International Association
for Cryptologic Research

In this paper, we propose a new family of low-latency pseudorandom functions (PRFs), dubbed Gleeok.Gleeok utilizes three 128-bit branches to achieve a 256-bit key size while maintaining low latency. The first two branches are specifically designed to defend against statistical attacks, especially for differential attacks, while the third branch provides resilience against algebraic attacks. This unique design enables Gleeok to offer ultralow latency while supporting 256-bit keys, setting it apart from existing ciphers dedicated to low-latency requirements. In addition, we propose wide-block variants having three 256-bit branches. We also present an application of Gleeok to short-input authenticated encryption which is crucial for memory encryption and various realtime communication applications. Furthermore, we present comprehensive hardware implementation results that establish the capabilities of Gleeok and demonstrate its competitiveness against related schemes in the literature. In particular, Gleeok achieves a minimum latency of roughly 360 ps with the NanGate 15 nm cell library and is thus on par with related low-latency schemes that only feature 128-bit keys while maintaining minimal overhead when equipped in an authenticated mode of operation.

We present a new block cipher mode of operation for authenticated encryption (AE), dubbed XOCB, that has the following features: (1) beyond-birthday-bound (BBB) security based on standard pseudorandom assumption of the internal block cipher if the maximum block length is sufficiently smaller than the birthday bound, (2) rate-1 computation, and (3) supporting any block cipher with any key length. Namely, XOCB has effectively the same efficiency as the seminal OCB while having stronger quantitative security without any change in the security model or the required primitive in OCB. Although numerous studies have been conducted in the past, our XOCB is the first mode of operation to achieve these multiple goals simultaneously.

In the real-world applications, the overwhelming majority of cases require hashing with relatively short input, say up to 2K bytes. The length of almost all TCP/IP packets is between 40 to 1.5K bytes, and the maximum packet lengths of major protocols, e.g., Zigbee, Bluetooth low energy, and Controller Area Network (CAN) are less than 128 bytes. However, existing schemes are not well optimized for short input. To bridge the gap between real-world needs (in future) and limited performances of state-of-the-art hash functions for short input, we design a family of wide-block permutations Areion that fully leverages the power of AES instructions, which are widely deployed in many devices. As its applications, we propose several hash functions. Areion significantly outperforms existing schemes for short input and even competitive to relatively long message. Indeed, our hash function is surprisingly fast, and its performance is less than 3 cycles/byte in the latest Intel architecture for any message size. Especially, it is about 10 times faster than existing state-of-the-art schemes for short message up to around 100 bytes, which are most widely-used input size in real-world applications, on both the latest CPU architectures (IceLake, Tiger Lake, and Alder Lake) and mobile platforms (Pixel 6 and iPhone 13).

This paper presents a provably secure, higher-order, and leakage-resilient (LR) rekeying scheme named LR Rekeying with Random oracle Repetition (LR4), along with a quantitative security evaluation methodology. Many existing LR primitives are based on a concept of leveled implementation, which still essentially require a leak-free sanctuary (i.e., differential power analysis (DPA)-resistant component(s)) for some parts. In addition, although several LR pseudorandom functions (PRFs) based on only bounded DPA-resistant components have been developed, their validity and effectiveness for rekeying usage still need to be determined. In contrast, LR4 is formally proven under a leakage model that captures the practical goal of side-channel attack (SCA) protection (e.g., masking with a practical order) and assumes no unbounded DPA-resistant sanctuary. This proof suggests that LR4 resists exponential invocations (up to the birthday bound of key size) without using any unbounded leak-free component, which is the first of its kind. Moreover, we present a quantitative SCA success rate evaluation methodology for LR4 that combines the bounded leakage models for LR cryptography and a state-of-the-art information-theoretical SCA evaluation method. We validate its soundness and effectiveness as a DPA countermeasure through a numerical evaluation; that is, the number of secure calls of a symmetric primitive increases exponentially by increasing a security parameter under practical conditions.

For an Authenticated Encryption with Associated Data (AEAD) scheme, the key committing security refers to the security notion of whether the adversary can produce a pair of distinct input tuples, including the key, that result in the same output. While the key committing security of various nonce-based AEAD schemes is known, the security analysis of Robust AE (RAE) is largely unexplored. In particular, we are interested in the key committing security of AEAD schemes built on the Encode-then-Encipher (EtE) approach from a wide block cipher. We first consider AEZ v5, the classical and the first dedicated RAE that employs the EtE approach. We focus our analysis on the core part of AEZ to show our best attacks depending on the length of the ciphertext expansion. In the general case where the Tweakable Block Cipher (TBC) is assumed to be ideal, we show a birthday attack and a matching provable security result. AEZ adopts a simpler key schedule and the prove-then-prune approach in the full specification, and we show a practical attack against it by exploiting the simplicity of the key schedule. The complexity is 227, and we experimentally verify the correctness with a concrete example. We also cover two AEAD schemes based on EtE. One is built on Adiantum, and the other one is built on HCTR2, which are two wide block ciphers that are used in real applications. We present key committing attacks against these schemes when used in EtE and matching proofs for particular cases.

We present Orthros, a 128-bit block pseudorandom function. It is designed with primary focus on latency of fully unrolled circuits. For this purpose, we adopt a parallel structure comprising two keyed permutations. The round function of each permutation is similar to Midori, a low-energy block cipher, however we thoroughly revise it to reduce latency, and introduce different rounds to significantly improve cryptographic strength in a small number of rounds. We provide a comprehensive, dedicated security analysis. For hardware implementation, Orthros achieves the lowest latency among the state-of-the-art low-latency primitives. For example, using the STM 90nm library, Orthros achieves a minimum latency of around 2.4 ns, while other constructions like PRINCE, Midori-128 and QARMA9-128- σ0 achieve 2.56 ns, 4.10 ns, 4.38 ns respectively.

I will talk about OCB2, an authenticated encryption (AE) mode of operation proposed at 2004. It is a very popular scheme for its innovative design. The tweakable block cipher-based modular architecture of OCB2 was influenced to countless subsequent schemes. However, our paper presented at CRYPTO 2019 showed that it is completely broken with negligible amount of computation. In addition to the description of our attacks, I will tell a bit more on the story behind this break, how it started and evolved, hoping that it contributes to our understanding of practical provable security.

In this article, we propose two new families of very lightweight and efficient authenticated encryption with associated data (AEAD) modes, Romulus and Remus, that provide security beyond the birthday bound with respect to the block-length n. The former uses a tweakable block cipher (TBC) as internal primitive and can be proven secure in the standard model. The later uses a block cipher (BC) as internal primitive and can be proven secure in the ideal cipher model. Both our modes allow to switch very easily from the nonce-respecting to the nonce-misuse scenario.Previous constructions, such as ΘCB3, are quite computationally efficient, yet needing a large memory for implementation, which makes them unsuitable for platforms where lightweight cryptography should play a key role. Romulus and Remus break this barrier by introducing a new architecture evolved from a BC mode COFB. They achieve the best of what can be possible with TBC – the optimal computational efficiency (rate-1 operation) and the minimum state size of a TBC mode (i.e., (n + t)-bit for n-bit block, t-bit tweak TBC), with almost equivalent provable security as ΘCB3. Actually, our comparisons show that both our designs present superior performances when compared to all other recent lightweight AEAD modes, being BC-based, TBC-based or sponge-based, in the nonce-respecting or nonce-misuse scenario. We eventually describe how to instantiate Romulus and Remus modes using the Skinny lightweight tweakable block cipher proposed at CRYPTO 2016, including the hardware implementation results

Misuse-resistant AE (MRAE) is a class of authenticated encryption (AE) that has a resistance against a potential misuse (repeat) of nonce. MRAE has received significant attention from the initial proposal by Rogaway and Shrimpton. They showed a generic MRAE construction called SIV. SIV becomes a de-facto scheme for MRAE, however, one notable drawback is its two-pass operation for both encryption and decryption. This implies that MRAE built on SIV is slower than the integrated nonce-based AE schemes, such as OCB.In this paper, we propose a new method to improve this situation. Particularly, our MRAE proposal (decryption-fast SIV or DFV) allows to decrypt as fast as a plain decryption, hence theoretically doubles its speed from the original SIV, while keeping the encryption speed equivalent to SIV. We present several generic compositions for DFV and their instantiations.

We present practical attacks on OCB2. This mode of operation of a blockcipher was designed with the aim to provide particularly efficient and provably secure authenticated encryption services, and since its proposal about 15 years ago it belongs to the top performers in this realm. OCB2 was included in an ISO standard in 2009. An internal building block of OCB2 is the tweakable blockcipher obtained by operating a regular blockcipher in $${\text {XEX}}^*$$ XEX ∗  mode. The latter provides security only when evaluated in accordance with certain technical restrictions that, as we note, are not always respected by OCB2. This leads to devastating attacks against OCB2’s security promises: We develop a range of very practical attacks that, amongst others, demonstrate universal forgeries and full plaintext recovery. We complete our report with proposals for (provably) repairing OCB2. As a direct consequence of our findings, OCB2 is currently in a process of removal from ISO standards. Our attacks do not apply to OCB1 and OCB3, and our privacy attacks on OCB2 require an active adversary.

Tweakable block ciphers (TBCs) have proven highly useful to boost the security guarantees of authentication schemes. In 2017, Cogliati et al. proposed two MACs combining TBC and universal hash functions: a nonce-based MAC called NaT and a deterministic MAC called HaT. While both constructions provide high security, their properties are complementary: NaT is almost fully secure when nonces are respected (i.e., n-bit security, where n is the block size of the TBC, and no security degradation in terms of the number of MAC queries when nonces are unique), while its security degrades gracefully to the birthday bound (n/2 bits) when nonces are misused. HaT has n-bit security and can be used naturally as a nonce-based MAC when a message contains a nonce. However, it does not have full security even if nonces are unique.This work proposes two highly secure and efficient MACs to fill the gap: NaT2 and eHaT. Both provide (almost) full security if nonces are unique and more than n/2-bit security when nonces can repeat. Based on NaT and HaT, we aim at achieving these properties in a modular approach. Our first proposal, Nonce-as-Tweak2 (NaT2), is the sum of two NaT instances. Our second proposal, enhanced Hash-as-Tweak (eHaT), extends HaT by adding the output of an additional nonce-depending call to the TBC and prepending nonce to the message. Despite the conceptual simplicity, the security proofs are involved. For NaT2 in particular, we rely on the recent proof framework for Double-block Hash-then-Sum by Kim et al. from Eurocrypt 2020.

This paper presents a lightweight blockcipher-based authenticated encryption mode mainly focusing on minimizing the implementation size, i.e., hardware gates or working memory on software. The mode is called $$\textsf {COFB}$$COFB, for COmbined FeedBack. $$\textsf {COFB}$$COFB uses an n-bit blockcipher as the underlying primitive and relies on the use of a nonce for security. In addition to the state required for executing the underlying blockcipher, $$\textsf {COFB}$$COFB needs only n / 2 bits state as a mask. Till date, for all existing constructions in which masks have been applied, at least n bit masks have been used. Thus, we have shown the possibility of reducing the size of a mask without degrading the security level much. Moreover, it requires one blockcipher call to process one input block. We show $$\textsf {COFB}$$COFB is provably secure up to $$O(2^{n/2}/n)$$O(2n/2/n) queries which is almost up to the standard birthday bound. We first present an idealized mode $$\textsf {iCOFB}$$iCOFB along with the details of its provable security analysis. Next, we extend the construction to the practical mode COFB. We instantiate COFB with two 128-bit blockciphers, AES-128 and GIFT-128, and present their implementation results on FPGAs. We present two implementations, with and without CAESAR hardware API. When instantiated with AES-128 and implemented without CAESAR hardware API, COFB achieves only a few more than 1000 Look-Up-Tables (LUTs) while maintaining almost the same level of provable security as standard AES-based AE, such as GCM. When instantiated with GIFT-128, COFB performs much better in hardware area. It consumes less than 1000 LUTs while maintaining the same security level. However, when implemented with CAESAR hardware API, there are significant overheads both in hardware area and in throughput. COFB with AES-128 achieves about 1475 LUTs. COFB with GIFT-128 achieves a few more than 1000 LUTs. Though there are overheads, still both these figures show competitive implementation results compared to other authenticated encryption constructions.

We define ZOCB and ZOTR for nonce-based authenticated encryption with associated data, and analyze their provable security. These schemes use a tweakable blockcipher (TBC) as the underlying primitive, and fully utilize its input to process a plaintext and associated data (AD). This property is commonly referred to as full absorption, and this has been explored for schemes based on a permutation or a pseudorandom function (PRF). Our schemes improve the efficiency of TBC-based counterparts of OCB and OTR called OCB3 (Krovetz and Rogaway, FSE 2011) and OTR (Minematsu, EUROCRYPT 2014). Specifically, ΘCB3 and OTR have an independent part to process AD, and our schemes integrate this process into the encryption part of a plaintext by using the tweak input of the TBC. Up to a certain length of AD, ZOCB and ZOTR completely eliminate the independent process for it. Even for longer AD, our schemes process it efficiently by fully using the tweak input of the TBC. For this purpose, based on previous tweak extension schemes for TBCs, we introduce a scheme called XTX*. To our knowledge, ZOCB and ZOTR are the first efficiency improvement of ΘCB3 and OTR in terms of the number of TBC calls. Compared to Sponge-based and PRF-based schemes, ZOCB and ZOTR allow fully parallel computation of the underlying primitive, and have a unique design feature that an authentication tag is independent of a part of AD. We present experimental results illustrating the practical efficiency gain and clarifying the efficiency cost for it with a concrete instantiation. The results show that for long input data, our schemes have gains, while we have efficiency loss for short input data.

We present practical attacks on OCB2. This mode of operation of a blockcipher was designed with the aim to provide particularly efficient and provably-secure authenticated encryption services, and since its proposal about 15 years ago it belongs to the top performers in this realm. OCB2 was included in an ISO standard in 2009.An internal building block of OCB2 is the tweakable blockcipher obtained by operating a regular blockcipher in $$ \text {XEX} ^*$$ mode. The latter provides security only when evaluated in accordance with certain technical restrictions that, as we note, are not always respected by OCB2. This leads to devastating attacks against OCB2’s security promises: We develop a range of very practical attacks that, amongst others, demonstrate universal forgeries and full plaintext recovery. We complete our report with proposals for (provably) repairing OCB2. To our understanding, as a direct consequence of our findings, OCB2 is currently in a process of removal from ISO standards. Our attacks do not apply to OCB1 and OCB3, and our privacy attacks on OCB2 require an active adversary.

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.

This paper presents a design of authenticated encryption (AE) focusing on minimizing the implementation size, i.e., hardware gates or working memory on software. The scheme is called $$\textsf {COFB}$$, for COmbined FeedBack. $$\textsf {COFB}$$ uses an n-bit blockcipher as the underlying primitive, and relies on the use of a nonce for security. In addition to the state required for executing the underlying blockcipher, $$\textsf {COFB}$$ needs only n / 2 bits state as a mask. Till date, for all existing constructions in which masks have been applied, at least n bit masks have been used. Thus, we have shown the possibility of reducing the size of a mask without degrading the security level much. Moreover, it requires one blockcipher call to process one input block. We show $$\textsf {COFB}$$ is provably secure up to $$O(2^{n/2}/n)$$ queries which is almost up to the standard birthday bound. We also present our hardware implementation results. Experimental implementation results suggest that our proposal has a good performance and the smallest footprint among all known blockcipher-based AE.

At CCS 2015, Gueron and Lindell proposed GCM-SIV, a provably secure authenticated encryption scheme that remains secure even if the nonce is repeated. While this is an advantage over the original GCM, we first point out that GCM-SIV allows a trivial distinguishing attack with about 248 queries, where each query has one plaintext block. This shows the tightness of the security claim and does not contradict the provable security result. However, the original GCM resists the attack, and this poses a question of designing a variant of GCM-SIV that is secure against the attack. We present a minor variant of GCM-SIV, which we call GCM-SIV1, and discuss that GCM-SIV1 resists the attack, and it offers a security trade-off compared to GCM-SIV. As the main contribution of the paper, we explore a scheme with a stronger security bound. We present GCM-SIV2 which is obtained by running two instances of GCM-SIV1 in parallel and mixing them in a simple way. We show that it is secure up to 285.3 query complexity, where the query complexity is measured in terms of the total number of blocks of the queries. Finally, we generalize this to show GCM-SIVr by running r instances of GCM-SIV1 in parallel, where r ≥ 3, and show that the scheme is secure up to 2128r/(r+1) query complexity. The provable security results are obtained under the standard assumption that the blockcipher is a pseudorandom permutation.