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    Robust Additive Randomized Encodings from IO and Pseudo-Non-linear Codes

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    Additive randomized encodings (ARE), introduced by Halevi, Ishai, Kushilevitz, and Rabin (CRYPTO 2023), reduce the computation of a k-party function f(x1,...,xk)f (x_1, . . . , x_k ) to locally computing encodings x^i\hat{x}_i of each input xi and then adding them together over some Abelian group into an output encoding y^=x^i\hat{y} = ∑ \hat{x}_i, which reveals nothing but the result. In robust ARE (RARE) the sum of any subset of x^i\hat{x}_i, reveals only the residual function obtained by restricting the corresponding inputs. The appeal of (R)ARE comes from the simplicity of the online part of the computation involving only addition, which yields for instance non-interactive multi-party computation in the shuffle model where messages from different parties are anonymously shuffled. Halevi, Ishai, Kushilevitz, and Rabin constructed ARE from standard assumptions and RARE in the ideal obfuscation model, leaving open the question of whether RARE can be constructed in the plain model. We construct RARE in the plain model from indistinguishability obfuscation, which is necessary, and a new primitive that we call pseudo-non-linear codes. We provide two constructions of this primitive assuming either Learning with Errors or Decision Diffie Hellman. A bonus feature of our construction is that it is online succinct. Specifically, encodings x^i\hat{x}_i can be decomposed to offline parts z^i\hat{z}_i that can be sent directly to the evaluator and short online parts g^i\hat{g}_i that are added together

    Divide and Surrender: Exploiting Variable Division Instruction Timing in HQC Key Recovery Attacks

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    We uncover a critical side-channel vulnerability in the Hamming Quasi-Cyclic (HQC) round 4 optimized implementation arising due to the use of the modulo operator. In some cases, compilers optimize uses of the modulo operator with compile-time known divisors into constant-time Barrett reductions. However, this optimization is not guaranteed: for example, when a modulo operation is used in a loop the compiler may emit division (div) instructions which have variable execution time depending on the numerator. When the numerator depends on secret data, this may yield a timing side-channel. We name vulnerabilities of this kind Divide and Surrender (DaS) vulnerabilities. For processors supporting Simultaneous Multithreading (SMT) we propose a new approach called DIV-SMT which enables precisely measuring small division timing variations using scheduler and/or execution unit contention. We show that using only 100 such side-channel traces we can build a Plaintext-Checking (PC) oracle with above 90% accuracy. Our approach may also prove applicable to other instances of the DaS vulnerability, such as KyberSlash. We stress that exploitation with DIV-SMT requires co-location of the attacker on the same physical core as the victim. We then apply our methodology to HQC and present a novel way to recover HQC secret keys faster, achieving an 8-fold decrease in the number of idealized oracle queries when compared to previous approaches. Our new PC oracle attack uses our newly developed Zero Tester method to quickly determine whether an entire block of bits contains only zero-bits. The Zero Tester method enables the DIV-SMT powered attack on HQC-128 to complete in under 2 minutes on our targeted AMD Zen2 machine

    Application-Aware Approximate Homomorphic Encryption: Configuring FHE for Practical Use

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    Fully Homomorphic Encryption (FHE) is a powerful tool for performing privacy-preserving analytics over encrypted data. A promising method for FHE over real and complex numbers is approximate homomorphic encryption, instantiated with the Cheon-Kim-Kim-Song (CKKS) scheme. The CKKS scheme enables efficient evaluation for many privacy-preserving machine learning applications. Despite its high efficiency, there is currently a lot of confusion on how to securely instantiate CKKS for a given application, especially after secret-key recovery attacks were proposed by Li and Micciancio (EUROCRYPT\u2721) for the INDCPADIND-CPA^{D} setting, i.e., where decryption results are shared with other parties. On the one hand, the generic definition of INDCPADIND-CPA^{D} is application-agnostic and often requires impractically large parameters. On the other hand, practical CKKS implementations target specific applications and use tighter parameters. A good illustration are the recent secret-key recovery attacks against a CKKS implementation in the OpenFHE library by Guo et al. (USENIX Security\u2724). We show that these attacks misuse the library by employing different (incompatible) circuits during parameter estimation and run-time computation, yet they do not violate the generic (application-agnostic) INDCPADIND-CPA^{D} definition. To address this confusion, we introduce the notion of application-aware homomorphic encryption and devise related security definitions, which correspond more closely to how homomorphic encryption schemes are implemented and used in practice. We then formulate the guidelines for implementing the application-aware homomorphic encryption model to achieve INDCPADIND-CPA^{D} security for practical applications of CKKS. We also show that our application-aware model can be used for secure, efficient instantiation of exact homomorphic encryption schemes

    Distributed Fiat-Shamir Transform

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    The recent surge of distribute technologies caused an increasing interest towards threshold signature protocols, that peaked with the recent NIST First Call for Multi-Party Threshold Schemes. Since its introduction, the Fiat-Shamir Transform has been the most popular way to design standard digital signature schemes. In this work, we translate the Fiat-Shamir Transform into a multi-party setting, building a framework that seeks to be an alternative, easier way to design threshold digital signatures. We do that by introducing the concept of threshold identification scheme and threshold sigma protocol, and showing necessary and sufficient conditions to prove the security of the threshold signature schemes derived from them. Lastly, we show a practical application of our framework providing an alternative security proof for Sparkle, a recent threshold Schnorr signature. In particular, we consider the threshold identification scheme underlying Sparkle and prove the security of the signature derived from it. We show that using our framework the effort required to prove the security of threshold signatures might be drastically lowered. In fact, instead of reducing explicitly its security to the security of a hard problem, it is enough to prove some properties of the underlying threshold sigma protocol and threshold identification scheme. Then, by applying the results that we prove in this paper it is guaranteed that the derived threshold signature is secure

    Efficient Zero-Knowledge Arguments and Digital Signatures via Sharing Conversion in the Head

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    We present a novel technique within the MPC-in-the-Head framework, aiming to design efficient zero-knowledge protocols and digital signature schemes. The technique allows for the simultaneous use of additive and multiplicative sharings of secret information, enabling efficient proofs of linear and multiplicative relations. The applications of our technique are manifold. It is first applied to construct zero-knowledge arguments of knowledge for Double Discrete Logarithms (DDLP). The resulting protocol achieves improved communication complexity without compromising efficiency. We also propose a new zero-knowledge argument of knowledge for the Permuted Kernel Problem. Eventually, we suggest a short (candidate) post-quantum digital signature scheme constructed from a new one-way function based on simple polynomials known as fewnomials. This scheme offers simplicity and ease of implementation. Finally, we present two additional results inspired by this work but using alternative approaches. We propose a zero-knowledge argument of knowledge of an RSA plaintext for a small public exponent that significantly improves the state-of-the-art communication complexity. We also detail a more efficient forward-backward construction for the DDLP

    Registered Attribute-Based Signature

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    This paper introduces the notion of registered attribute-based signature (registered ABS). Distinctly different from classical attribute-based signature (ABS), registered ABS allows any user to generate their own public/secret key pair and register it with the system. The key curator is critical to keep the system flowing, which is a fully transparent entity that does not retain secrets. Our results can be summarized as follows. -This paper provides the first definition of registered ABS, which has never been defined. -This paper presents the first generic fully secure registered ABS over the prime-order group from kk-Lin assumption under the standard model, which supports various classes of predicate. -This paper gives the first concrete registered ABS scheme for arithmetic branching program (ABP), which achieves full security in the standard model. Technically, our registered ABS is inspired by the blueprint of Okamoto and Takashima[PKC\u2711]. We convert the prime-order registered attribute-based encryption (registered ABE) scheme of Zhu et al.[ASIACRYPT\u2723] via predicate encoding to registered ABS by employing the technique of re-randomization with specialized delegation, while we employ the different dual-system method considering the property of registration. Prior to our work, the work of solving the key-escrow issue was presented by Okamoto and Takashima[PKC\u2713] while their work considered the weak adversary in the random oracle model

    Breaking DPA-protected Kyber via the pair-pointwise multiplication

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    We introduce a novel template attack for secret key recovery in Kyber, leveraging side-channel information from polynomial multiplication during decapsulation. Conceptually, our attack exploits that Kyber\u27s incomplete number-theoretic transform (NTT) causes each secret coefficient to be used multiple times, unlike when performing a complete NTT. Our attack is a single trace \emph{known} ciphertext attack that avoids machine-learning techniques and instead relies on correlation-matching only. Additionally, our template generation method is very simple and easy to replicate, and we describe different attack strategies, varying on the number of templates required. Moreover, our attack applies to both masked implementations as well as designs with multiplication shuffling. We demonstrate its effectiveness by targeting a masked implementation from the \emph{mkm4} repository. We initially perform simulations in the noisy Hamming-Weight model and achieve high success rates with just 1331613\,316 templates while tolerating noise values up to σ=0.3\sigma=0.3. In a practical setup, we measure power consumption and notice that our attack falls short of expectations. However, we introduce an extension inspired by known online template attacks, enabling us to recover 128128 coefficient pairs from a single polynomial multiplication. Our results provide evidence that the incomplete NTT, which is used in Kyber-768 and similar schemes, introduces an additional side-channel weakness worth further exploration

    On the Feasibility of Identity-based Encryption with Equality Test against Insider Attacks

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    Public key encryption with equality test, proposed by Yang et al. (CT-RSA 2010), allows anyone to check whether two ciphertexts of distinct public keys are encryptions of the same plaintext or not using trapdoors, and identity-based encryption with equality test (IBEET) is its identity-based variant. As a variant of IBEET, IBEET against insider attacks (IBEETIA) was proposed by Wu et al. (ACISP 2017), where a token is defined for each identity and is used for encryption. Lee et al. (ACISP 2018) and Duong et al. (ProvSec 2019) proposed IBEETIA schemes constructed by identity-based encryption (IBE) related complexity assumptions. Later, Emura and Takayasu (IEICE Transactions 2023) demonstrated that symmetric key encryption and pseudo-random permutations are sufficient to construct IBEETIA which is secure in the previous security definition. In this paper, we demonstrate a sufficient condition that IBEETIA implies IBE. We define one-wayness against chosen-plaintext/ciphertext attacks for the token generator (OW-TG-CPA/CCA) and for token holders (OW-TH-CPA/CCA), which were not considered in the previous security definition. We show that OW-TG-CPA secure IBEETIA with additional conditions implies OW-CPA secure IBE. On the other hand, we propose a generic construction of OW-TH-CCA secure IBEETIA from public key encryption. Our results suggest a design principle to efficiently construct IBEETIA without employing IBE-related complexity assumptions

    On the practical CPAD security of “exact” and threshold FHE schemes and libraries

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    In their 2021 seminal paper, Li and Micciancio presented a passive attack against the CKKS approximate FHE scheme and introduced the notion of CPAD security. The current status quo is that this line of attacks does not apply to ``exact\u27\u27 FHE. In this paper, we challenge this status quo by exhibiting a CPAD key recovery attack on the linearly homomorphic Regev cryptosystem which easily generalizes to other xHE schemes such as BFV, BGV and TFHE showing that these cryptosystems are not CPAD secure in their basic form. We also show that existing threshold variants of BFV, BGV and CKKS are particularily exposed to CPAD attackers and would be CPAD-insecure without smudging noise addition after partial decryption. Finally we successfully implement our attack against several mainstream FHE libraries and discuss a number of natural countermeasures as well as their consequences in terms of FHE practice, security and efficiency. The attack itself is quite practical as it typically takes less than an hour on an average laptop PC, requiring a few thousand ciphertexts as well as up to around a million evaluations/decryptions, to perform a full key recovery

    Memory Checking Requires Logarithmic Overhead

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    We study the complexity of memory checkers with computational security and prove the first general tight lower bound. Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS \u2791, Algorithmica \u2794), allow a user to store and maintain a large memory on a remote and unreliable server by using small trusted local storage. The user can issue instructions to the server and after every instruction, obtain either the correct value or a failure (but not an incorrect answer) with high probability. The main complexity measure of interest is the size of the local storage and the number of queries the memory checker makes upon every logical instruction. The most efficient known construction has query complexity O(logn/loglogn)O(\log n/\log\log n) and local space proportional to a computational security parameter, assuming one-way functions, where nn is the logical memory size. Dwork, Naor, Rothblum, and Vaikuntanathan (TCC \u2709) showed that for a restricted class of ``deterministic and non-adaptive\u27\u27 memory checkers, this construction is optimal, up to constant factors. However, going beyond the small class of deterministic and non-adaptive constructions has remained a major open problem. In this work, we fully resolve the complexity of memory checkers by showing that any construction with local space pp and query complexity qq must satisfy pn(logn)O(q)  . p \ge \frac{n}{(\log n)^{O(q)}} \;. This implies, as a special case, that qΩ(logn/loglogn)q\ge \Omega(\log n/\log\log n) in any scheme, assuming that pn1εp\le n^{1-\varepsilon} for ε>0\varepsilon>0. The bound applies to any scheme with computational security, completeness 2/32/3, and inverse polynomial in nn soundness (all of which make our lower bound only stronger). We further extend the lower bound to schemes where the read complexity qrq_r and write complexity qwq_w differ. For instance, we show the tight bound that if qr=O(1)q_r=O(1) and pn1εp\le n^{1-\varepsilon} for ε>0\varepsilon>0, then qwnΩ(1)q_w\ge n^{\Omega(1)}. This is the first lower bound, for any non-trivial class of constructions, showing a read-write query complexity trade-off. Our proof is via a delicate compression argument showing that a ``too good to be true\u27\u27 memory checker can be used to compress random bits of information. We draw inspiration from tools recently developed for lower bounds for relaxed locally decodable codes. However, our proof itself significantly departs from these works, necessitated by the differences between settings

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