Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm. The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible

Continuously non-malleable codes with split-state refresh

Non-malleable codes for the split-state model allow to encode a message into two parts, such that arbitrary independent tampering on each part, and subsequent decoding of the corresponding modified codeword, yields either the same as the original message, or a completely unrelated value. Continuously non-malleable codes further allow to tolerate an unbounded (polynomial) number of tampering attempts, until a decoding error happens. The drawback is that, after an error happens, the system must self-destruct and stop working, otherwise generic attacks become possible. In this paper we propose a solution to this limitation, by leveraging a split-state refreshing procedure. Namely, whenever a decoding error happens, the two parts of an encoding can be locally refreshed (i.e., without any interaction), which allows to avoid the self-destruct mechanism. An additional feature of our security model is that it captures directly security against continual leakage attacks. We give an abstract framework for building such codes in the common reference string model, and provide a concrete instantiation based on the external Diffie-Hellman assumption. Finally, we explore applications in which our notion turns out to be essential. The first application is a signature scheme tolerating an arbitrary polynomial number of split-state tampering attempts, without requiring a self-destruct capability, and in a model where refreshing of the memory happens only after an invalid output is produced. This circumvents an impossibility result from a recent work by Fuijisaki and Xagawa (Asiacrypt 2016). The second application is a compiler for tamper-resilient RAM programs. In comparison to other tamper-resilient compilers, ours has several advantages, among which the fact that, for the first time, it does not rely on the self-destruct feature

Efficient Fully-Leakage Resilient One-More Signature Schemes

In a recent paper Faonio, Nielsen and Venturi (ICALP 2015) gave new constructions of leakage-resilient signature schemes. The signature schemes proposed remain unforgeable against an adversary leaking arbitrary information on the entire state of the signer, including the random coins of the signing algorithm. The main feature of their signature schemes is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible. The notion, put forward by Nielsen, Venturi, and Zottarel (PKC 2014), defines a slack parameter $\gamma$ which, roughly speaking, describes how gracefully the security degrades. Unfortunately, the standard-model signature scheme of Faonio,Nielsen and Venturi has a slack parameter that depends on the number of signatures queried by the adversary. In this paper we show two new constructions in the standard model where the above limitation is avoided. Specifically, the first scheme achieves slack parameter $O(1/\lambda)$ where $\lambda$ is the security parameter and it is based on standard number theoretic assumptions, the second scheme achieves optimal slack parameter (i.e. $\gamma = 1$) and it is based on knowledge of the exponent assumptions. Our constructions are efficient and have leakage rate $1 - o(1)$, most notably our second construction has signature size of only 8 group elements which makes it the leakage-resilient signature scheme with the shortest signature size known to the best of our knowledge

Mix-Nets from Re-Randomizable and Replayable CCA-secure Public-Key Encryption

Mix-nets are protocols that allow a set of senders to send messages anonymously. Faonio et al. (ASIACRYPT’19) showed how to instantiate mix-net protocols based on Public-Verifiable Re-randomizable Replayable CCA-secure (Rand-RCCA) PKE schemes. The bottleneck of their approach is that public-verifiable Rand-RCCA PKEs are less efficient than typical CPA-secure re-randomizable PKEs. In this paper, we revisit their mix-net protocol, showing how to get rid of the cumbersome public-verifiability property, and we give a more efficient instantiation for the mix-net protocol based on a (non publicly-verifiable) Rand-RCCA scheme. Additionally, we give a more careful security analysis of their mix-net protocol

Fully Leakage-Resilient Codes

Leakage resilient codes (LRCs) are probabilistic encoding schemes that guarantee message hiding even under some bounded leakage on the codeword. We introduce the notion of \emph{fully} leakage resilient codes (FLRCs), where the adversary can leak some $\lambda_0$ bits from the encoding process, i.e., the message and the randomness involved during the encoding process. In addition the adversary can as usual leak from the codeword. We give a simulation-based definition requiring that the adversary\u27s leakage from the encoding process and the codework can be simulated given just $\lambda_0$ bits of leakage from the message. For $\lambda_0 = 0$ our new simulation-based notion is equivalent to the usual game-based definition. A FLRC would be interesting in its own right and would be useful in building other leakage-resilient primitives in a composable manner. We give a fairly general impossibility result for FLRCs in the popular split-state model, where the codeword is broken into independent parts and where the leakage occurs independently on the parts. We show that if the leakage is allowed to be any poly-time function of the secret and if collision-resistant hash functions exist, then there is no FLRC for the split-state model. The result holds only when the message length can be linear in the security parameter. However, we can extend the impossibility result to FLRCs for constant-length messages under assumptions related to differing-input obfuscation. These results show that it is highly unlikely that we can build FLRCs for the split-state model when the leakage can be any poly-time function of the secret state. We then give two feasibility results for weaker models. First, we show that for \NC^0-bounded leakage from the randomness and arbitrary poly-time leakage from the parts of the codeword the inner-product construction proposed by Daví \etal (SCN\u2710) and successively improved by Dziembowski and Faust (ASIACRYPT\u2711) is a FLRC for the split-state model. Second, we provide a compiler from any LRC to a FLRC in the common reference string model for any fixed leakage family of small cardinality. In particular, this compiler applies to the split-state model but also to many other models

Leakage-Resilient Identification Schemes from Zero-Knowledge Proofs of Storage

We provide a framework for constructing leakage-resilient identification(ID) protocols in the bounded retrieval model (BRM) from proofs of storage(PoS) that hide partial information about the file. More precisely, we describe a generic transformation from any zero-knowledge PoS to a leakage-resilient ID protocol in the BRM. We then describe a ZK-PoS based on RSA which, under our transformation, yields the first ID protocol in the BRM based on RSA (in the ROM). The resulting protocol relies on a different computational assumption and is more efficient than previously-known constructions

Almost Tightly-Secure Re-Randomizable and Replayable CCA-secure Public Key Encryption

Re-randomizable Replayable CCA-secure public key encryption (Rand-RCCA PKE) schemes guarantee security against chosen-ciphertext attacks while ensuring the useful property of re-randomizable ciphertexts. We introduce the notion of multi-user and multi-ciphertext Rand-RCCA PKE and we give the first construction of such a PKE scheme with an almost tight security reduction to a standard assumption. Our construction is structure preserving and can be instantiated over Type-1 pairing groups. Technically, our work borrows ideas from the state of the art Rand-RCCA PKE scheme of Faonio et al. (ASIACRYPT’19) and the adaptive partitioning technique of Hofheinz (EUROCRYPT’17). Additionally, we show (1) how to turn our scheme into a publicly-verifiable (pv) Rand-RCCA scheme and (2) that plugging our pv-Rand-RCCA PKE scheme into the MixNet protocol of Faonio et al. we can obtain the first almost tightly-secure MixNet protocol

Rate-Optimizing Compilers for Continuously Non-Malleable Codes

We study the *rate* of so-called *continuously* non-malleable codes, which allow to encode a message in such a way that (possibly adaptive) continuous tampering attacks on the codeword yield a decoded value that is unrelated to the original message. Our results are as follows: -) For the case of bit-wise independent tampering, we establish the existence of rate-one continuously non-malleable codes with information-theoretic security, in the plain model. -) For the case of split-state tampering, we establish the existence of rate-one continuously non-malleable codes with computational security, in the (non-programmable) random oracle model. We further exhibit a rate-1/2 code and a rate-one code in the common reference string model, but the latter only withstands *non-adaptive* tampering. It is well known that computational security is inherent for achieving continuous non-malleability in the split-state model (even in the presence of non-adaptive tampering). Continuously non-malleable codes are useful for protecting *arbitrary* cryptographic primitives against related-key attacks, as well as for constructing non-malleable public-key encryption schemes. Our results directly improve the efficiency of these applications

Continuously Non-Malleable Secret Sharing: Joint Tampering, Plain Model and Capacity

We study non-malleable secret sharing against joint leakage and joint tampering attacks. Our main result is the first threshold secret sharing scheme in the plain model achieving resilience to noisy-leakage and continuous tampering. The above holds under (necessary) minimal computational assumptions (i.e., the existence of one-to-one one-way functions), and in a model where the adversary commits to a fixed partition of all the shares into non-overlapping subsets of at most $t-1$ shares (where $t$ is the reconstruction threshold), and subsequently jointly leaks from and tampers with the shares within each partition. We also study the capacity (i.e., the maximum achievable asymptotic information rate) of continuously non-malleable secret sharing against joint continuous tampering attacks. In particular, we prove that whenever the attacker can tamper jointly with $k > t/2$ shares, the capacity is at most $t - k$. The rate of our construction matches this upper bound. An important corollary of our results is the first non-malleable secret sharing scheme against independent tampering attacks breaking the rate-one barrier (under the same computational assumptions as above)

Subversion-Resilient Enhanced Privacy ID

Anonymous attestation for secure hardware platforms leverages tailored group signature schemes and assumes the hardware to be trusted. Yet, there is an ever increasing concern on the trustworthiness of hardware components and embedded systems. A subverted hardware may, for example, use its signatures to exfiltrate identifying information or even the signing key. In this paper we focus on Enhanced Privacy ID (EPID)---a popular anonymous attestation scheme used in commodity secure hardware platforms like Intel SGX. We define and instantiate a \emph{subversion resilient} EPID scheme (or SR-EPID). In a nutshell, SR-EPID provides the same functionality and security guarantees of the original EPID, despite potentially subverted hardware. In our design, a ``sanitizer\u27\u27 ensures no covert channel between the hardware and the outside world both during enrollment and during attestation (i.e., when signatures are produced). We design a practical SR-EPID scheme secure against adaptive corruptions and based on a novel combination of malleable NIZKs and hash functions modeled as random oracles. Our approach has a number of advantages over alternative designs. Namely, the sanitizer bears no secret information---hence, a memory leak does not erode security. Further, the role of sanitizer may be distributed in a cascade fashion among several parties so that sanitization becomes effective as long as one of the parties has access to a good source of randomness. Also, we keep the signing protocol non-interactive, thereby minimizing latency during signature generation