## CryptoDB

### Ashwin Jha

#### Publications

**Year**

**Venue**

**Title**

2021

TOSC

On Length Independent Security Bounds for the PMAC Family
📺
Abstract

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.

2021

ASIACRYPT

Fine-tuning the ISO/IEC Standard LightMAC
📺
Abstract

LightMAC, by Luykx et al., is a block cipher based message authentication code (MAC). The simplicity of design and low overhead allows it to have very compact implementations. As a result, it has been recently chosen as an ISO/IEC standard MAC for lightweight applications. LightMAC has been shown to achieve query-length independent security bound of $O(q^2/2^n)$ when instantiated with two independently keyed $n$-bit block ciphers, where $q$ denotes the number of MAC queries and the query-length is upper bounded by $(n-s)2^s$ bits for a fixed counter size $s$. In this paper, we aim to minimize the number of block cipher keys in LightMAC. First, we show that the original LightMAC instantiated with a single block cipher key, referred as 1k-LightMAC, achieves security bound of $O(q^2/2^n)$ while the query-length is at least $(n-s)$ bits and at most $(n-s)\min\{2^{n/4},2^s\}$ bits. Second, we show that a minor variant of 1k-LightMAC, dubbed as LightMAC-ds, achieves security bound of $O(q^2/2^n)$ while query-length is upper bounded by $(n-s)2^{s-1}$ bits. Of independent interest, our security proof of 1k-LightMAC employs a novel sampling approach, called the reset-sampling, as a subroutine within the H-coefficient proof setup.

2020

TOSC

INT-RUP Secure Lightweight Parallel AE Modes
📺
Abstract

Owing to the growing demand for lightweight cryptographic solutions, NIST has initiated a standardization process for lightweight cryptographic algorithms. Specific to authenticated encryption (AE), the NIST draft demands that the scheme should have one primary member that has key length of 128 bits, and it should be secure for at least 250 − 1 byte queries and 2112 computations. Popular (lightweight) modes, such as OCB, OTR, CLOC, SILC, JAMBU, COFB, SAEB, Beetle, SUNDAE etc., require at least 128-bit primitives to meet the NIST criteria, as all of them are just birthday bound secure. Furthermore, most of them are sequential, and they either use a two pass mode or they do not offer any security when the adversary has access to unverified plaintext (RUP model). In this paper, we propose two new designs for lightweight AE modes, called LOCUS and LOTUS, structurally similar to OCB and OTR, respectively. These modes achieve notably higher AE security bounds with lighter primitives (only a 64-bit tweakable block cipher). Especially, they satisfy the NIST requirements: secure as long as the data complexity is less than 264 bytes and time complexity is less than 2128, even when instantiated with a primitive with 64-bit block and 128-bit key. Both these modes are fully parallelizable and provide full integrity security under the RUP model. We use TweGIFT-64[4,16,16,4] (also referred as TweGIFT-64), a tweakable variant of the GIFT block cipher, to instantiate our AE modes. TweGIFT-64-LOCUS and TweGIFT-64-LOTUS are significantly light in hardware implementation. To justify, we provide our FPGA based implementation results, which demonstrate that TweGIFT-64-LOCUS consumes only 257 slices and 690 LUTs, while TweGIFT-64-LOTUS consumes only 255 slices and 664 LUTs.

2020

TOSC

ESTATE: A Lightweight and Low Energy Authenticated Encryption Mode
📺
Abstract

NIST has recently initiated a standardization project for efficient lightweight authenticated encryption schemes. SUNDAE, a candidate in this project, achieves optimal state size which results in low circuit overhead on top of the underlying block cipher. In addition, SUNDAE provides security in nonce-misuse scenario as well. However, in addition to the block cipher circuit, SUNDAE also requires some additional circuitry for multiplication by a primitive element. Further, it requires an additional block cipher invocation to create the starting state. In this paper, we propose a new lightweight and low energy authenticated encryption family, called ESTATE, that significantly improves the design of SUNDAE in terms of implementation costs (both hardware area and energy) and efficient processing of short messages. In particular, ESTATE does not require an additional multiplication circuit, and it reduces the number of block cipher calls by one. Moreover, it provides integrity security even under the release of unverified plaintext (or RUP) model. ESTATE is based on short-tweak tweakable block ciphers (or tBC, small ’t’ denotes short tweaks) and we instantiate it with two recently designed tBCs: TweAES and TweGIFT. We also propose a low latency variant of ESTATE, called sESTATE, that uses a round-reduced (6 rounds) variant of TweAES called TweAES-6. We provide comprehensive FPGA based hardware implementation for all the three instances. The implementation results depict that ESTATE_TweGIFT-128 (681 LUTs, 263 slices) consumes much lesser area as compared to SUNDAE_GIFT-128 (931 LUTs, 310 slices). When we moved to the AES variants, along with the area-efficiency (ESTATE_TweAES consumes 1901 LUTs, 602 slices while SUNDAE_AES-128 needs 1922 LUTs, 614 slices), we also achieve higher throughput for short messages (For 16-byte message, a throughput of 1251.10 and 945.36 Mbps for ESTATE_TweAES and SUNDAE_AES-128 respectively).

2020

TOSC

From Combined to Hybrid: Making Feedback-based AE even Smaller
📺
Abstract

In CHES 2017, Chakraborti et al. proposed COFB, a rate-1 sequential block cipher-based authenticated encryption (AE) with only 1.5n-bit state, where n denotes the block size. They used a novel approach, the so-called combined feedback, where each block cipher input has a combined effect of the previous block cipher output and the current plaintext block. In this paper, we first study the security of a general rate-1 feedback-based AE scheme in terms of its overall internal state size. For a large class of feedback functions, we show that the overlying AE scheme can be attacked in 2r queries if the internal state size is n + r bits for some r ≥ 0. This automatically shows that a birthday bound (i.e. 2n/2 queries) secure AE scheme must have at least 1.5n-bit state, whence COFB is almost-optimal (use 1.5n-bit state and provides security up to 2n/2/n queries). We propose a new feedback function, called the hybrid feedback or HyFB, which is a hybrid composition of plaintext and ciphertext feedbacks. HyFB has a key advantage of lower XOR counts over the combined feedback function. This essentially helps in reducing the hardware footprint. Based on HyFB we propose a new AE scheme, called HyENA, that achieves the state size, rate, and security of COFB. In addition, HyENA has significantly lower XOR counts as compared to COFB, whence it is expected to have a smaller implementation as compared to COFB.

2020

TOSC

On the Security of Sponge-type Authenticated Encryption Modes
📺
Abstract

The sponge duplex is a popular mode of operation for constructing authenticated encryption schemes. In fact, one can assess the popularity of this mode from the fact that around 25 out of the 56 round 1 submissions to the ongoing NIST lightweight cryptography (LwC) standardization process are based on this mode. Among these, 14 sponge-type constructions are selected for the second round consisting of 32 submissions. In this paper, we generalize the duplexing interface of the duplex mode, which we call Transform-then-Permute. It encompasses Beetle as well as a new sponge-type mode SpoC (both are round 2 submissions to NIST LwC). We show a tight security bound for Transform-then-Permute based on b-bit permutation, which reduces to finding an exact estimation of the expected number of multi-chains (defined in this paper). As a corollary of our general result, authenticated encryption advantage of Beetle and SpoC is about T(D+r2r)/2b where T, D and r denotes the number of offline queries (related to time complexity of the attack), number of construction queries (related to data complexity) and rate of the construction (related to efficiency). Previously the same bound has been proved for Beetle under the limitation that T << min{2r, 2b/2} (that compels to choose larger permutation with higher rate). In the context of NIST LwC requirement, SpoC based on 192-bit permutation achieves the desired security with 64-bit rate, which is not achieved by either duplex or Beetle (as per the previous analysis).

2020

ASIACRYPT

How to Build Optimally Secure PRFs Using Block Ciphers
📺
Abstract

In EUROCRYPT '96, Aiello and Venkatesan proposed two candidates for $ 2n $-bit to $ 2n $-bit pseudorandom functions (PRFs), called Benes and modified Benes (or mBenes), based on $ n $-bit to $ n $-bit PRFs. While Benes is known to be secure up to $ 2^n $ queries (Patarin, AFRICACRYPT '08), the security of mBenes has only been proved up to $ 2^{n(1-\epsilon)} $ queries for all $ \epsilon > 0 $ by Patarin and Montreuil in ICISC '05. In this work, we show that the composition of a $ 2n $-bit hash function with mBenes is a secure variable input length (VIL) PRF up to $ 2^{n-2} $ queries (given appropriate hash function bounds). We extend our analysis with block ciphers as the underlying primitive and obtain two optimally secure VIL PRFs using block ciphers. The first of these candidates requires $ 6 $ calls to the block cipher. The second candidate requires just $ 4 $ calls to the block cipher, but here the proof is based on Patarin's mirror theory. Further, we instantiate the hash function with a PMAC+/LightMAC+ like hash, to get six candidates for deterministic message authentication codes with optimal security.

2020

JOFC

Tight Security of Cascaded LRW2
Abstract

At CRYPTO ’12, Landecker et al. introduced the cascaded LRW2 (or CLRW2 ) construction and proved that it is a secure tweakable block cipher up to roughly $$ 2^{2n/3} $$ 2 2 n / 3 queries. Recently, Mennink has presented a distinguishing attack on CLRW2 in $$ 2n^{1/2}2^{3n/4} $$ 2 n 1 / 2 2 3 n / 4 queries. In the same paper, he discussed some non-trivial bottlenecks in proving tight security bound, i.e., security up to $$ 2^{3n/4} $$ 2 3 n / 4 queries. Subsequently, he proved security up to $$ 2^{3n/4} $$ 2 3 n / 4 queries for a variant of CLRW2 using 4-wise independent AXU assumption and the restriction that each tweak value occurs at most $$ 2^{n/4} $$ 2 n / 4 times. Moreover, his proof relies on a version of mirror theory which is yet to be publicly verified. In this paper, we resolve the bottlenecks in Mennink’s approach and prove that the original CLRW2 is indeed a secure tweakable block cipher up to roughly $$ 2^{3n/4} $$ 2 3 n / 4 queries. To do so, we develop two new tools: First, we give a probabilistic result that provides improved bound on the joint probability of some special collision events, and second, we present a variant of Patarin’s mirror theory in tweakable permutation settings with a self-contained and concrete proof. Both these results are of generic nature and can be of independent interests. To demonstrate the applicability of these tools, we also prove tight security up to roughly $$ 2^{3n/4} $$ 2 3 n / 4 queries for a variant of DbHtS , called DbHtS-p , that uses two independent universal hash functions.

2017

TOSC

On The Exact Security of Message Authentication Using Pseudorandom Functions
Abstract

Traditionally, modes of Message Authentication Codes(MAC) such as Cipher Block Chaining (CBC) are instantiated using block ciphers or keyed Pseudo Random Permutations(PRP). However, one can also use domain preserving keyed Pseudo Random Functions(PRF) to instantiate MAC modes. The very first security proof of CBC-MAC [BKR00], essentially modeled the PRP as a PRF. Until now very little work has been done to investigate the difference between PRP vs PRF instantiations. Only known result is the rather loose folklore PRP-PRF transition of any PRP based security proof, which looses a factor of Ο( σ2/2n ) (domain of PRF/PRP is {0, 1}n and adversary makes σ many PRP/PRF calls in total). This loss is significant, considering the fact tight Θ( q2/2n ) security bounds have been known for PRP based EMAC and ECBC constructions (where q is the total number of adversary queries). In this work, we show for many variations of encrypted CBC MACs (i.e. EMAC, ECBC, FCBC, XCBC and TCBC), random function based instantiation has a security bound Ο( qσ/2n ). This is a significant improvement over the folklore PRP/PRF transition. We also show this bound is optimal by providing an attack against the underlying PRF based CBC construction. This shows for EMAC, ECBC and FCBC, PRP instantiations are substantially more secure than PRF instantiations. Where as, for XCBC and TMAC, PRP instantiations are at least as secure as PRF instantiations.

2017

TOSC

Tight Security Analysis of EHtM MAC
Abstract

The security of a probabilistic Message Authentication Code (MAC) usually depends on the uniqueness of the random salt which restricts the security to birthday bound of the salt size due to the collision on random salts (e.g XMACR). To overcome the birthday bound limit, the natural approach to use (a) either a larger random salt (e.g MACRX3 uses 3n bits of random salt where n is the input and output size of the underlying non-compressing pseudorandom function or PRF) or (b) a PRF with increased domain size (e.g RWMAC or Randomized WMAC). Enhanced Hashthen- Mask (EHtM), proposed by Minematsu in FSE 2010, is the first probabilistic MAC scheme that provides beyond birthday bound security without increasing the randomness of the salt and the domain size of the non-compressing PRF. The author proved the security of EHtM as long as the number of MAC query is smaller than 22n/3 where n is the input size of the underlying non-compressing PRF. In this paper, we provide the exact security bound of EHtM and prove that this construction offers security up to 23n/4 MAC queries. The exactness is shown by demonstrating a matching attack.

#### Coauthors

- Avik Chakraborti (3)
- Bishwajit Chakraborty (2)
- Soumya Chattopadhyay (2)
- Benoît Cogliati (1)
- Nilanjan Datta (3)
- Avijit Dutta (1)
- Cuauhtemoc Mancillas-Lopez (2)
- Avradip Mandal (1)
- Snehal Mitragotri (1)
- Mridul Nandi (10)
- Yu Sasaki (2)