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Register a new userA New Path to Code-based Signatures via Identification Schemes with Restricted Errors
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Added by
Violetta Weger
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the NP-completeness of R-SDP, via a reduction from the classical SDP, and describe algorithms which solve such new problem. We study the properties of random codes under this new decoding perspective, in the fashion of traditional coding theory results, and assess the complexity of solving a random R-SDP instance. As a concrete application, we describe how Zero-Knowledge Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to compact public keys as well as significantly reduced communication costs. Thus, these schemes offer an improved basis for the construction of code-based digital signature schemes derived from identification schemes through the well-know Fiat-Shamir transformation.
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We consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional lattice $E_8$, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulus q with comparable error probability. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed $2^{24}$, which is roughly comparable to the current population of the Netherlands. We develop the basic scheme further to achieve the strongest anonymity notion, i.e., CCA-anonymity, with a small overhead in terms of efficiency. The feasibility of two proposed schemes is supported by implementation results. Our two schemes are the first in their respective classes of provably secure groups signature schemes. Additionally, the techniques introduced in this work might be of independent interest. These are a new verifiable encryption protocol for the randomized McEliece encryption and a novel approach to design formal security reductions from the Syndrome Decoding problem.
User privacy can be compromised by matching user data traces to records of their previous behavior. The matching of the statistical characteristics of traces to prior user behavior has been widely studied. However, an adversary can also identify a user deterministically by searching data traces for a pattern that is unique to that user. Our goal is to thwart such an adversary by applying small artificial distortions to data traces such that each potentially identifying pattern is shared by a large number of users. Importantly, in contrast to statistical approaches, we develop data-independent algorithms that require no assumptions on the model by which the traces are generated. By relating the problem to a set of combinatorial questions on sequence construction, we are able to provide provable guarantees for our proposed constructions. We also introduce data-dependent approaches for the same problem. The algorithms are evaluated on synthetic data traces and on the Reality Mining Dataset to demonstrate their utility.
A new scenario for generating a secret key and two private keys among three Terminals in the presence of an external eavesdropper is considered. Terminals 1, 2 and 3 intend to share a common secret key concealed from the external eavesdropper (Terminal 4) and simultaneously, each of Terminals 1 and 2 intends to share a private key with Terminal 3 while keeping it concealed from each other and from Terminal 4. All four Terminals observe i.i.d. outputs of correlated sources and there is a public channel from Terminal 3 to Terminals 1 and 2. An inner bound of the secret key-private keys capacity region is derived and the single letter capacity regions are obtained for some special cases.
A new protograph-based framework for message passing (MP) decoding of low density parity-check (LDPC) codes with Hamming weight amplifiers (HWAs), which are used e.g. in the NIST post-quantum crypto candidate LEDAcrypt, is proposed. The scheme exploits the correlations in the error patterns introduced by the HWA using a turbo-like decoding approach where messages between the decoders for the outer code given by the HWA and the inner LDPC code are exchanged. Decoding thresholds for the proposed scheme are computed using density evolution (DE) analysis for belief propagation (BP) and ternary message passing (TMP) decoding and compared to existing decoding approaches. The proposed scheme improves upon the basic approach of decoding LDPC code from the amplified error and has a similar performance as decoding the corresponding moderate-density parity-check (MDPC) code but with a significantly lower computational complexity.
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