Tweakable Block Cipher Research Articles

Tweakable Blockciphers for Efficient Authenticated Encryptions with Beyond the Birthday-Bound Security

Modular design via a tweakable blockcipher (TBC) offers efficient authenticated encryption (AE) schemes (with associated data) that call a blockcipher once for each data block (of associated data or a plaintext). However, the existing efficient blockcipher-based TBCs are secure up to the birthday bound, where the underlying keyed blockcipher is a secure strong pseudorandom permutation. Existing blockcipher-based AE schemes with beyond-birthday-bound (BBB) security are not efficient, that is, a blockcipher is called twice or more for each data block. In this paper, we present a TBC, XKX, that offers efficient blockcipher-based AE schemes with BBB security, by combining with efficient TBC-based AE schemes such as ΘCB3 and

Tweakable Blockciphers for Efficient Authenticated Encryptions with Beyond the Birthday-Bound Security

Modular design via a tweakable blockcipher (TBC) offers efficient authenticated encryption (AE) schemes (with associated data) that call a blockcipher once for each data block (of associated data or a plaintext). However, the existing efficient blockcipher-based TBCs are secure up to the birthday bound, where the underlying keyed blockcipher is a secure strong pseudorandom permutation. Existing blockcipher-based AE schemes with beyond-birthday-bound (BBB) security are not efficient, that is, a blockcipher is called twice or more for each data block. In this paper, we present a TBC, XKX, that offers efficient blockcipher-based AE schemes with BBB security, by combining with efficient TBC-based AE schemes such as ΘCB3 and

Cryptanalysis of PMACx, PMAC2x, and SIVx

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.

Turning Online Ciphers Off

CAESAR has caused a heated discussion regarding the merits of one-pass encryption and online ciphers. The latter is a keyed, length preserving function which outputs ciphertext blocks as soon as the respective plaintext block is available as input. The immediacy of an online cipher affords a clear performance advantage, but it comes at a price: ciphertext blocks cannot depend on later plaintext blocks, limiting diffusion and hence security. We show how one can attain the best of both worlds by providing provably secure constructions, achieving full cipher security, based on applications of an online cipher around blockwise reordering layers. Explicitly, we show that with just two calls to the online cipher, prp security up to the birthday bound is both attainable and maximal. Moreover, we demonstrate that three calls to the online cipher suffice to obtain beyond birthday bound security. We provide a full proof of this for a prp construction, and, in the ±prp setting, security against adversaries who make queries of any single length. As part of our investigation, we extend an observation by Rogaway and Zhang by further highlighting the close relationship between online ciphers and tweakable blockciphers with variable-length tweaks.

Linear Cryptanalysis: Key Schedules and Tweakable Block Ciphers

This paper serves as a systematization of knowledge of linear cryptanalysis and provides novel insights in the areas of key schedule design and tweakable block ciphers. We examine in a step by step manner the linear hull theorem in a general and consistent setting. Based on this, we study the influence of the choice of the key scheduling on linear cryptanalysis, a – notoriously difficult – but important subject. Moreover, we investigate how tweakable block ciphers can be analyzed with respect to linear cryptanalysis, a topic that surprisingly has not been scrutinized until now.

The QARMA Block Cipher Family. Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes

This paper introduces QARMA, a new family of lightweight tweakable block ciphers targeted at applications such as memory encryption, the generation of very short tags for hardware-assisted prevention of software exploitation, and the construction of keyed hash functions. QARMA is inspired by reflection ciphers such as PRINCE, to which it adds a tweaking input, and MANTIS. However, QARMA differs from previous reflector constructions in that it is a three-round Even-Mansour scheme instead of a FX-construction, and its middle permutation is non-involutory and keyed. We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {0, 1}-matrices. The purpose of all these design choices is to harden the cipher against various classes of attacks. We also describe new S-Box search heuristics aimed at minimising the critical path. QARMA exists in 64- and 128-bit block sizes, where block and tweak size are equal, and keys are twice as long as the blocks. We argue that QARMA provides sufficient security margins within the constraints determined by the mentioned applications, while still achieving best-in-class latency. Implementation results on a state-of-the art manufacturing process are reported. Finally, we propose a technique to extend the length of the tweak by using, for instance, a universal hash function, which can also be used to strengthen the security of QARMA.

The QARMA Block Cipher Family. Almost MDS Matrices Over Rings With Zero Divisors, Nearly Symmetric Even-Mansour Constructions With Non-Involutory Central Rounds, and Search Heuristics for Low-Latency S-Boxes

This paper introduces QARMA, a new family of lightweight tweakable block ciphers targeted at applications such as memory encryption, the generation of very short tags for hardware-assisted prevention of software exploitation, and the construction of keyed hash functions. QARMA is inspired by reflection ciphers such as PRINCE, to which it adds a tweaking input, and MANTIS. However, QARMA differs from previous reflector constructions in that it is a three-round Even-Mansour scheme instead of a FX-construction, and its middle permutation is non-involutory and keyed . We introduce and analyse a family of Almost MDS matrices defined over a ring with zero divisors that allows us to encode rotations in its operation while maintaining the minimal latency associated to {0, 1}-matrices. The purpose of all these design choices is to harden the cipher against various classes of attacks. We also describe new S-Box search heuristics aimed at minimising the critical path. QARMA exists in 64- and 128-bit block sizes, where block and tweak size are equal, and keys are twice as long as the blocks. We argue that QARMA provides sufficient security margins within the constraints determined by the mentioned applications, while still achieving best-in-class latency. Implementation results on a state-of-the art manufacturing process are reported. Finally, we propose a technique to extend the length of the tweak by using, for instance, a universal hash function, which can also be used to strengthen the security of QARMA.

Connecting tweakable and multi-key blockcipher security

The significance of understanding blockcipher security in the multi-key setting is highlighted by the extensive literature on attacks, and how effective key size can be significantly reduced. Nevertheless, little attention has been paid in formally understanding the design of multi-key secure blockciphers. In this work, we formalize the multi-key security of tweakable blockciphers in case of general key derivation functions. We show an equivalence between blockcipher multi-key security and tweakable blockcipher security. Our equivalence connects two objects of study, the iterated Even–Mansour (EUROCRYPT 2012) and the iterated Tweakable Even–Mansour (CRYPTO 2015), which establishes that results in both areas are, to a certain extent, transferable. Using our novel equivalence relation, we derive new bounds for both constructions, pave the path towards the solution of two well-studied conjectures, and show that, contrary to common knowledge, key derivation functions need not necessarily be pseudorandom functions in order to provide security: for the iterated Even–Mansour universal hash functions suffice.

Multi-key Analysis of Tweakable Even-Mansour with Applications to Minalpher and OPP

The tweakable Even-Mansour construction generalizes the conventional Even-Mansour scheme through replacing round keys by strings derived from a master key and a tweak. Besides providing plenty of inherent variability, such a design builds a tweakable block cipher from some lower level primitive. In the present paper, we evaluate the multi-key security of TEM-1, one of the most commonly used one-round tweakable Even-Mansour schemes (formally introduced at CRYPTO 2015), which is constructed from a single n-bit permutation P and a function f(k, t) linear in k from some tweak space to {0, 1} n. Based on giant component theorem in random graph theory, we propose a collision-based multi-key attack on TEM-1 in the known-plaintext setting. Furthermore, inspired by the methodology of Fouque et al. presented at ASIACRYPT 2014, we devise a novel way of detecting collisions and eventually obtain a memory-efficient multi-key attack in the adaptive chosen-plaintext setting. As important applications, we utilize our techniques to analyze the authenticated encryption algorithms Minalpher (a second-round candidate of CAESAR) and OPP (proposed at EUROCRYPT 2016) in the multi-key setting. We describe knownplaintext attacks on Minalpher and OPP without nonce misuse, which enable us to recover almost all O(2n/3) independent masks by making O(2n/3) queries per key and costing O(22n/3) memory overall. After defining appropriate iterated functions and accordingly changing the mode of creating chains, we improve the basic blockwiseadaptive chosen-plaintext attack to make it also applicable for the nonce-respecting setting. While our attacks do not contradict the security proofs of Minalpher and OPP in the classical setting, nor pose an immediate threat to their uses, our results demonstrate their security margins in the multi-user setting should be carefully considered. We emphasize this is the very first third-party analysis on Minalpher and OPP.

Practical Key-Recovery Attack on MANTIS5

MANTIS is a lightweight tweakable block cipher published at CRYPTO 2016. In addition to the full 14-round version, MANTIS7, the designers also propose an aggressive 10-round version, MANTIS5. The security claim for MANTIS5 is resistance against “practical attacks”, defined as related-tweak attacks with data complexity 2d less than 230 chosen plaintexts (or 240 known plaintexts), and computational complexity at most 2126−d. We present a key-recovery attack against MANTIS5 with 228 chosen plaintexts and a computational complexity of about 238 block cipher calls, which violates this claim. Our attack is based on a family of differential characteristics and exploits several properties of the lightweight round function and tweakey schedule. To verify the validity of the attack, we also provide a practical implementation which recovers the full key in about 1 core hour using 230 chosen plaintexts.

Is AEZ v4.1 Sufficiently Resilient Against Key-Recovery Attacks?

AEZ is a parallelizable, AES-based authenticated encryption algorithm that is well suited for software implementations on processors equipped with the AES-NI instruction set. It aims at offering exceptionally strong security properties such as nonce and decryption-misuse resistance and optimal security given the selected ciphertext expansion. AEZ was submitted to the authenticated ciphers competition CAESAR and was selected in 2015 for the second round of the competition. In this paper, we analyse the resilience of the latest algorithm version, AEZ v4.1 (October 2015), against key-recovery attacks. While AEZ modifications introduced in 2015 were partly motivated by thwarting a key-recovery attack of birthday complexity against AEZ v3 published at Asiacrypt 2015 by Fuhr, Leurent and Suder, we show that AEZ v4.1 remains vulnerable to a key-recovery attack of similar complexity and security impact. Our attack leverages the use, in AEZ, of an underlying tweakable block cipher based on a 4-round version of AES. Although the presented key-recovery attack does not violate the security claims of AEZ since the designers made no claim for beyond-birthday security, it can be interpreted as an indication that AEZ does not fully meet the objective of being an extremely conservative and misuse-resilient algorithm.

Is AEZ v4.1 Sufficiently Resilient Against Key-Recovery Attacks?

AEZ is a parallelizable, AES-based authenticated encryption algorithm that is well suited for software implementations on processors equipped with the AES-NI instruction set. It aims at offering exceptionally strong security properties such as nonce and decryption-misuse resistance and optimal security given the selected ciphertext expansion. AEZ was submitted to the authenticated ciphers competition CAESAR and was selected in 2015 for the second round of the competition. In this paper, we analyse the resilience of the latest algorithm version, AEZ v4.1 (October 2015), against key-recovery attacks. While AEZ modifications introduced in 2015 were partly motivated by thwarting a key-recovery attack of birthday complexity against AEZ v3 published at Asiacrypt 2015 by Fuhr, Leurent and Suder, we show that AEZ v4.1 remains vulnerable to a key-recovery attack of similar complexity and security impact. Our attack leverages the use, in AEZ, of an underlying tweakable block cipher based on a 4-round version of AES. Although the presented key-recovery attack does not violate the security claims of AEZ since the designers made no claim for beyond-birthday security, it can be interpreted as an indication that AEZ does not fully meet the objective of being an extremely conservative and misuse-resilient algorithm.

Building blockcipher from small-block tweakable blockcipher

How to build a secure blockcipher is one of the central problems in symmetric cryptography. While the popular approach, initiated by the seminal paper of Luby and Rackoff, is based on a pseudorandom function, Minematsu (in: Dunkelman (ed.) FSE, 2009) and Minematsu and Iwata (in: Chen (ed.) IMA, 2011) proposed different schemes to efficiently achieve a better security. The point of these works is that they use tweakable blockcipher (TBC) as an internal module rather than pseudorandom function. This paper further extends the previous schemes and considers the case that the target blockcipher has much larger block size than that of the TBC we use. Assuming the tweak of TBC is long, we propose a scheme similar to unbalanced Feistel cipher that achieves stronger security than the previous schemes of Minematsu and Minematsu-Iwata. We also present a blockcipher-based instantiation of our scheme for the encryption over some unusual domains, such as decimal space, as a typical problem of format-preserving encryption.

An Efficient FPGA Hardware Implementation of the Threefish Tweakable Block Cipher

Computer security has a significant importance in today's world. Encryption and decryption of sensitive and important data are required for everyday tasks including electronic, data communications, and internet transactions. A large number of encryption and decryption algorithms have been developed in literature to fulfil the job. Many of these algorithms have been standardized. This paper examines the ThreeFish tweakable block cipher and provides an efficient field programmable gate array hardware implementation of the ThreeFish-256, ThreeFish-512, and ThreeFish-1024 encryption and decryption algorithms. Experimental results are provided and comparisons with the state of the art implementations are made. Experimental results illustrate the efficiency of the proposed implementation.

Tweakable Block Ciphers

A common trend in applications of block ciphers over the past decades has been to employ block ciphers as one piece of a “mode of operation”—possibly, a way to make a secure symmetric-key cryptosystem, but more generally, any cryptographic application. Most of the time, these modes of operation use a wide variety of techniques to achieve a subgoal necessary for their main goal: instantiation of “essentially different” instances of the block cipher. We formalize a cryptographic primitive, the “tweakable block cipher.” Such a cipher has not only the usual inputs—message and cryptographic key—but also a third input, the “tweak.” The tweak serves much the same purpose that an initialization vector does for CBC mode or that a nonce does for OCB mode. Our abstraction brings this feature down to the primitive block-cipher level, instead of incorporating it only at the higher modes-of-operation levels. We suggest that (1) tweakable block ciphers are easy to design, (2) the extra cost of making a block cipher “tweakable” is small, and (3) it is easier to design and prove the security of applications of block ciphers that need this variability using tweakable block ciphers.

Generalization and Extension of XEX* Mode

This paper describes an extension of XEX* mode, which is a method to convert a block cipher into a tagged tweakable block cipher, a notion introduced by Rogaway in 2004 as an extension of the tweakable block cipher by Liskov et al. Our extension attaches an additional encryption function to the original XEX*, which has some limitation but is slightly faster than the encryption implemented by XEX*. We prove our scheme's security in a general form, where the offset function, a key component of our construction, is not restricted to the one used by XEX*. We also provide some applications of our result, in particular to OCB 2.0, an authenticated encryption based on XEX*.

A General Construction of Tweakable Block Ciphers and Different Modes of Operations

This work builds on earlier work by Rogaway at Asiacrypt 2004 on tweakable block cipher (TBC) and modes of operations. Our first contribution is to generalize Rogaway's TBC construction by working over a ring and by the use of a masking sequence of functions. The ring can be instantiated as either GF or as . Further, over GF, efficient instantiations of the masking sequence of functions can be done using either a binary linear feedback shift register (LFSR); a powering construction; a cellular automata map; or by using a word-oriented LFSR. Rogaway's TBC construction was built from the powering construction over GF. Our second contribution is to use the general TBC construction to instantiate constructions of various modes of operations including authenticated encryption (AE) and message authentication code (MAC). In particular, this gives rise to a family of efficient one-pass AE modes of operation. Out of these, the mode of operation obtained by the use of word-oriented LFSR promises to provide a masking method which is more efficient than the one used in the well known AE protocol called OCB1.

HCH: A New Tweakable Enciphering Scheme Using the Hash-Counter-Hash Approach

The notion of tweakable block ciphers was formally introduced by Liskov-Rivest-Wagner at Crypto 2002 (the 2002 Annual International Cryptology Conference). The extension and the first construction, called CMC, of this notion to tweakable enciphering schemes which can handle variable length messages was given by Halevi-Rogaway at Crypto 2003. In this paper, we present HCH, which is a new construction of such a scheme. The construction uses two universal hash computations with a counter mode of encryption in-between. This approach was first proposed by McGrew-Viega to build a scheme called XCB and later used by Wang-Feng-Wu, to obtain a scheme called HCTR. A unique feature of HCH compared to all known tweakable enciphering schemes is that HCH uses a single key, can handle arbitrary length messages, and has a quadratic security bound. An important application of a tweakable enciphering scheme is disk encryption. HCH is well suited for this application. We also describe a variant, which can utilize precomputation and makes one less block cipher call. This compares favorably to other hash-encrypt-hash-type constructions, supports better key agility and requires less key material.

Cryptanalysis of the TAE Mode and Its Improvement

The TAE (tweakable authenticated encryption) mode is an authenticated encryption mode which is based on a tweakable block cipher. Previous research results show that the secure tweakable block cipher is not sufficient for the security of the authenticated encryption TAE mode. Only when the tweakable block cipher is strong will the TAE be secure. Some improvements to the TAE mode are also given in this paper, resulting in a MTAE (modified tweakable authenticated encryption) mode with security proof.