We introduce the notion of two-factor signatures (2FS), a generalization of a two-out-of-two threshold signature scheme in which one of the parties is a hardware token which can store a high-entropy secret, and the other party is a human who knows a low-entropy password. The security (unforgeability) property of 2FS requires that an external adversary corrupting either party (the token or the computer the human is using) cannot forge a signature. This primitive is useful in contexts like hardware cryptocurrency wallets in which a signature conveys the authorization of a transaction. By the above security property, a hardware wallet implementing a two-factor signature scheme is secure against attacks mounted by a malicious hardware vendor; in contrast, all currently used wallet systems break under such an attack (and as such are not secure under our definition). We construct efficient provably-secure 2FS schemes which produce either Schnorr signature (assuming the DLOG assumption), or EC-DSA signatures (assuming security of EC-DSA and the CDH assumption) in the Random Oracle Model, and evaluate the performance of implementations of them. Our EC-DSA based 2FS scheme can directly replace currently used hardware wallets for Bitcoin and other major cryptocurrencies to enable security against malicious hardware vendors.
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On the Multi-User Security of Short Schnorr Signatures with Preprocessing
The Schnorr signature scheme is an efficient digital signature scheme with short signature lengths, i.e., $4k$-bit signatures for $k$ bits of security. A Schnorr signature $\sigma$ over a group of size $p\approx 2^{2k}$ consists of a tuple $(s,e)$, where $e \in \{0,1\}^{2k}$ is a hash output and $s\in \mathbb{Z}_p$ must be computed using the secret key. While the hash output $e$ requires $2k$ bits to encode, Schnorr proposed that it might be possible to truncate the hash value without adversely impacting security.
In this paper, we prove that \emph{short} Schnorr signatures of length $3k$ bits provide $k$ bits of multi-user security in the (Shoup's) generic group model and the programmable random oracle model. We further analyze the multi-user security of key-prefixed short Schnorr signatures against preprocessing attacks, showing that it is possible to obtain secure signatures of length $3k + \log S + \log N$ bits. Here, $N$ denotes the number of users and $S$ denotes the size of the hint generated by our preprocessing attacker, e.g., if $S=2^{k/2}$, then we would obtain secure $3.75k$-bit signatures for groups of up to $N \leq 2^{k/4}$ users.
Our techniques easily generalize to several other Fiat-Shamir-based signature schemes, allowing us to establish analogous results for Chaum-Pedersen signatures and Katz-Wang signatures. As a building block, we also analyze the $1$-out-of-$N$ discrete-log problem in the generic group model, with and without preprocessing.
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- NSF-PAR ID:
- 10322481
- Date Published:
- Journal Name:
- Advances in Cryptology - EUROCRYPT
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Trustworthy and Efficient Digital Twins in Post-Quantum Era with Hybrid Hardware-Assisted Signaturesmore » « less
Digital Twins (DT) virtually model cyber-physical objects via sensory inputs by simulating or monitoring their behavior. Therefore, DTs usually harbor vast quantities of Internet of Things (IoT) components (e.g., sensors) that gather, process, and offload sensitive information (e.g., healthcare) to the cloud. It is imperative to ensure the trustworthiness of such sensitive information with long-term and compromise-resilient security guarantees. Digital signatures provide scalable authentication and integrity with non-repudiation and are vital tools for DTs. Post-quantum cryptography (PQC) and forward-secure signatures are two fundamental tools to offer long-term security and breach resiliency. However, NIST-PQC signature standards are exorbitantly costly for embedded DT components and are infeasible when forward-security is also considered. Moreover, NIST-PQC signatures do not admit aggregation, which is a highly desirable feature to mitigate the heavy storage and transmission burden in DTs. Finally, NIST recommends hybrid PQ solutions to enable cryptographic agility and transitional security. Yet, there is a significant gap in the state of the art in the achievement of all these advanced features simultaneously. Therefore, there is a significant need for lightweight digital signatures that offer compromise resiliency and compactness while permitting transitional security into the PQ era for DTs.
We create a series of highly lightweight digital signatures called Hardware-ASisted Efficient Signature (
HASES ) that meets the above requirements. The core ofHASES is a hardware-assisted cryptographic commitment construct oracle (CCO ) that permits verifiers to obtain expensive commitments without signer interaction. We created threeHASES schemes:PQ-HASES is a forward-secure PQ signature,LA-HASES is an efficient aggregate Elliptic-Curve signature, andHY-HASES is a novel hybrid scheme that combinesPQ-HASES andLA-HASES with novel strong nesting and sequential aggregation.HASES does not require a secure-hardware on the signer. We prove thatHASES schemes are secure and implemented them on commodity hardware and and 8-bit AVR ATmega2560. Our experiments confirm thatPQ-HASES andLA-HASES are two magnitudes of times more signer efficient than their PQ and conventional-secure counterparts, respectively.HY-HASES outperforms NIST PQC and conventional signature combinations, offering a standard-compliant transitional solution for emerging DTs. We open-sourceHASES schemes for public-testing and adaptation. -
One of the primary research challenges in Attribute-Based Encryption (ABE) is constructing and proving cryptosystems that are adaptively secure. To date the main paradigm for achieving adaptive security in ABE is dual system encryption. However, almost all such solutions in bilinear groups rely on (variants of) either the subgroup decision problem over composite order groups or the decision linear assumption. Both of these assumptions are decisional rather than search assumptions and the target of the assumption is a source or bilinear group element. This is in contrast to earlier selectively secure ABE systems which can be proven secure from either the decisional or search Bilinear Diffie-Hellman assumption. In this work we make progress on closing this gap by giving a new ABE construction for the subset functionality and prove security under the Search Bilinear Diffie-Hellman assumption. We first provide a framework for proving adaptive security in Attribute-Based Encryption systems. We introduce a concept of ABE with deletable attributes where any party can take a ciphertext encrypted under the attribute string and modify it into a ciphertext encrypted under any string where is derived by replacing any bits of with symbols (i.e. ``deleting" attributes of ). The semantics of the system are that any private key for a circuit can be used to decrypt a ciphertext associated with if none of the input bits read by circuit are symbols and . We show a pathway for combining ABE with deletable attributes with constrained psuedorandom functions to obtain adaptively secure ABE building upon the recent work of Tsabary. Our new ABE system will be adaptively secure and be a ciphertext-policy ABE that supports the same functionality as the underlying constrained PRF as long as the PRF is ``deletion conforming". Here we also provide a simple constrained PRF construction that gives subset functionality. Our approach enables us to access a broader array of Attribute-Based Encryption schemes support deletion of attributes. For example, we show that both the Goyal~et al.~(GPSW) and Boyen ABE schemes can trivially handle a deletion operation. And, by using a hardcore bit variant of GPSW scheme we obtain an adaptively secure ABE scheme under the Search Bilinear Diffie-Hellman assumption in addition to pseudo random functions in NC1. This gives the first adaptively secure ABE from a search assumption as all prior work relied on decision assumptions over source group elements.more » « less
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Digital signatures provide scalable authentication with non-repudiation and therefore are vital tools for the Internet of Things (IoT). IoT applications harbor vast quantities of low-end devices that are expected to operate for long periods with a risk of compromise. Hence, IoT needs post-quantum cryptography (PQC) that respects the resource limitations of low-end devices while offering compromise resiliency (e.g., forward security). However, as seen in NIST PQC efforts, quantum-safe signatures are extremely costly for low-end IoT. These costs become prohibitive when forward security is considered. We propose a highly lightweight post-quantum digital signature called HArdware-Supported Efficient Signature (HASES) that meets the stringent requirements of resource-limited signers (processor, memory, bandwidth) with forward security. HASES transforms a key-evolving one-time hash-based signature into a polynomial unbounded one by introducing a public key oracle via secure enclaves. The signer is non-interactive and only generates a few hashes per signature. Unlike existing hardware-supported alternatives, HASES does not require secure-hardware on the signer, which is infeasible for low-end IoT. HASES also does not assume non-colluding servers that permit scalable verification. We proved that HASES is secure and implemented it on the commodity hardware and the 8-bit AVR ATmega2560 microcontroller. Our experiments confirm that HASES is 271 and 34 faster than (forward-secure) XMSS and (plain) Dilithium. HASES is more than twice and magnitude more energy-efficient than (forward-secure) ANT and (plain) BLISS, respectively, on an 8-bit device. We open-source HASES for public testing and adaptation.more » « less
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The epsilon-approximate degree, deg_epsilon(f), of a Boolean function f is the least degree of a real-valued polynomial that approximates f pointwise to within epsilon. A sound and complete certificate for approximate degree being at least k is a pair of probability distributions, also known as a dual polynomial, that are perfectly k-wise indistinguishable, but are distinguishable by f with advantage 1 - epsilon. Our contributions are: - We give a simple, explicit new construction of a dual polynomial for the AND function on n bits, certifying that its epsilon-approximate degree is Omega (sqrt{n log 1/epsilon}). This construction is the first to extend to the notion of weighted degree, and yields the first explicit certificate that the 1/3-approximate degree of any (possibly unbalanced) read-once DNF is Omega(sqrt{n}). It draws a novel connection between the approximate degree of AND and anti-concentration of the Binomial distribution. - We show that any pair of symmetric distributions on n-bit strings that are perfectly k-wise indistinguishable are also statistically K-wise indistinguishable with at most K^{3/2} * exp (-Omega (k^2/K)) error for all k < K <= n/64. This bound is essentially tight, and implies that any symmetric function f is a reconstruction function with constant advantage for a ramp secret sharing scheme that is secure against size-K coalitions with statistical error K^{3/2} * exp (-Omega (deg_{1/3}(f)^2/K)) for all values of K up to n/64 simultaneously. Previous secret sharing schemes required that K be determined in advance, and only worked for f=AND. Our analysis draws another new connection between approximate degree and concentration phenomena. As a corollary of this result, we show that for any d <= n/64, any degree d polynomial approximating a symmetric function f to error 1/3 must have coefficients of l_1-norm at least K^{-3/2} * exp ({Omega (deg_{1/3}(f)^2/d)}). We also show this bound is essentially tight for any d > deg_{1/3}(f). These upper and lower bounds were also previously only known in the case f=AND.more » « less
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