30 research outputs found
Sequential Indifferentiability of Confusion-Diffusion Networks
A large proportion of modern symmetric cryptographic building blocks are designed using the Substitution-Permutation Networks (SPNs), or more generally, Shannon\u27s confusion-diffusion paradigm. To justify its theoretical soundness, Dodis et al. (EUROCRYPT 2016) recently introduced the theoretical model of confusion-diffusion networks, which may be viewed as keyless SPNs using random permutations as S-boxes and combinatorial primitives as permutation layers, and established provable security in the plain indifferentiability framework of Maurer, Renner, and Holenstein (TCC 2004).
We extend this work and consider Non-Linear Confusion-Diffusion Networks (NLCDNs), i.e., networks using non-linear permutation layers, in weaker indifferentiability settings. As the main result, we prove that 3-round NLCDNs achieve the notion of sequential indifferentiability of Mandal et al. (TCC 2012). We also exhibit an attack against 2-round NLCDNs, which shows the tightness of our positive result on 3 rounds. It implies correlation intractability of 3-round NLCDNs, a notion strongly related to known-key security of block ciphers and secure hash functions. Our results provide additional insights on understanding the complexity for known-key security, as well as using confusion-diffusion paradigm for designing cryptographic hash functions
Indifferentiable Authenticated Encryption
We study Authenticated Encryption with Associated Data (AEAD) from the viewpoint of composition in arbitrary (single-stage) environments. We use the indifferentiability framework to formalize the intuition that a “good” AEAD scheme should have random ciphertexts subject to decryptability. Within this framework, we can then apply the indifferentiability composition theorem to show that such schemes offer extra safeguards wherever the relevant security properties are not known, or cannot be predicted in advance, as in general-purpose crypto libraries and standards. We show, on the negative side, that generic composition (in many of its configurations) and well-known classical and recent schemes fail to achieve indifferentiability. On the positive side, we give a provably indifferentiable Feistel-based construction, which reduces the round complexity from at least 6, needed for blockciphers, to only 3 for encryption. This result is not too far off the theoretical optimum as we give a lower bound that rules out the indifferentiability of any construction with less than 2 rounds
Minimizing Even-Mansour Ciphers for Sequential Indifferentiability (Without Key Schedules)
Iterated Even-Mansour (IEM) schemes consist of a small number of fixed permutations separated by round key additions. They enjoy provable security, assuming the permutations are public and random. In particular, regarding chosen-key security in the sense of sequential indifferentiability (seq-indifferentiability), Cogliati and Seurin (EUROCRYPT 2015) showed that without key schedule functions, the 4-round Even-Mansour with Independent Permutations and no key schedule is sequentially indifferentiable.
Minimizing IEM variants for classical strong (tweakable) pseudorandom security has stimulated an attractive line of research. In this paper, we seek for minimizing the construction while retaining seq-indifferentiability. We first consider , a natural variant of using a single round permutation. Unfortunately, we exhibit a slide attack against with any number of rounds. In light of this, we show that the 4-round using 2 independent random permutations is seq-indifferentiable. This provides the minimal seq-indifferentiable IEM without key schedule
On Quantum Indifferentiability
We study the indifferentiability of classical constructions in the quantum setting, such as the Sponge construction or Feistel networks. (But the approach easily generalizes to other constructions, too.) We
give evidence that, while those constructions are known to be
indifferentiable in the classical setting, they are not
indifferentiable in the quantum setting. Our approach is based on
an quantum-information-theoreoretical conjecture
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
IMPROVING THE ROUND COMPLEXITY OF IDEAL-CIPHER CONSTRUCTIONS
Block ciphers are an essential ingredient of modern cryptography.
They are widely used as building blocks in many cryptographic constructions
such as encryption schemes, hash functions etc.
The security of block ciphers is not currently
known to reduce to well-studied, easily formulated, computational
problems.
Nevertheless, modern block-cipher constructions
are far from ad-hoc,
and a strong theory for their design has been developed.
Two classical paradigms for block cipher design are the Feistel network and the
key-alternating cipher (which is encompassed by the popular
substitution-permutation network).
Both of these paradigms that are iterated structures
that involve applications of random-looking functions/permutations
over many rounds.
An important area of research is to understand the provable
security guarantees offered by these classical design paradigms for block cipher constructions.
This can be done using a security notion called indifferentiability which formalizes
what it means for a block cipher to be ideal.
In particular, this notion allows us to assert the structural robustness
of a block cipher design.
In this thesis, we apply the indifferentiability notion to the two classical paradigms
mentioned above and improve upon the previously known round complexity
in both cases.
Specifically, we make the following two contributions:
(1) We show that a 10-round Feistel network behaves as an ideal block cipher
when the keyed round functions are built using a random oracle.
(2) We show that a 5-round key-alternating cipher (also known as the iterated Even-Mansour
construction) with identical round keys behaves as an ideal block cipher when the round permutations are independent, public random permutations
Small-Box Cryptography
One of the ultimate goals of symmetric-key cryptography is to find a rigorous theoretical framework for building block ciphers from small components, such as cryptographic S-boxes, and then argue why iterating such small components for sufficiently many rounds would yield a secure construction. Unfortunately, a fundamental obstacle towards reaching this goal comes from the fact that traditional security proofs cannot get security beyond 2^{-n}, where n is the size of the corresponding component.
As a result, prior provably secure approaches - which we call "big-box cryptography" - always made n larger than the security parameter, which led to several problems: (a) the design was too coarse to really explain practical constructions, as (arguably) the most interesting design choices happening when instantiating such "big-boxes" were completely abstracted out; (b) the theoretically predicted number of rounds for the security of this approach was always dramatically smaller than in reality, where the "big-box" building block could not be made as ideal as required by the proof. For example, Even-Mansour (and, more generally, key-alternating) ciphers completely ignored the substitution-permutation network (SPN) paradigm which is at the heart of most real-world implementations of such ciphers.
In this work, we introduce a novel paradigm for justifying the security of existing block ciphers, which we call small-box cryptography. Unlike the "big-box" paradigm, it allows one to go much deeper inside the existing block cipher constructions, by only idealizing a small (and, hence, realistic!) building block of very small size n, such as an 8-to-32-bit S-box. It then introduces a clean and rigorous mixture of proofs and hardness conjectures which allow one to lift traditional, and seemingly meaningless, "at most 2^{-n}" security proofs for reduced-round idealized variants of the existing block ciphers, into meaningful, full-round security justifications of the actual ciphers used in the real world.
We then apply our framework to the analysis of SPN ciphers (e.g, generalizations of AES), getting quite reasonable and plausible concrete hardness estimates for the resulting ciphers. We also apply our framework to the design of stream ciphers. Here, however, we focus on the simplicity of the resulting construction, for which we managed to find a direct "big-box"-style security justification, under a well studied and widely believed eXact Linear Parity with Noise (XLPN) assumption.
Overall, we hope that our work will initiate many follow-up results in the area of small-box cryptography
Naor-Reingold Goes Public: The Complexity of Known-key Security
We study the complexity of building secure block ciphers in the setting where the key is known to the attacker. In particular, we consider two security notions with useful implications, namely public-seed pseudorandom permutations (or psPRPs, for short) (Soni and Tessaro, EUROCRYPT \u2717) and correlation-intractable ciphers (Knudsen and Rijmen, ASIACRYPT \u2707; Mandal, Seurin, and Patarin, TCC \u2712).
For both these notions, we exhibit constructions which make only two calls to an underlying non-invertible primitive, matching the complexity of building a pseudorandom permutation in the secret-key setting. Our psPRP result instantiates the round functions in the Naor-Reingold (NR) construction with a secure UCE hash function. For correlation intractability, we instead instantiate them from a (public) random function, and replace the pairwise-independent permutations in the NR construction with (almost) -wise independent permutations, where is the arity of the relations for which we want correlation intractability.
Our constructions improve upon the current state of the art, requiring five- and six-round Feistel networks, respectively, to achieve psPRP security and correlation intractability. To do so, we rely on techniques borrowed from Impagliazzo-Rudich-style black-box impossibility proofs for our psPRP result, for which we give what we believe to be the first constructive application, and on techniques for studying randomness with limited independence for correlation intractability
Revisiting Cascade Ciphers in Indifferentiability Setting
Shannon defined an ideal -blockcipher as a secrecy system consisting of independent -bit random permutations.
In this paper, we revisit the following question: in the ideal cipher model, can a cascade of several ideal -blockciphers realize an ideal -blockcipher? The motivation goes back to Shannon\u27s theory on product secrecy systems, and similar question was considered by Even and Goldreich (CRYPTO \u2783) in different settings. We give the first positive answer: for the cascade of independent ideal -blockciphers with two alternated independent keys, four stages are necessary and sufficient to realize an ideal -blockcipher, in the sense of indifferentiability of Maurer et al. (TCC 2004). This shows cascade capable of achieving key-length extension in the settings where keys are \emph{not necessarily secret}
Security analysis of NIST-LWC contest finalists
Dissertação de mestrado integrado em Informatics EngineeringTraditional cryptographic standards are designed with a desktop and server environment in mind, so, with the
relatively recent proliferation of small, resource constrained devices in the Internet of Things, sensor networks,
embedded systems, and more, there has been a call for lightweight cryptographic standards with security,
performance and resource requirements tailored for the highly-constrained environments these devices find
themselves in.
In 2015 the National Institute of Standards and Technology began a Standardization Process in order to select
one or more Lightweight Cryptographic algorithms. Out of the original 57 submissions ten finalists remain, with
ASCON and Romulus being among the most scrutinized out of them.
In this dissertation I will introduce some concepts required for easy understanding of the body of work, do
an up-to-date revision on the current situation on the standardization process from a security and performance
standpoint, a description of ASCON and Romulus, and new best known analysis, and a comparison of the two,
with their advantages, drawbacks, and unique traits.Os padrões criptográficos tradicionais foram elaborados com um ambiente de computador e servidor em mente.
Com a proliferação de dispositivos de pequenas dimensões tanto na Internet of Things, redes de sensores e
sistemas embutidos, apareceu uma necessidade para se definir padrões para algoritmos de criptografia leve, com
prioridades de segurança, performance e gasto de recursos equilibrados para os ambientes altamente limitados
em que estes dispositivos operam.
Em 2015 o National Institute of Standards and Technology lançou um processo de estandardização com o
objectivo de escolher um ou mais algoritmos de criptografia leve. Das cinquenta e sete candidaturas originais
sobram apenas dez finalistas, sendo ASCON e Romulus dois desses finalistas mais examinados.
Nesta dissertação irei introduzir alguns conceitos necessários para uma fácil compreensão do corpo deste
trabalho, assim como uma revisão atualizada da situação atual do processo de estandardização de um ponto
de vista tanto de segurança como de performance, uma descrição do ASCON e do Romulus assim como as
suas melhores análises recentes e uma comparação entre os dois, frisando as suas vantagens, desvantagens e
aspectos únicos