On hashing with tweakable ciphers

Cryptographic hash functions are often built on block ciphers in order to reduce the security analysis of the hash to that of the cipher, and to minimize the hardware size. Well known hash constructs are used in international standards like MD5 and SHA-1. Recently, researchers proposed new modes of operations for hash functions to protect against generic attacks, and it remains open how to base such functions on block ciphers. An attracting and intuitive choice is to combine previous constructions with tweakable block ciphers. We investigate such constructions, and show the surprising result that combining a provably secure mode of operation with a provably secure tweakable cipher does not guarantee the security of the constructed hash function. In fact, simple attacks can be possible when the interaction between secure components leaves some additional "freedom" to an adversary. Our techniques are derived from the principle of slide attacks, which were introduced for attacking block ciphers

Provable Security of (Tweakable) Block Ciphers Based on Substitution-Permutation Networks

Substitution-Permutation Networks (SPNs) refer to a family of constructions which build a wn-bit block cipher from n-bit public permutations (often called S-boxes), which alternate keyless and “local” substitution steps utilizing such S-boxes, with keyed and “global” permu- tation steps which are non-cryptographic. Many widely deployed block ciphers are constructed based on the SPNs, but there are essentially no provable-security results about SPNs. In this work, we initiate a comprehensive study of the provable security of SPNs as (possibly tweakable) wn-bit block ciphers, when the underlying n-bit permutation is modeled as a public random permutation. When the permutation step is linear (which is the case for most existing designs), we show that 3 SPN rounds are necessary and sufficient for security. On the other hand, even 1-round SPNs can be secure when non-linearity is allowed. Moreover, 2-round non-linear SPNs can achieve “beyond- birthday” (up to 2 2n/3 adversarial queries) security, and, as the number of non-linear rounds increases, our bounds are meaningful for the number of queries approaching 2 n . Finally, our non-linear SPNs can be made tweakable by incorporating the tweak into the permutation layer, and provide good multi-user security. As an application, our construction can turn two public n-bit permuta- tions (or fixed-key block ciphers) into a tweakable block cipher working on wn-bit inputs, 6n-bit key and an n-bit tweak (for any w ≥ 2); the tweakable block cipher provides security up to 2 2n/3 adversarial queries in the random permutation model, while only requiring w calls to each permutation, and 3w field multiplications for each wn-bit input

Notions and relations for RKA-secure permutation and function families

The theory of designing block ciphers is mature, having seen signi¯cant progress since the early 1990s for over two decades, especially during the AES devel- opment e®ort. Nevertheless, interesting directions exist, in particular in the study of the provable security of block ciphers along similar veins as public-key primitives, i.e. the notion of pseudorandomness (PRP) and indistinguishability (IND). Furthermore, recent cryptanalytic progress has shown that block ciphers well designed against known cryptanalysis techniques including related-key attacks (RKA) may turn out to be less secure against related-key attacks than expected. The notion of provable security of block ciphers against related-key attacks was initiated by Bellare and Kohno, and sub- sequently treated by Lucks. Concrete block cipher constructions were proposed therein with provable security guarantees. In this paper, we are interested in the security no- tions for RKA-secure block ciphers

Elastic-Tweak: A Framework for Short Tweak Tweakable Block Cipher

Tweakable block cipher (TBC), a stronger notion than standard block ciphers, has wide-scale applications in symmetric-key schemes. At a high level, it provides flexibility in design and (possibly) better security bounds. In multi-keyed applications, a TBC with short tweak values can be used to replace multiple keys. However, the existing TBC construction frameworks, including TWEAKEY and XEX, are designed for general purpose tweak sizes. Specifically, they are not optimized for short tweaks, which might render them inefficient for certain resource constrained applications. So a dedicated paradigm to construct short-tweak TBCs (tBC) is highly desirable. In this paper, as a first contribution, we present a dedicated framework, called the Elastic-Tweak framework (ET in short), to convert any reasonably secure SPN block cipher into a secure tBC. We apply the ET framework on GIFT and AES to construct efficient tBCs, named TweGIFT and TweAES. These short-tweak TBCs have already been employed in recent NIST lightweight competition candidates, LOTUS-LOCUS and ESTATE. As our second contribution, we show some concrete applications of ET-based tBCs, which are better than their block cipher counterparts in terms of key size, state size, number of block cipher calls, and short message processing. Some notable applications include, Twe-FCBC (reduces the key size of FCBC and gives better security than CMAC), Twe-LightMAC Plus (better rate than LightMAC Plus), Twe-CLOC, and Twe-SILC (reduces the number of block cipher calls and simplifies the design of CLOC and SILC)

Elastic-Tweak: A Framework for Short Tweak Tweakable Block Cipher

Tweakable block cipher (TBC), a stronger notion than standard block ciphers, has wide-scale applications in symmetric-key schemes. At a high level, it provides flexibility in design and (possibly) better security bounds. In multi-keyed applications, a TBC with short tweak values can be used to replace multiple keys. However, the existing TBC construction frameworks, including TWEAKEY and XEX, are designed for general purpose tweak sizes. Specifically, they are not optimized for short tweaks, which might render them inefficient for certain resource constrained applications. So a dedicated paradigm to construct short-tweak TBCs (tBC) is highly desirable. In this paper, we present a dedicated framework, called the Elastic-Tweak framework (ET in short), to convert any reasonably secure SPN block cipher into a secure tBC. We apply the ET framework on GIFT and AES to construct efficient tBCs, named TweGIFT and TweAES. We present hardware and software results to show that the performance overheads for these tBCs are minimal. We perform comprehensive security analysis and observe that TweGIFT and TweAES provide sufficient security without any increase in the number of block cipher rounds when compared to GIFT and AES. We also show some concrete applications of ET-based tBCs, which are better than their block cipher counterparts in terms of key size, state size, number of block cipher calls, and short message processing. Some notable applications include, Twe-FCBC (reduces the key size of FCBC and gives better security than CMAC), Twe-LightMAC Plus (better rate than LightMAC Plus), Twe-CLOC, and Twe-SILC (reduces the number of block cipher calls and simplifies the design of CLOC and SILC)

Implementation of the SCREAM Tweakable Block Cipher in MSP430 Assembly Language

The encryption mode of the Tweakable Block Cipher (TBC) of the SCREAM Authenticated Cipher is implemented in the MSP430 microcontroller. Assembly language versions of the TBC are prepared using both precomputed tweak keys and tweak keys computed “on-the-fly.” Both versions are compared against published results for the assembly language version of SCREAM on the ATMEL AVR microcontroller, and against the C reference implementation in terms of performance and size. The assembly language version using precomputed tweak keys achieves a speedup of 1.7 and memory savings of 9 percent over the reported SCREAM implementation in the ATMEL AVR. The assembly language version using tweak keys computed “on-the-fly” achieves a speedup of 1.6 over the ATMEL AVR version while reducing memory usage by 15 percent

Tweaks and Keys for Block Ciphers: the TWEAKEY Framework

We propose the TWEAKEY framework with goal to unify the design of tweakable block ciphers and of block ciphers resistant to related-key attacks. Our framework is simple, extends the key-alternating construction, and allows to build a primitive with arbitrary tweak and key sizes, given the public round permutation (for instance, the AES round). Increasing the sizes renders the security analysis very difficult and thus we identify a subclass of TWEAKEY, that we name STK, which solves the size issue by the use of finite field multiplications on low hamming weight constants. We give very efficient instances of STK, in particular, a 128-bit tweak/key/state block cipher Deoxys-BC that is the first AES-based ad-hoc tweakable block cipher. At the same time, Deoxys-BC could be seen as a secure alternative to AES-256, which is known to be insecure in the related-key model. As another member of the TWEAKEY framework, we describe Kiasu-BC, which is a very simple and even more efficient tweakable variation of AES-128 when the tweak size is limited to 64 bits. In addition to being efficient, our proposals, compared to the previous schemes that use AES as a black box, offer security beyond the birthday bound. Deoxys-BC and Kiasu-BC represent interesting pluggable primitives for authenticated encryption schemes, for instance, OCB instantiated with Kiasu-BC runs at about 0.75 c/B on Intel Haswell. Our work can also be seen as advances on the topic of secure key schedule design for AES-like ciphers, describing several proposals in this direction