19,977 research outputs found
Signing on Elements in Bilinear Groups for Modular Protocol Design
A signature scheme is called structure-preserving if its verification keys, messages, and signatures are group elements and the verification predicate is a conjunction of pairing product equations. We answer to the open problem of constructing a constant-size structure-preserving signature scheme. The security is proven in the standard model based on a novel non-interactive assumption that can be justified and has an optimal bound in the generic bilinear group model. We also present efficient structure-preserving signature schemes with advanced properties including signing unbounded number of group elements, allowing simulation in the common reference string model, signing messages from mixed groups in the asymmetric bilinear group setting, and strong unforgeability. Among many applications, we show two examples; an adaptively secure round optimal blind signature scheme and a group signature scheme with efficient concurrent join. As a bi-product, several homomorphic trapdoor commitment schemes and one-time signature schemes are presented, too. In combination with the Groth-Sahai non-interactive proof system, these schemes contribute to give efficient instantiations to modular constructions of cryptographic protocols
Pairing-based identification schemes
We propose four different identification schemes that make use of bilinear
pairings, and prove their security under certain computational assumptions.
Each of the schemes is more efficient and/or more secure than any known
pairing-based identification scheme
Fiat-Shamir for highly sound protocols is instantiable
The Fiat–Shamir (FS) transformation (Fiat and Shamir, Crypto '86) is a popular paradigm for constructing very efficient non-interactive zero-knowledge (NIZK) arguments and signature schemes from a hash function and any three-move interactive protocol satisfying certain properties. Despite its wide-spread applicability both in theory and in practice, the known positive results for proving security of the FS paradigm are in the random oracle model only, i.e., they assume that the hash function is modeled as an external random function accessible to all parties. On the other hand, a sequence of negative results shows that for certain classes of interactive protocols, the FS transform cannot be instantiated in the standard model.
We initiate the study of complementary positive results, namely, studying classes of interactive protocols where the FS transform does have standard-model instantiations. In particular, we show that for a class of “highly sound” protocols that we define, instantiating the FS transform via a q-wise independent hash function yields NIZK arguments and secure signature schemes. In the case of NIZK, we obtain a weaker “q-bounded” zero-knowledge flavor where the simulator works for all adversaries asking an a-priori bounded number of queries q; in the case of signatures, we obtain the weaker notion of random-message unforgeability against q-bounded random message attacks.
Our main idea is that when the protocol is highly sound, then instead of using random-oracle programming, one can use complexity leveraging. The question is whether such highly sound protocols exist and if so, which protocols lie in this class. We answer this question in the affirmative in the common reference string (CRS) model and under strong assumptions. Namely, assuming indistinguishability obfuscation and puncturable pseudorandom functions we construct a compiler that transforms any 3-move interactive protocol with instance-independent commitments and simulators (a property satisfied by the Lapidot–Shamir protocol, Crypto '90) into a compiled protocol in the CRS model that is highly sound. We also present a second compiler, in order to be able to start from a larger class of protocols, which only requires instance-independent commitments (a property for example satisfied by the classical protocol for quadratic residuosity due to Blum, Crypto '81). For the second compiler we require dual-mode commitments.
We hope that our work inspires more research on classes of (efficient) 3-move protocols where Fiat–Shamir is (efficiently) instantiable
Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model
We consider a type of zero-knowledge protocols that are of interest for their
practical applications within networks like the Internet: efficient
zero-knowledge arguments of knowledge that remain secure against concurrent
man-in-the-middle attacks. In an effort to reduce the setup assumptions
required for efficient zero-knowledge arguments of knowledge that remain secure
against concurrent man-in-the-middle attacks, we consider a model, which we
call the Authenticated Public-Key (APK) model. The APK model seems to
significantly reduce the setup assumptions made by the CRS model (as no trusted
party or honest execution of a centralized algorithm are required), and can be
seen as a slightly stronger variation of the Bare Public-Key (BPK) model from
\cite{CGGM,MR}, and a weaker variation of the registered public-key model used
in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK
model. Our main result is a constant-round concurrent non-malleable
zero-knowledge argument of knowledge for any polynomial-time relation
(associated to a language in ), under the (minimal) assumption of
the existence of a one-way function family. Furthermore,We show time-efficient
instantiations of our protocol based on known number-theoretic assumptions. We
also note a negative result with respect to further reducing the setup
assumptions of our protocol to those in the (unauthenticated) BPK model, by
showing that concurrently non-malleable zero-knowledge arguments of knowledge
in the BPK model are only possible for trivial languages
The Random Oracle Methodology, Revisited
We take a critical look at the relationship between the security of
cryptographic schemes in the Random Oracle Model, and the security of the
schemes that result from implementing the random oracle by so called
"cryptographic hash functions". The main result of this paper is a negative
one: There exist signature and encryption schemes that are secure in the Random
Oracle Model, but for which any implementation of the random oracle results in
insecure schemes.
In the process of devising the above schemes, we consider possible
definitions for the notion of a "good implementation" of a random oracle,
pointing out limitations and challenges.Comment: 31 page
Security of discrete log cryptosystems in the random oracle and the generic model
We introduce novel security proofs that use combinatorial counting arguments rather than reductions to the discrete logarithm or to the Diffie-Hellman problem. Our security results are sharp and clean with no polynomial reduction times involved. We consider a combination of the random oracle model and the generic model. This corresponds to assuming an ideal hash function H given by an oracle and an ideal group of prime order q, where the binary encoding of the group elements is useless for cryptographic attacks In this model, we first show that Schnorr signatures are secure against the one-more signature forgery : A generic adversary performing t generic steps including l sequential interactions with the signer cannot produce l+1 signatures with a better probability than (t 2)/q. We also characterize the different power of sequential and of parallel attacks. Secondly, we prove signed ElGamal encryption is secure against the adaptive chosen ciphertext attack, in which an attacker can arbitrarily use a decryption oracle except for the challenge ciphertext. Moreover, signed ElGamal encryption is secure against the one-more decryption attack: A generic adversary performing t generic steps including l interactions with the decryption oracle cannot distinguish the plaintexts of l + 1 ciphertexts from random strings with a probability exceeding (t 2)/q
A Touch of Evil: High-Assurance Cryptographic Hardware from Untrusted Components
The semiconductor industry is fully globalized and integrated circuits (ICs)
are commonly defined, designed and fabricated in different premises across the
world. This reduces production costs, but also exposes ICs to supply chain
attacks, where insiders introduce malicious circuitry into the final products.
Additionally, despite extensive post-fabrication testing, it is not uncommon
for ICs with subtle fabrication errors to make it into production systems.
While many systems may be able to tolerate a few byzantine components, this is
not the case for cryptographic hardware, storing and computing on confidential
data. For this reason, many error and backdoor detection techniques have been
proposed over the years. So far all attempts have been either quickly
circumvented, or come with unrealistically high manufacturing costs and
complexity.
This paper proposes Myst, a practical high-assurance architecture, that uses
commercial off-the-shelf (COTS) hardware, and provides strong security
guarantees, even in the presence of multiple malicious or faulty components.
The key idea is to combine protective-redundancy with modern threshold
cryptographic techniques to build a system tolerant to hardware trojans and
errors. To evaluate our design, we build a Hardware Security Module that
provides the highest level of assurance possible with COTS components.
Specifically, we employ more than a hundred COTS secure crypto-coprocessors,
verified to FIPS140-2 Level 4 tamper-resistance standards, and use them to
realize high-confidentiality random number generation, key derivation, public
key decryption and signing. Our experiments show a reasonable computational
overhead (less than 1% for both Decryption and Signing) and an exponential
increase in backdoor-tolerance as more ICs are added
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