## CryptoDB

### Shahram Rasoolzadeh

#### Publications

**Year**

**Venue**

**Title**

2024

TOSC

Addendum to Classification of All t-Resilient Boolean Functions with t + 4 Variables: Classification of Quadratic and Cubic t-Resilient Boolean Functions with t + 5 Variables
Abstract

In ToSC 2023(3), Rasoolzadeh presented an algorithm for classifying (n−m)-resilient Boolean functions with n variables, up to extended variable-permutation equivalence, for a small given positive integer m and any positive integer n with n ≥ m. By applying this algorithm along with several speed-up techniques, he classified n-variable (n − 4)-resilient Boolean functions up to equivalence for any n ≥ 4. However, for m = 5, due to the large number of representative functions, he was unable to classify n-variable (n − 5)-resilient Boolean functions for n > 6.In this work, we apply this algorithm together with a technique to restrict the ANF degree to classify quadratic and cubic (n − 5)-resilient Boolean functions with n variables, up to the same equivalence. We show that there are only 131 quadratic representative functions for any n ≥ 8. Additionally, we show that there are 359 078 cubic representative functions for any n ≥ 14.

2024

ASIACRYPT

Multiple-Tweak Differential Attack Against SCARF
Abstract

In this paper, we present the first third-party cryptanalysis of SCARF, a tweakable low-latency block cipher designed to thwart contention-based cache attacks through cache randomization. We focus on multiple-tweak differential attacks, exploiting biases across multiple tweaks. We establish a theoretical framework explaining biases for any number of rounds and verify this framework experimentally. Then, we use these properties to develop a key recovery attack on 7-round SCARF with a time complexity of 2^76, achieving a 98.9% success rate in recovering the 240-bit secret key. Additionally, we introduce a distinguishing attack on the full 8-round SCARF in a multi-key setting, with a complexity of c x 2^67.55, demonstrating that SCARF does not provide 80-bit security under these conditions. We also explore whether our approach could be extended to the single-key model and discuss the implications of different S-box choices on the attack success.

2023

TOSC

Classification of All t-Resilient Boolean Functions with t + 4 Variables
Abstract

We apply Siegenthaler’s construction, along with several techniques, to classify all (n−4)-resilient Boolean functions with n variables, for all values of n ≥ 4, up to the extended variable-permutation equivalence. We show that, up to this equivalence, there are only 761 functions for any n larger than or equal to 10, and for smaller values of n, i.e., for n increasing from 4 to 9, there are 58, 256, 578, 720, 754, and 760 functions, respectively. Furthermore, we classify all 1-resilient 6-variable Boolean functions and show that there are 1 035 596 784 such functions up to the extended variable-permutation equivalence.

2023

TOSC

Cryptanalysis of HALFLOOP Block Ciphers: Destroying HALFLOOP-24
★
Abstract

HALFLOOP is a family of tweakable block ciphers that are used for encrypting automatic link establishment (ALE) messages in high frequency radio, a technology commonly used by the military, other government agencies and industries which require high robustness in long-distance communications. Recently, it was shown in [DDLS22] that the smallest version of the cipher, HALFLOOP-24, can be attacked within a practical time and memory complexity. However, in the real-word ALE setting, it turns out that this attack require to wait more than 500 years to collect the necessary amount of plaintext-tweak-ciphertext pairs fulfilling the conditions of the attack.In this paper, we present real-world practical attacks against HALFLOOP-24 which are based on a probability-one differential distinguisher. In our attacks, we significantly reduce the data complexity to three differential pairs in the chosen-plaintext (CPA) setting which is optimal in the sense that even a brute force attack needs at least six plaintext-tweak-ciphertext pairs to uniquely identify the correct key. Considering the same ALE setting as [DDLS22], this translates to a reduction from 541 years to 2 hours worth of intercepted traffic.Besides, we provide the first, non generic, public cryptanalysis of HALFLOOP-48 and HALFLOOP-96. More precisely, we present Demirci-Selçuk meet-in-the-middle attacks against full-round HALFLOOP-48 and round-reduced HALFLOOP-96 to recover the complete master key in a CPA setting. However, unlike the attacks on HALFLOOP-24, our attacks on the larger versions are only theoretical. Moreover for HALFLOOP-96 the known generic time-memory trade-off attack, based on a flawed tweak handling, remains the strongest attack vector.In conclusion, we iterate what was already stated in [DDLS22]: HALFLOOP does not provide adequate protection and should not be used.

2022

TOSC

Weak Tweak-Keys for the CRAFT Block Cipher
📺
Abstract

CRAFT is a lightweight tweakable Substitution-Permutation-Network (SPN) block cipher optimized for efficient protection of its implementations against Differential Fault Analysis (DFA) attacks. In this paper, we present an equivalent description of CRAFT up to a simple mapping on the plaintext, ciphertext and round tweakeys. We show that the new representation, for a sub-class of keys, leads to a new structure which is a Feistel network, with non-linear operation and key addition only on half the state. Consequently, it reveals a class of weak keys for which CRAFT is less resistant against differential and linear cryptanalyses. As a result, we present one weak-key single-tweak differential attack on 23 rounds (with time complexity of 294 encryptions and data complexity of 274 chosen plaintext/tweak/ciphertext tuples and works for 2112 weak keys) and one weak-key related-tweak attack on 26 rounds of the cipher (with time complexity of 2105 encryptions and data complexity 273 chosen plaintext/tweak/ciphertext tuples and works for 2108 weak keys). Note that these attacks do not break the security claim of the CRAFT block cipher.

2022

TOSC

Low-Latency Boolean Functions and Bijective S-boxes
Abstract

In this paper, we study the gate depth complexity of (vectorial) Boolean functions in the basis of {NAND, NOR, INV} as a new metric, called latency complexity, to mathematically measure the latency of Boolean functions. We present efficient algorithms to find all Boolean functions with low-latency complexity, or to determine the latency complexity of the (vectorial) Boolean functions, and to find all the circuits with the minimum latency complexity for a given Boolean function. Then, we present another algorithm to build bijective S-boxes with low-latency complexity which with respect to the computation cost, this algorithm overcomes the previous methods of building S-boxes.As a result, for latency complexity 3, we present n-bit S-boxes of 3 ≤ n ≤ 8 with linearity 2n−1 and uniformity 2n−2 (except for 5-bit S-boxes for whose the minimum achievable uniformity is 6). Besides, for latency complexity 4, we present several n-bit S-boxes of 5 ≤ n < 8 with linearity 2n−2 and uniformity 2n−4.

2022

TCHES

BipBip: A Low-Latency Tweakable Block Cipher with Small Dimensions
Abstract

Recently, a memory safety concept called Cryptographic Capability Computing (C3) has been proposed. C3 is the first memory safety mechanism that works without requiring extra storage for metadata and hence, has the potential to significantly enhance the security of modern IT-systems at a rather low cost. To achieve this, C3 heavily relies on ultra-low-latency cryptographic primitives. However, the most crucial primitive required by C3 demands uncommon dimensions. To partially encrypt 64-bit pointers, a 24-bit tweakable block cipher with a 40-bit tweak is needed. The research on low-latency tweakable block ciphers with such small dimensions is not very mature. Therefore, designing such a cipher provides a great research challenge, which we take on with this paper. As a result, we present BipBip, a 24-bit tweakable block cipher with a 40-bit tweak that allows for ASIC implementations with a latency of 3 cycles at a 4.5 GHz clock frequency on a modern 10 nm CMOS technology.

2021

TCHES

The SPEEDY Family of Block Ciphers: Engineering an Ultra Low-Latency Cipher from Gate Level for Secure Processor Architectures
📺
Abstract

We introduce SPEEDY, a family of ultra low-latency block ciphers. We mix engineering expertise into each step of the cipher’s design process in order to create a secure encryption primitive with an extremely low latency in CMOS hardware. The centerpiece of our constructions is a high-speed 6-bit substitution box whose coordinate functions are realized as two-level NAND trees. In contrast to other low-latency block ciphers such as PRINCE, PRINCEv2, MANTIS and QARMA, we neither constrain ourselves by demanding decryption at low overhead, nor by requiring a super low area or energy. This freedom together with our gate- and transistor-level considerations allows us to create an ultra low-latency cipher which outperforms all known solutions in single-cycle encryption speed. Our main result, SPEEDY-6-192, is a 6-round 192-bit block and 192-bit key cipher which can be executed faster in hardware than any other known encryption primitive (including Gimli in Even-Mansour scheme and the Orthros pseudorandom function) and offers 128-bit security. One round more, i.e., SPEEDY-7-192, provides full 192-bit security. SPEEDY primarily targets hardware security solutions embedded in high-end CPUs, where area and energy restrictions are secondary while high performance is the number one priority.

2019

TOSC

CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks
📺
Abstract

Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of cryptanalytic security. This picture has been changed by the introduction of PICARO, ZORRO, and FIDES, where efficient protection against Side-Channel Analysis (SCA) attacks has been considered in their design. In this work we present the tweakable block cipher CRAFT: the efficient protection of its implementations against Differential Fault Analysis (DFA) attacks has been one of the main design criteria, while we provide strong bounds for its security in the related-tweak model. Considering the area footprint of round-based hardware implementations, CRAFT outperforms the other lightweight ciphers with the same state and key size. This holds not only for unprotected implementations but also when fault-detection facilities, side-channel protection, and their combination are integrated into the implementation. In addition to supporting a 64-bit tweak, CRAFT has the additional property that the circuit realizing the encryption can support the decryption functionality as well with very little area overhead.

2017

TOSC

Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds
Abstract

The current paper studies the probability of differential characteristics for an unkeyed (or with a fixed key) construction. Most notably, it focuses on the gap between two probabilities of differential characteristics: probability with independent S-box assumption, pind, and exact probability, pexact. It turns out that pexact is larger than pind in Feistel network with some S-box based inner function. The mechanism of this gap is then theoretically analyzed. The gap is derived from interaction of S-boxes in three rounds, and the gap depends on the size and choice of the S-box. In particular the gap can never be zero when the S-box is bigger than six bits. To demonstrate the power of this improvement, a related-key differential characteristic is proposed against a lightweight block cipher RoadRunneR. For the 128-bit key version, pind of 2−48 is improved to pexact of 2−43. For the 80-bit key version, pind of 2−68 is improved to pexact of 2−62. The analysis is further extended to SPN with an almost-MDS binary matrix in the core primitive of the authenticated encryption scheme Minalpher: pind of 2−128 is improved to pexact of 2−96, which allows to extend the attack by two rounds.

#### Program Committees

- Asiacrypt 2024

#### Coauthors

- Christof Beierle (1)
- Yanis Belkheyar (1)
- Christina Boura (1)
- Anne Canteaut (1)
- Joan Daemen (1)
- Christoph Dobraunig (1)
- Santosh Ghosh (1)
- Eran Lambooij (1)
- Gregor Leander (4)
- Thorben Moos (1)
- Amir Moradi (2)
- Samuel Neves (1)
- Shahram Rasoolzadeh (10)
- Dhiman Saha (1)
- Yu Sasaki (1)
- Lukas Stennes (1)
- Marc Stevens (1)
- Yosuke Todo (1)