against LAC
Abstract

Cryptosystems based on Learning with Errors or related problems are central topics in recent cryptographic research. One main witness to this is the NIST Post-Quantum Cryptography Standardization effort. Many submitted proposals rely on problems related to Learning with Errors. Such schemes often include the possibility of decryption errors with some very small probability. Some of them have a somewhat larger error probability in each coordinate, but use an error correcting code to get rid of errors. In this paper we propose and discuss an attack for secret key recovery based on generating decryption errors, for schemes using error correcting codes. In particular we show an attack on the scheme LAC, a proposal to the NIST Post-Quantum Cryptography Standardization that has advanced to round 2.In a standard setting with CCA security, the attack first consists of a precomputation of special messages and their corresponding error vectors. This set of messages are submitted for decryption and a few decryption errors are observed. In a statistical analysis step, these vectors causing the decryption errors are processed and the result reveals the secret key. The attack only works for a fraction of the secret keys. To be specific, regarding LAC256, the version for achieving the 256-bit classical security level, we recover one key among approximately $$2^{64}$$ public keys with complexity $$2^{79}$$, if the precomputation cost of $$2^{162}$$ is excluded. We also show the possibility to attack a more probable key (say with probability $$2^{-16}$$). This attack is verified via extensive simulation.We further apply this attack to LAC256-v2, a new version of LAC256 in round 2 of the NIST PQ-project and obtain a multi-target attack with slightly increased precomputation complexity (from $$2^{162}$$ to $$2^{171}$$). One can also explain this attack in the single-key setting as an attack with precomputation complexity of $$2^{171}$$ and success probability of $$2^{-64}$$.

2000

EPRINT

New Constructions of Resilent and Correlation Immune Boolean Functions achieving Upper Bounds on Nonlinearity
Abstract

Recently weight divisibility results on resilient and correlation
immune Boolean functions have received a lot of attention. These
results have direct consequences towards the upper bound on nonlinearity
of resilient and correlation immune Boolean functions of certain order.
Now the clear benchmark in the design of resilient Boolean functions
(which optimizes Sigenthaler's inequality) is to provide results
which attain the upper bound on nonlinearity. Here we construct a
7-variable, 2-resilient Boolean function with nonlinearity 56. This
solves the maximum nonlinearity issue for 7-variable functions with
any order of resiliency. Using this 7-variable function, we also
construct a 10-variable, 4-resilient Boolean function with nonlinearity
480. Construction of these two functions were justified as important
open questions in Crypto 2000. Also we provide methods to generate an
infinite sequence of Boolean functions on $n = 7 + 3i$ variables
$(i \geq 0)$ with order of resiliency $m = 2 + 2i$, algebraic degree
$4 + i$ and nonlinearity $2^{n-1} - 2^{m+1}$, which were not known
earlier. We conclude with a few interesting construction results
on unbalanced correlation immune functions of 5 and 6 variables.

2000

EPRINT

A Construction of Resilient Functions with High Nonlinearity
Abstract

The relationship between nonlinearity and
resiliency for a function $F:\mathbb{F}_2^n \mapsto
\mathbb{F}_2^m$ is considered. We give a construction of resilient
functions with high nonlinearity. The construction leads to the
problem of finding a set of linear codes with a fixed minimum
distance, having the property that the intersection
between any two codes is the all zero codeword only. This problem is
considered, and existence results are provided. The constructed
functions obtain a nonlinearity superior to previous construction
methods.

#### Program Committees

- Crypto 2015
- Eurocrypt 2013
- Eurocrypt 2012
- Asiacrypt 2010
- FSE 2010
- Asiacrypt 2009
- Eurocrypt 2009
- FSE 2008
- Crypto 2008
- Asiacrypt 2007
- FSE 2007
- FSE 2006
- Asiacrypt 2005
- FSE 2005
- Eurocrypt 2004
- FSE 2004
- FSE 2003
- FSE 2002
- Eurocrypt 2002
- FSE 2001
- Eurocrypt 2001
- Eurocrypt 2000
- Eurocrypt 1998

#### Coauthors

- Jürgen Bierbrauer (1)
- Vladimor V. Chepyzhov (1)
- Jan-Pieter D’Anvers (1)
- Patrik Ekdahl (3)
- Håkan Englund (3)
- Qian Guo (7)
- Martin Hell (8)
- Tor Helleseth (1)
- Fredrik Jönsson (3)
- Gregory Kabatianskii (2)
- Kaoru Kurosawa (2)
- Carl Löndahl (2)
- Subhamoy Maitra (1)
- Erik Mårtensson (1)
- Alexander Maximov (4)
- Willi Meier (2)
- Frédéric Muller (1)
- Alexander Nilsson (2)
- Enes Pasalic (2)
- Palash Sarkar (1)
- Ben J. M. Smeets (4)
- Paul Stankovski (6)
- Douglas R. Stinson (2)
- Ingrid Verbauwhede (1)
- Frederik Vercauteren (1)
- Jing Yang (4)