IACR Communications in Cryptology
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Implicit Factorization with Shared Any Bits
Get PDFAt PKC 2009, May and Ritzenhofen proposed the implicit factorization problem (IFP). They showed that it is undemanding to factor two h-bit RSA moduli N1=p1q1, N2=p2q2 where q1, q2 are both αh-bit, and p1, p2 share uh>2αh the least significant bits (LSBs). Subsequent works mainly focused on extending the IFP to the cases where p1, p2 share some of the most significant bits (MSBs) or the middle bits (MBs). In this paper, we propose a novel generalized IFP where p1 and p2 share an arbitrary number of bit blocks, with each block having a consistent displacement in its position between p1 and p2, and we solve it successfully based on Coppersmith’s method. Specifically, we generate a new set of shift polynomials to construct the lattice and optimize the structure of the lattice by introducing a new variable z=p1. We derive that we can factor the two moduli in polynomial time when u>2(n+1)α(1−α^1/(n+1)) with p1, p2 sharing n blocks. Further, no matter how many blocks are shared, we can theoretically factor the two moduli as long as u>2αln(1/α). In addition, we consider two other cases where the positions of the shared blocks are arbitrary or there are k>2 known moduli. Meanwhile, we provide the corresponding solutions for the two cases. Our work is verified by experiments. </p
Efficient Boolean-to-Arithmetic Mask Conversion in Hardware
Get PDFMasking schemes are key in thwarting side-channel attacks due to their robust theoretical foundation. Transitioning from Boolean to arithmetic (B2A) masking is a necessary step in various cryptography schemes, including hash functions, ARX-based ciphers, and lattice-based cryptography. While there exists a significant body of research focusing on B2A software implementations, studies pertaining to hardware implementations are quite limited, with the majority dedicated solely to creating efficient Boolean masked adders. In this paper, we present first- and second-order secure hardware implementations to perform B2A mask conversion efficiently without using masked adder structures. We first introduce a first-order secure low-latency gadget that executes a B2A2k in a single cycle. Furthermore, we propose a second-order secure B2A2k gadget that has a latency of only 4 clock cycles. Both gadgets are independent of the input word size k. We then show how these new primitives lead to improved B2Aq hardware implementations that perform a B2A mask conversion of integers modulo an arbitrary number. Our results show that our new gadgets outperform comparable solutions by more than a magnitude in terms of resource requirements and are at least 3 times faster in terms of latency and throughput. All gadgets have been formally verified and proven secure in the glitch-robust PINI security model. We additionally confirm the security of our gadgets on an FPGA platform using practical TVLA tests. </p
Revisiting the Slot-to-Coefficient Transformation for BGV and BFV
Get PDFNumerous applications in homomorphic encryption require an operation that moves the slots of a ciphertext to the coefficients of a different ciphertext. For the BGV and BFV schemes, the only efficient algorithms to implement this slot-to-coefficient transformation were proposed in the setting of non-power-of-two cyclotomic rings. In this paper, we devise an FFT-like method to decompose the slot-to-coefficient transformation (and its inverse) for power-of-two cyclotomic rings. The proposed method can handle both fully and sparsely packed slots. Our algorithm brings down the computational complexity of the slot-to-coefficient transformation from a linear to a logarithmic number of FHE operations, which is shown via a detailed complexity analysis.The new procedures are implemented in Microsoft SEAL for BFV. The experiments report a speedup of up to 44 times when packing 2^12 elements from GF(8191^8). We also study a fully packed bootstrapping operation that refreshes 2^15 elements from GF(65537) and obtain an amortized speedup of 12 times. </p
Inspector Gadget
Get PDF We introduce InspectorGadget, an Open-Source Python-based software for assessing and comparing the complexity of masking gadgets. By providing a limited set of characteristics of a hardware platform, our tool allows to estimate the cost of a masking gadget in terms of cycle count equivalent and memory footprint. InspectorGadget is highly flexible. It enables the user to define her own estimation functions, as well as to expand the set of gadgets and predefined microcontrollers. As a case-study, we produce a fair comparison of several masked versions of Kyber compression function from the literature, together with novel alternatives automatically generated by our tool. Our results confirm that an interesting middle ground exists between theoretical performance measures (asymptotic complexity or operations count) and real implementations benchmarks (clock cycle accurate evaluations). InspectorGadget offers both simplicity and genericity while capturing the main performance-related parameters of a hardware platform. </p
Towards the Impossibility of Quantum Public Key Encryption with Classical Keys from One-Way Functions
Get PDF There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC\u2789). However, the distribution of quantum public keys is a challenging task. Therefore, the main question that motivates our work is if quantum PKE from OWF is possible if we have classical public keys. Such protocols are impossible if ciphertexts are also classical, given the impossibility result of Austrin et al.(CRYPTO\u2722) of quantum enhanced key-agreement (KA) with classical communication. In this paper, we focus on black-box separation for PKE with classical public key and quantum ciphertext from OWF under the polynomial compatibility conjecture, first introduced in Austrin et al.. More precisely, we show the separation when the decryption algorithm of the PKE does not query the OWF. We prove our result by extending the techniques of Austrin et al. and we show an attack for KA in an extended classical communication model where the last message in the protocol can be a quantum state. </p
How to Make Rational Arguments Practical and Extractable
Get PDF We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded.Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have to read the entire input). In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold.We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest.As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for . </p
A New Paradigm for Server-Aided MPC
Get PDFThe server-aided model for multiparty computation (MPC) was introduced to capture a real-world scenario where clients wish to off-load the heavy computation of MPC protocols to dedicated servers. A rich body of work has studied various trade-offs between security guarantees (e.g., semi-honest vs malicious), trust assumptions (e.g., the threshold on corrupted servers), and efficiency.However, all existing works make the assumption that all clients must agree on employing the same servers, and accept the same corruption threshold. In this paper, we challenge this assumption and introduce a new paradigm for server-aided MPC, where each client can choose their own set of servers and their own threshold of corrupted servers. In this new model, the privacy of each client is guaranteed as long as their own threshold is satisfied, regardless of the other servers/clients. We call this paradigm per-party private server-aided MPC to highlight both a security and efficiency guarantee: (1) per-party privacy, which means that each party gets their own privacy guarantees that depend on their own choice of the servers; (2) per-party complexity, which means that each party only needs to communicate with their chosen servers. Our primary contribution is a new theoretical framework for server-aided MPC. We provide two protocols to show feasibility, but leave it as a future work to investigate protocols that focus on concrete efficiency. </p
On Loopy Belief Propagation for SASCAs An Analysis and Empirical Study of the Inference Problem
Get PDF Profiled power analysis is one of the most powerful forms of passive side-channel attacks. Over the last two decades, many works have analyzed their impact on cryptographic implementations as well as corresponding countermeasure techniques. To date, the most advanced variants of profiled power analysis are based on Soft-analytical Side-Channel Attacks (SASCA). After the initial profiling phase, a SASCA adversary creates a probabilistic graphical model, called a factor graph, of the target implementation and encodes the results of the previous step as prior information. Then, an inference algorithm such as loopy Belief Propagation (BP) can be used to recover the distribution of a target variable in the graph, i.e., sensitive data/keys. Designers of cryptographic implementations aim to reduce information leakage as much as possible and assess how much leakage can be allowed without compromising security requirements. Despite the existence of many works on profiled power analysis, it is still notoriously difficult to state under which conditions a cryptographic implementation provides sufficient protection against a profiling attacker with certain capabilities. In particular, it is unknown when a BP-based attack is optimal or whether tuning some heuristics in that algorithm may significant strengthen the attack. This knowledge gap led us to investigate the effectiveness of BP for SASCAs by studying the modes of failures of BP in the context of the SASCA, and systematically analyzing the behavior of BP on practically-relevant factor graphs. We use exact inference to gauge the quality of the approximation provided by BP. Through this assessment, we show that there exists a significant disparity between BP and exact inference in terms of guessing entropy when performing SASCAs on several classes of factor graphs. We further review and analyze various BP improvement heuristics from the literature. </p
Masked Computation of the Floor Function and Its Application to the FALCON Signature
Get PDF FALCON is a signature selected for standardisation of the new Post-Quantum Cryptography (PQC) primitives by the National Institute of Standards and Technology (NIST). However, it remains a challenge to define efficient countermeasures against side-channel attacks (SCA) for this algorithm. FALCON is a lattice-based signature that relies on rational numbers, which is unusual in the cryptography field. Although recent work proposed a solution to mask the addition and the multiplication, some roadblocks remain, most noticeably, how to protect the floor function. In this work, we propose to complete the first existing tests of hardening FALCON against SCA. We perform the mathematical proofs of our methods as well as formal security proofs in the probing model by ensuring Multiple Input Multiple Output Strong Non-Interference (MIMO-SNI) security. We provide performances on a laptop computer of our gadgets as well as of a complete masked FALCON. We notice significant overhead in doing so and discuss the deployability of our method in a real-world context. </p
On the Key-Commitment Properties of Forkcipher-based AEADs
Get PDF Forkcipher-based AEADs have emerged as lightweight and efficient cryptographic modes, making them suitable for resource-constrained environments such as IoT devices and distributed decryption through MPC. These schemes, including prominent examples like Eevee (Jolteon, Espeon, and Umbreon), PAEF, RPAEF, and SAEF, leverage the properties of forkciphers to achieve enhanced performance. However, their security in terms of key commitment, a critical property for certain applications such as secure cloud services, as highlighted by Albertini et al. (USENIX 2022), has not been comprehensively analyzed until now.In this work, we analyze the key-commitment properties of forkcipher-based AEADs. We found that some of the forkcipher-based AEAD schemes lack key-commitment properties, primarily due to the distinctive manner in which they process associated data and plaintext. For two different keys and the same nonce, an adversary can identify associated data and plaintext blocks that produce identical ciphertext-tags with a complexity of . Our findings apply to various forkcipher-based AEADs, including Eevee, PAEF, and SAEF, and naturally extend to less strict frameworks, such as CMT-1 and CMT-4.These findings highlight a significant limitation in the robustness of forkcipher-based AEADs. While these modes are attractive for their lightweight design and efficiency, their deployment should be restricted in scenarios where explicit robustness or key-commitment security is required. </p