Tight Security of TNT: Reinforcing Khairallah\u27s Birthday-bound Attack

In a recent paper, Khairallah demonstrated a birthday-bound attack on TNT, thereby invalidating its (beyond-the-birthday-bound) CCA security claims. In this short note, we reestablish a birthday-bound CCA security bound for TNT. Furthermore, using a minor variant of Khairallah\u27s attack, we show that our security bound is tight. We provide a rigorous and complete attack advantage calculations to further enhance the confidence in Khairallah\u27s proposed attack strategy

A Simple Security Analysis of Hash-CBC and a New Efficient One-Key Online Cipher

In Crypto 2001, Bellare {\em et al.} introduced {\em online cipher} (or online permutation) and proposed two Hash-CBC mode constructions, namely {\bf HCBC} and {\bf HPCBC} along with security proofs. We observe that, the security proofs in their paper are {\em wrong} and it may not be fixed easily. In this paper, we provide a {\em simple} security analysis of these online ciphers. Moreover, we propose two variants of HPCBC, namely {\bf MHCBC-1} and {\bf MHCBC-2}. The first variant, MHCBC-1, is a slight modification of HPCBC so that it is more efficient in performance as well as in memory compare to HPCBC. The other one, MHCBC-2 requires only {\em one-key} (note that, HCBC and HPCBC require at least two and three keys respectively) and does not require any $\varepsilon$-$\mathrm{\Delta}$Universal Hash Family (which is costly in general)

The Design Space of Lightweight Cryptography

For constrained devices, standard cryptographic algorithms can be too big, too slow or too energy-consuming. The area of lightweight cryptography studies new algorithms to overcome these problems. In this paper, we will focus on symmetric-key encryption, authentication and hashing. Instead of providing a full overview of this area of research, we will highlight three interesting topics. Firstly, we will explore the generic security of lightweight constructions. In particular, we will discuss considerations for key, block and tag sizes, and explore the topic of instantiating a pseudorandom permutation (PRP) with a non-ideal block cipher construction. This is inspired by the increasing prevalence of lightweight designs that are not secure against related-key attacks, such as PRINCE, PRIDE or Chaskey. Secondly, we explore the efficiency of cryptographic primitives. In particular, we investigate the impact on efficiency when the input size of a primitive doubles. Lastly, we provide some considerations for cryptographic design. We observe that applications do not always use cryptographic algorithms as they were intended, which negatively impacts the security and/or efficiency of the resulting implementations

The Design Space of Lightweight Cryptography

International audienceFor constrained devices, standard cryptographic algorithms can be too big, too slow or too energy-consuming. The area of lightweight cryptography studies new algorithms to overcome these problems. In this paper, we will focus on symmetric-key encryption, authentication and hashing. Instead of providing a full overview of this area of research, we will highlight three interesting topics. Firstly, we will explore the generic security of lightweight constructions. In particular, we will discuss considerations for key, block and tag sizes, and explore the topic of instantiating a pseudorandom permutation (PRP) with a non-ideal block cipher construction. This is inspired by the increasing prevalence of lightweight designs that are not secure against related-key attacks, such as PRINCE, PRIDE or Chaskey. Secondly, we explore the efficiency of cryptographic primitives. In particular, we investigate the impact on efficiency when the input size of a primitive doubles. Lastly, we provide some considerations for cryptographic design. We observe that applications do not always use cryptographic algorithms as they were intended, which negatively impacts the security and/or efficiency of the resulting implementations

On the Optimality of Non-Linear Computations of Length-Preserving Encryption Schemes

It is well known that three and four rounds of balanced Feistel cipher or Luby-Rackoff (LR) encryption for two blocks messages are pseudorandom permutation (PRP) and strong pseudorandom permutation (SPRP) respectively. A {\bf block} is $n$-bit long for some positive integer $n$ and a (possibly keyed) {\bf block-function} is a nonlinear function mapping all blocks to themselves, e.g. blockcipher. XLS (eXtended Latin Square) with three blockcipher calls was claimed to be SPRP and later which is shown to be wrong. Motivating with these observations, we consider the following questions in this paper: {\em What is the minimum number of invocations of block-functions required to achieve PRP or SPRP security over $\ell$ blocks inputs}? To answer this question, we consider all those length-preserving encryption schemes, called {\bf linear encryption mode}, for which only nonlinear operations are block-functions. Here, we prove the following results for these encryption schemes: (1) At least $2\ell$ (or $2\ell-1$) invocations of block-functions are required to achieve SPRP (or PRP respectively). These bounds are also tight. (2) To achieve the above bound for PRP over $\ell > 1$ blocks, either we need at least two keys or it can not be {\em inverse-free} (i.e., need to apply the inverses of block-functions in the decryption). In particular, we show that a single-keyed block-function based, inverse-free PRP needs $2\ell$ invocations. (3) We show that 3-round LR using a single-keyed pseudorandom function (PRF) is PRP if we xor a block of input by a masking key

A Unified Method for Improving PRF Bounds for a Class of Blockcipher based MACs

This paper provides a unified framework for {\em improving} \PRF(pseudorandom function) advantages of several popular MACs (message authentication codes) based on a blockcipher modeled as \tx{RP} (random permutation). In many known MACs, the inputs of the underlying blockcipher are defined to be some deterministic affine functions of previously computed outputs of the blockcipher. Keeping the similarity in mind, we introduce a class of \tx{ADE}s (affine domain extensions) and a wide subclass of \tx{SADE}s (secure \tx{ADE}) containing \mathcal{C} = \{ \tx{CBC-MAC},\ \tx{GCBC}^*,\ \tx{OMAC},\ \tx{PMAC} \}. We define a parameter $N(t,q)$ for each domain extension and show that all \tx{SADE}s have \PRF advantages $O(tq/2^n + N(t,q)/2^n)$ where $t$ is the total number of blockcipher computations needed for all $q$ queries. We prove that \PRF advantage of any \tx{SADE} is $O(t^2/2^n)$ by showing that $N(t,q)$ is always at most ${t \choose 2}$. We provide a better estimate $O(tq)$ of $N(t,q)$ for all members of $\mathcal{C}$ and hence these MACs have {\em improved advantages $O(tq / 2^n)$}. Our proposed bounds for \tx{CBC-MAC} and \tx{GCBC}^* are better than previous best known bounds

More Rounds, Less Security?

This paper focuses on a surprising class of cryptanalysis results for symmetric-key primitives: when the number of rounds of the primitive is increased, the complexity of the cryptanalysis result decreases. Our primary target will be primitives that consist of identical round functions, such as PBKDF1, the Unix password hashing algorithm, and the Chaskey MAC function. However, some of our results also apply to constructions with non-identical rounds, such as the PRIDE block cipher. First, we construct distinguishers for which the data complexity decreases when the number of rounds is increased. They are based on two well-known observations: iterating a random permutation increases the expected number of fixed points, and iterating a random function decreases the expected number of image points. We explain that these effects also apply to components of cryptographic primitives, such as a round of a block cipher. Second, we introduce a class of key-recovery and preimage-finding techniques that correspond to exhaustive search, however on a smaller part (e.g. one round) of the primitive. As the time complexity of a cryptanalysis result is usually measured by the number of full-round evaluations of the primitive, increasing the number of rounds will lower the time complexity. None of the observations in this paper result in more than a small speed-up over exhaustive search. Therefore, for lightweight applications, implementation advantages may outweigh the presence of these observations

More Rounds, Less Security?

This paper focuses on a surprising class of cryptanalysis results for symmetric-key primitives: when the number of rounds of the primitive is increased, the complexity of the cryptanalysis result decreases. Our primary target will be primitives that consist of identical round functions, such as PBKDF1, the Unix password hashing algorithm, and the Chaskey MAC function. However, some of our results also apply to constructions with non-identical rounds, such as the PRIDE block cipher. First, we construct distinguishers for which the data complexity decreases when the number of rounds is increased. They are based on two well-known observations: iterating a random permutation increases the expected number of fixed points, and iterating a random function decreases the expected number of image points. We explain that these effects also apply to components of cryptographic primitives, such as a round of a block cipher. Second, we introduce a class of key-recovery and preimage-finding techniques that correspond to exhaustive search, however on a smaller part (e.g. one round) of the primitive. As the time complexity of a cryptanalysis result is usually measured by the number of full-round evaluations of the primitive, increasing the number of rounds will lower the time complexity. None of the observations in this paper result in more than a small speed-up over exhaustive search. Therefore, for lightweight applications, implementation advantages may outweigh the presence of these observations

The Iterated Random Function Problem

At CRYPTO 2015, Minaud and Seurin introduced and studied the iterated random permutation problem, which is to distinguish the $r$-th iterate of a random permutation from a random permutation. In this paper, we study the closely related iterated random function problem, and prove the first almost-tight bound in the adaptive setting. More specifically, we prove that the advantage to distinguish the $r$-th iterate of a random function from a random function using $q$ queries is bounded by $O(q^2r(\log r)^3/N)$, where $N$ is the size of the domain. In previous work, the best known bound was $O(q^2r^2/N)$, obtained as a direct result of interpreting the iterated random function problem as a special case of CBC-MAC based on a random function. For the iterated random function problem, the best known attack has an advantage of $\Omega(q^2r/N)$, showing that our security bound is tight up to a factor of $(\log r)^3$

Information-theoretic Indistinguishability via the Chi-squared Method

Proving tight bounds on information-theoretic indistinguishability is a central problem in symmetric cryptography. This paper introduces a new method for information-theoretic indistinguishability proofs, called ``the chi-squared method\u27\u27. At its core, the method requires upper-bounds on the so-called $\chi^2$ divergence (due to Neyman and Pearson) between the output distributions of two systems being queries. The method morally resembles, yet also considerably simplifies, a previous approach proposed by Bellare and Impagliazzo (ePrint, 1999), while at the same time increasing its expressiveness and delivering tighter bounds. We showcase the chi-squared method on some examples. In particular: (1) We prove an optimal bound of $q/2^n$ for the XOR of two permutations, and our proof considerably simplifies previous approaches using the $H$-coefficient method, (2) we provide improved bounds for the recently proposed encrypted Davies-Meyer PRF construction by Cogliati and Seurin (CRYPTO \u2716), and (3) we give a tighter bound for the Swap-or-not cipher by Hoang, Morris, and Rogaway (CRYPTO \u2712)