scholarly journals Almost-Minimal-Round BBB-Secure Tweakable Key-Alternating Feistel Block Cipher

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 649
Author(s):  
Ming Jiang ◽  
Lei Wang
Keyword(s):  
Block Cipher ◽  
Security Proof ◽  
Tweakable Block Cipher ◽  
Beyond Birthday Bound ◽  
Security Bound

This paper focuses on designing a tweakable block cipher via by tweaking the Key-Alternating Feistel (KAF for short) construction. Very recently Yan et al. published a tweakable KAF construction. It provides a birthday-bound security with 4 rounds and Beyond-Birthday-Bound (BBB for short) security with 10 rounds. Following their work, we further reduce the number of rounds in order to improve the efficiency while preserving the same level of security bound. More specifically, we rigorously prove that 6-round tweakable KAF cipher is BBB- secure. The main technical contribution is presenting a more refined security proof framework, which makes significant efforts to deal with several subtle and complicated sub-events. Note that Yan et al. showed that 4-round KAF provides exactly Birthday-Bound security by a concrete attack. Thus, 6 rounds are (almost) minimal rounds to achieve BBB security for tweakable KAF construction.

scholarly journals Iterative Block Ciphers from Tweakable Block Ciphers with Long Tweaks

2020 ◽  
pp. 54-80
Author(s):  
Ryota Nakamichi ◽  
Tetsu Iwata
Keyword(s):  
Block Cipher ◽  
Block Ciphers ◽  
Simple Iteration ◽  
Tweakable Block Cipher ◽  
Beyond Birthday Bound ◽  
Security Bound

We consider a problem of constructing a secure block cipher from a tweakable block cipher (TBC) with long tweaks. Given a TBC with n-bit blocks and Γn-bit tweaks for Γ ≥ 1, one of the constructions by Minematsu in DCC 2015 shows that a simple iteration of the TBC for 3d rounds yields a block cipher with dn-bit blocks that is secure up to 2dn/2 queries, where d = Γ + 1. In this paper, we show three results.1. Iteration of 3d − 2 rounds is enough for the security up to 2dn/2 queries, i.e., the security remains the same even if we reduce the number of rounds by two.2. When the number of queries is limited to 2n, d+1 rounds are enough, and with d + l rounds for 1 ≤ l ≤ d − 1, the security bound improves as l grows.3. A d-round construction gives a block cipher secure up to 2n/2 queries, i.e., it achieves the classical birthday-bound security. Our results show that a block cipher with beyond-birthday-bound (BBB) security (with respect to n) is obtained as low as d + 1 rounds, and we draw the security spectrum of d + l round version in the range of 1 ≤ l ≤ d−1 and l = 2d−2 for BBB security, and l = 0 for birthday-bound security.

scholarly journals On Length Independent Security Bounds for the PMAC Family

2021 ◽  
pp. 423-445
Author(s):  
Bishwajit Chakraborty ◽  
Soumya Chattopadhyay ◽  
Ashwin Jha ◽  
Mridul Nandi
Keyword(s):  
Block Cipher ◽  
Block Size ◽  
Gray Code ◽  
Tight Bound ◽  
Simple Modification ◽  
Security Proof ◽  
Tight Security ◽  
Pseudorandom Function ◽  
Exact Security ◽  
Query Length

At FSE 2017, Gaži et al. demonstrated a pseudorandom function (PRF) distinguisher (Gaži et al., ToSC 2016(2)) on PMAC with Ω(lq2/2n) advantage, where q, l, and n, denote the number of queries, maximum permissible query length (in terms of n-bit blocks), and block size of the underlying block cipher. This, in combination with the upper bounds of Ο(lq2/2n) (Minematsu and Matsushima, FSE 2007) and Ο(qσ/2n) (Nandi and Mandal, J. Mathematical Cryptology 2008(2)), resolved the long-standing problem of exact security of PMAC. Gaži et al. also showed that the dependency on l can be dropped (i.e. O(q2/2n) bound up to l ≤ 2n/2) for a simplified version of PMAC, called sPMAC, by replacing the Gray code-based masking in PMAC with any 4-wise independent universal hash-based masking. Recently, Naito proposed another variant of PMAC with two powering-up maskings (Naito, ToSC 2019(2)) that achieves l-free bound of O(q2/2n), provided l ≤ 2n/2. In this work, we first identify a flaw in the analysis of Naito’s PMAC variant that invalidates the security proof. Apparently, the flaw is not easy to fix under the existing proof setup. We then formulate an equivalent problem which must be solved in order to achieve l-free security bounds for this variant. Second, we show that sPMAC achieves O(q2/2n) bound for a weaker notion of universality as compared to the earlier condition of 4-wise independence. Third, we analyze the security of PMAC1 (a popular variant of PMAC) with a simple modification in the linear combination of block cipher outputs. We show that this simple modification of PMAC1 has tight security O(q2/2n) provided l ≤ 2n/4. Even if l < 2n/4, we still achieve same tight bound as long as total number of blocks in all queries is less than 22n/3.

scholarly journals Cryptanalysis of PMACx, PMAC2x, and SIVx

2017 ◽  
pp. 162-176
Author(s):  
Kazuhiko Minematsu ◽  
Tetsu Iwata
Keyword(s):  
Provable Security ◽  
Block Cipher ◽  
Query Complexity ◽  
Block Length ◽  
Encryption Scheme ◽  
Authenticated Encryption ◽  
Pseudorandom Functions ◽  
Tweakable Block Cipher ◽  
Deterministic Authenticated Encryption ◽  
Provably Secure

At CT-RSA 2017, List and Nandi proposed two variable input length pseudorandom functions (VI-PRFs) called PMACx and PMAC2x, and a deterministic authenticated encryption scheme called SIVx. These schemes use a tweakable block cipher (TBC) as the underlying primitive, and are provably secure up to the query complexity of 2n, where n denotes the block length of the TBC. In this paper, we falsify the provable security claims by presenting concrete attacks. We show that with the query complexity of O(2n/2), i.e., with the birthday complexity, PMACx, PMAC2x, and SIVx are all insecure.

Length-Preserving Encryption Based on Single-Key Tweakable Block Cipher

2018 ◽  
pp. 313-326
Author(s):  
Xiangyang Zhang ◽  
Yaobin Shen ◽  
Hailun Yan ◽  
Ying Zou ◽  
Ming Wan ◽  
...  
Keyword(s):  
Block Cipher ◽  
Tweakable Block Cipher

scholarly journals Improved Rectangle Attacks on SKINNY and CRAFT

2021 ◽  
pp. 140-198
Author(s):  
Hosein Hadipour ◽  
Nasour Bagheri ◽  
Ling Song
Keyword(s):  
General Framework ◽  
Block Cipher ◽  
Security Analysis ◽  
Differential Cryptanalysis ◽  
Advanced Method ◽  
Model Based ◽  
Tweakable Block Cipher ◽  
First Time

The boomerang and rectangle attacks are adaptions of differential cryptanalysis that regard the target cipher E as a composition of two sub-ciphers, i.e., E = E1 ∘ E0, to construct a distinguisher for E with probability p2q2 by concatenating two short differential trails for E0 and E1 with probability p and q respectively. According to the previous research, the dependency between these two differential characteristics has a great impact on the probability of boomerang and rectangle distinguishers. Dunkelman et al. proposed the sandwich attack to formalise such dependency that regards E as three parts, i.e., E = E1 ∘ Em ∘ E0, where Em contains the dependency between two differential trails, satisfying some differential propagation with probability r. Accordingly, the entire probability is p2q2r. Recently, Song et al. have proposed a general framework to identify the actual boundaries of Em and systematically evaluate the probability of Em with any number of rounds, and applied their method to accurately evaluate the probabilities of the best SKINNY’s boomerang distinguishers. In this paper, using a more advanced method to search for boomerang distinguishers, we show that the best previous boomerang distinguishers for SKINNY can be significantly improved in terms of probability and number of rounds. More precisely, we propose related-tweakey boomerang distinguishers for up to 19, 21, 23, and 25 rounds of SKINNY-64-128, SKINNY-128-256, SKINNY-64-192 and SKINNY-128-384 respectively, which improve the previous boomerang distinguishers of these variants of SKINNY by 1, 2, 1, and 1 round respectively. Based on the improved boomerang distinguishers for SKINNY, we provide related-tweakey rectangle attacks on 23 rounds of SKINNY-64-128, 24 rounds of SKINNY-128-256, 29 rounds of SKINNY-64-192, and 30 rounds of SKINNY-128-384. It is worth noting that our improved related-tweakey rectangle attacks on SKINNY-64-192, SKINNY-128-256 and SKINNY-128-384 can be directly applied for the same number of rounds of ForkSkinny-64-192, ForkSkinny-128-256 and ForkSkinny-128-384 respectively. CRAFT is another SKINNY-like tweakable block cipher for which we provide the security analysis against rectangle attack for the first time. As a result, we provide a 14-round boomerang distinguisher for CRAFT in the single-tweak model based on which we propose a single-tweak rectangle attack on 18 rounds of this cipher. Moreover, following the previous research regarding the evaluation of switching in multiple rounds of boomerang distinguishers, we also introduce new tools called Double Boomerang Connectivity Table (DBCT), LBCT⫤, and UBCT⊨ to evaluate the boomerang switch through the multiple rounds more accurately.

scholarly journals Boomeyong: Embedding Yoyo within Boomerang and its Applications to Key Recovery Attacks on AES and Pholkos

2021 ◽  
pp. 137-169
Author(s):  
Mostafizar Rahman ◽  
Dhiman Saha ◽  
Goutam Paul
Keyword(s):  
Time Complexity ◽  
Block Cipher ◽  
New Technique ◽  
Small Scale ◽  
Key Recovery ◽  
Boomerang Attack ◽  
Tweakable Block Cipher ◽  
Key Recovery Attack ◽  
Key Recovery Attacks

This work investigates a generic way of combining two very effective and well-studied cryptanalytic tools, proposed almost 18 years apart, namely the boomerang attack introduced by Wagner in FSE 1999 and the yoyo attack by Ronjom et al. in Asiacrypt 2017. In doing so, the s-box switch and ladder switch techniques are leveraged to embed a yoyo trail inside a boomerang trail. As an immediate application, a 6-round key recovery attack on AES-128 is mounted with time complexity of 278. A 10-round key recovery attack on recently introduced AES-based tweakable block cipher Pholkos is also furnished to demonstrate the applicability of the new technique on AES-like constructions. The results on AES are experimentally verified by applying and implementing them on a small scale variant of AES. We provide arguments that draw a relation between the proposed strategy with the retracing boomerang attack devised in Eurocrypt 2020. To the best of our knowledge, this is the first attempt to merge the yoyo and boomerang techniques to analyze SPN ciphers and warrants further attention as it has the potential of becoming an important cryptanalysis tool.

scholarly journals Efficient Length Doubling From Tweakable Block Ciphers

2017 ◽  
pp. 253-270 ◽  
Author(s):  
Yu Long Chen ◽  
Atul Luykx ◽  
Bart Mennink ◽  
Bart Preneel
Keyword(s):  
Block Cipher ◽  
Block Ciphers ◽  
Encryption Scheme ◽  
Authenticated Encryption ◽  
Arbitrary Length ◽  
Pseudorandom Permutation ◽  
Cryptographic Primitive ◽  
Length Data ◽  
Tweakable Block Cipher ◽  
Integral Data

We present a length doubler, LDT, that turns an n-bit tweakable block cipher into an efficient and secure cipher that can encrypt any bit string of length [n..2n − 1]. The LDT mode is simple, uses only two cryptographic primitive calls (while prior work needs at least four), and is a strong length-preserving pseudorandom permutation if the underlying tweakable block ciphers are strong tweakable pseudorandom permutations. We demonstrate that LDT can be used to neatly turn an authenticated encryption scheme for integral data into a mode for arbitrary-length data.

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