Improved Power Analysis Attacks on Falcon

Falcon is one of the three post-quantum signature schemes selected for standardization by NIST. Due to its low bandwidth and high efficiency, Falcon is seen as an attractive option for quantum-safe embedded systems. In this work, we study Falcon\u27s side-channel resistance by analysing its Gaussian samplers. Our results are mainly twofold. The first result is an improved key recovery exploiting the leakage within the base sampler investigated by Guerreau et al. (CHES 2022). Instead of resorting to the fourth moment as in former parallelepiped-learning attacks, we work with the second order statistics covariance and use its spectral decomposition to recover the secret information. Our approach substantially reduces the requirement for measurements and computation resources: $220\,000$ traces is sufficient to recover the secret key of Falcon 512 within half an hour with a probability of $\approx 25\%$. As a comparison, even with $10^6$ traces, the former attack still needs about 1000 hours CPU time of lattice reduction for a full key recovery. In addition, our approach is robust to inaccurate leakage classification, which is another advantage over parallelepiped-learning attacks. Our second result is a practical power analysis targeting the integer Gaussian sampler of Falcon. The analysis relies on the leakage of random sign flip within the integer Gaussian sampling. This leakage was exposed in 2018 by Kim and Hong, but it is not considered in Falcon\u27s implementation and unexploited for side channel analysis until now. We identify the leakage within the reference implementation of Falcon on an ARM Cortex-M4 STM32F407IGT6 microprocessor. We also show that this single bit of leakage is in effect enough for practical key recovery: with $170\,000$ traces one can fully recover the key of Falcon-512 within half an hour. Furthermore, combining the sign leakage and the aforementioned leakage, one can recover the key with only $45\,000$ signature measurements in a short time. As a by-product, we also extend our power analysis to Mitaka which is a recent variant of Falcon. The same leakages exist within the integer Gaussian samplers of Mitaka, and they can also be used to mount key recovery attacks. Nevertheless, the key recovery in Mitaka requires much more traces than it does in Falcon, due to their different lattice Gaussian samplers

Algorithmic Security is Insufficient: A Comprehensive Survey on Implementation Attacks Haunting Post-Quantum Security

This survey is on forward-looking, emerging security concerns in post-quantum era, i.e., the implementation attacks for 2022 winners of NIST post-quantum cryptography (PQC) competition and thus the visions, insights, and discussions can be used as a step forward towards scrutinizing the new standards for applications ranging from Metaverse, Web 3.0 to deeply-embedded systems. The rapid advances in quantum computing have brought immense opportunities for scientific discovery and technological progress; however, it poses a major risk to today's security since advanced quantum computers are believed to break all traditional public-key cryptographic algorithms. This has led to active research on PQC algorithms that are believed to be secure against classical and powerful quantum computers. However, algorithmic security is unfortunately insufficient, and many cryptographic algorithms are vulnerable to side-channel attacks (SCA), where an attacker passively or actively gets side-channel data to compromise the security properties that are assumed to be safe theoretically. In this survey, we explore such imminent threats and their countermeasures with respect to PQC. We provide the respective, latest advancements in PQC research, as well as assessments and providing visions on the different types of SCAs

Antrag: Annular NTRU Trapdoor Generation

In this paper, we introduce a novel trapdoor generation technique for Prest\u27s hybrid sampler over NTRU lattices. Prest\u27s sampler is used in particular in the recently proposed Mitaka signature scheme (Eurocrypt 2022), a variant of the Falcon signature scheme, one of the candidates selected by NIST for standardization. Mitaka was introduced to address Falcon\u27s main drawback, namely the fact that the lattice Gaussian sampler used in its signature generation is highly complex, difficult to implement correctly, to parallelize or protect against side-channels, and to instantiate over rings of dimension not a power of two to reach intermediate security levels. Prest\u27s sampler is considerably simpler and solves these various issues, but when applying the same trapdoor generation approach as Falcon, the resulting signatures have far lower security in equal dimension. The Mitaka paper showed how certain randomness-recycling techniques could be used to mitigate this security loss, but the resulting scheme is still substantially less secure than Falcon (by around 20 to 50 bits of CoreSVP security depending on the parameters), and has much slower key generation. Our new trapdoor generation techniques solves all of those issues satisfactorily: it gives rise to a much simpler and faster key generation algorithm than Mitaka\u27s (achieving similar speeds to Falcon), and is able to comfortably generate trapdoors reaching the same NIST security levels as Falcon as well. It can also be easily adapted to rings of intermediate dimensions, in order to support the same versatility as Mitaka in terms of parameter selection. All in all, this new technique combines all the advantages of both Falcon and Mitaka (and more) with none of the drawbacks

잡음키를 가지는 신원기반 동형암호에 관한 연구

학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2020. 2. 천정희.클라우드 상의 데이터 분석 위임 시나리오는 동형암호의 가장 효과적인 응용 시나리오 중 하나이다. 그러나, 다양한 데이터 제공자와 분석결과 요구자가 존재하는 실제 현실의 모델에서는 기본적인 암복호화와 동형 연산 외에도 여전히 해결해야 할 과제들이 남아있는 실정이다. 본 학위논문에서는 이러한 모델에서 필요한 여러 요구사항들을 포착하고, 이에 대한 해결방안을 논하였다. 먼저, 기존의 알려진 동형 데이터 분석 솔루션들은 데이터 간의 층위나 수준을 고려하지 못한다는 점에 착안하여, 신원기반 암호와 동형암호를 결합하여 데이터 사이에 접근 권한을 설정하여 해당 데이터 사이의 연산을 허용하는 모델을 생각하였다. 또한 이 모델의 효율적인 동작을 위해서 동형암호 친화적인 신원기반 암호에 대하여 연구하였고, 기존에 알려진 NTRU 기반의 암호를 확장하여 module-NTRU 문제를 정의하고 이를 기반으로 한 신원기반 암호를 제안하였다. 둘째로, 동형암호의 복호화 과정에는 여전히 비밀키가 관여하고 있고, 따라서 비밀키 관리 문제가 남아있다는 점을 포착하였다. 이러한 점에서 생체정보를 활용할 수 있는 복호화 과정을 개발하여 해당 과정을 동형암호 복호화에 적용하였고, 이를 통해 암복호화와 동형 연산의 전 과정을 어느 곳에도 키가 저장되지 않은 상태로 수행할 수 있는 암호시스템을 제안하였다. 마지막으로, 동형암호의 구체적인 안전성 평가 방법을 고려하였다. 이를 위해 동형암호가 기반하고 있는 이른바 Learning With Errors (LWE) 문제의 실제적인 난해성을 면밀히 분석하였고, 그 결과 기존의 공격 알고리즘보다 평균적으로 1000배 이상 빠른 공격 알고리즘들을 개발하였다. 이를 통해 현재 사용하고 있는 동형암호 파라미터가 안전하지 않음을 보였고, 새로운 공격 알고리즘을 통한 파라미터 설정 방법에 대해서 논하였다.Secure data analysis delegation on cloud is one of the most powerful application that homomorphic encryption (HE) can bring. As the technical level of HE arrive at practical regime, this model is also being considered to be a more serious and realistic paradigm. In this regard, this increasing attention requires more versatile and secure model to deal with much complicated real world problems. First, as real world modeling involves a number of data owners and clients, an authorized control to data access is still required even for HE scenario. Second, we note that although homomorphic operation requires no secret key, the decryption requires the secret key. That is, the secret key management concern still remains even for HE. Last, in a rather fundamental view, we thoroughly analyze the concrete hardness of the base problem of HE, so-called Learning With Errors (LWE). In fact, for the sake of efficiency, HE exploits a weaker variant of LWE whose security is believed not fully understood. For the data encryption phase efficiency, we improve the previously suggested NTRU-lattice ID-based encryption by generalizing the NTRU concept into module-NTRU lattice. Moreover, we design a novel method that decrypts the resulting ciphertext with a noisy key. This enables the decryptor to use its own noisy source, in particular biometric, and hence fundamentally solves the key management problem. Finally, by considering further improvement on existing LWE solving algorithms, we propose new algorithms that shows much faster performance. Consequently, we argue that the HE parameter choice should be updated regarding our attacks in order to maintain the currently claimed security level.1 Introduction 1 1.1 Access Control based on Identity 2 1.2 Biometric Key Management 3 1.3 Concrete Security of HE 3 1.4 List of Papers 4 2 Background 6 2.1 Notation 6 2.2 Lattices 7 2.2.1 Lattice Reduction Algorithm 7 2.2.2 BKZ cost model 8 2.2.3 Geometric Series Assumption (GSA) 8 2.2.4 The Nearest Plane Algorithm 9 2.3 Gaussian Measures 9 2.3.1 Kullback-Leibler Divergence 11 2.4 Lattice-based Hard Problems 12 2.4.1 The Learning With Errors Problem 12 2.4.2 NTRU Problem 13 2.5 One-way and Pseudo-random Functions 14 3 ID-based Data Access Control 16 3.1 Module-NTRU Lattices 16 3.1.1 Construction of MNTRU lattice and trapdoor 17 3.1.2 Minimize the Gram-Schmidt norm 22 3.2 IBE-Scheme from Module-NTRU 24 3.2.1 Scheme Construction 24 3.2.2 Security Analysis by Attack Algorithms 29 3.2.3 Parameter Selections 31 3.3 Application to Signature 33 4 Noisy Key Cryptosystem 36 4.1 Reusable Fuzzy Extractors 37 4.2 Local Functions 40 4.2.1 Hardness over Non-uniform Sources 40 4.2.2 Flipping local functions 43 4.2.3 Noise stability of predicate functions: Xor-Maj 44 4.3 From Pseudorandom Local Functions 47 4.3.1 Basic Construction: One-bit Fuzzy Extractor 48 4.3.2 Expansion to multi-bit Fuzzy Extractor 50 4.3.3 Indistinguishable Reusability 52 4.3.4 One-way Reusability 56 4.4 From Local One-way Functions 59 5 Concrete Security of Homomorphic Encryption 63 5.1 Albrecht's Improved Dual Attack 64 5.1.1 Simple Dual Lattice Attack 64 5.1.2 Improved Dual Attack 66 5.2 Meet-in-the-Middle Attack on LWE 69 5.2.1 Noisy Collision Search 70 5.2.2 Noisy Meet-in-the-middle Attack on LWE 74 5.3 The Hybrid-Dual Attack 76 5.3.1 Dimension-error Trade-o of LWE 77 5.3.2 Our Hybrid Attack 79 5.4 The Hybrid-Primal Attack 82 5.4.1 The Primal Attack on LWE 83 5.4.2 The Hybrid Attack for SVP 86 5.4.3 The Hybrid-Primal attack for LWE 93 5.4.4 Complexity Analysis 96 5.5 Bit-security estimation 102 5.5.1 Estimations 104 5.5.2 Application to PKE 105 6 Conclusion 108 Abstract (in Korean) 120Docto

Cryptanalysis of the Peregrine Lattice-Based Signature Scheme

The Peregrine signature scheme is one of the candidates in the ongoing Korean post-quantum cryptography competition. It is proposed as a high-speed variant of Falcon, which is a hash-and-sign signature scheme over NTRU lattices and one of the schemes selected by NIST for standardization. To this end, Peregrine replaces the lattice Gaussian sampler in the Falcon signing procedure with a new sampler based on the centered binomial distribution. While this modification offers significant advantages in terms of efficiency and implementation, it does not come with a provable guarantee that signatures do not leak information about the signing key. Unfortunately, lattice-based signature schemes in the hash-and-sign paradigm that lack such a guarantee (such as GGH, NTRUSign or DRS) have generally proved insecure. In this paper, we show that Peregrine is no exception, by demonstrating a practical key recovery attack against it. We observe that the support of Peregrine signatures is a hidden transformation of some public distribution and still leaks information about the signing key. By adapting the parallelepiped-learning technique of Nguyen and Regev (Eurocrypt 2006), we show that the signing key can be recovered from a relatively small number of signatures. The learning technique alone yields an approximate version of the key, from which we can recover the exact key using a decoding technique due to Thomas Prest (PKC 2023). For the reference implementation (resp. the official specification version) of Peregrine-512, we fully recover the secret key with good probability in a few hours given around 25,000 (resp. 11 million) signature samples

Loop-Abort Faults on Lattice-Based Fiat–Shamir and Hash-and-Sign Signatures

As the advent of general-purpose quantum computers appears to be drawing closer, agencies and advisory bodies have started recommending that we prepare the transition away from factoring and discrete logarithm-based cryptography, and towards postquantum secure constructions, such as lattice- based schemes. Almost all primitives of classical cryptography (and more!) can be realized with lattices, and the efficiency of primitives like encryption and signatures has gradually improved to the point that key sizes are competitive with RSA at similar security levels, and fast performance can be achieved both in soft- ware and hardware. However, little research has been conducted on physical attacks targeting concrete implementations of postquantum cryptography in general and lattice-based schemes in particular, and such research is essential if lattices are going to replace RSA and elliptic curves in our devices and smart cards. In this paper, we look in particular at fault attacks against implementations of lattice-based signature schemes, looking both at Fiat–Shamir type constructions (particularly BLISS, but also GLP, PASSSing and Ring-TESLA) and at hash-and-sign schemes (particularly the GPV-based scheme of Ducas–Prest– Lyubashevsky). These schemes include essentially all practical lattice-based signatures, and achieve the best efficiency to date in both software and hardware. We present several fault attacks against those schemes yielding a full key recovery with only a few or even a single faulty signature, and discuss possible countermeasures to protect against these attacks

Hawk: Module LIP makes Lattice Signatures Fast, Compact and Simple

We propose the signature scheme Hawk, a concrete instantiation of proposals to use the Lattice Isomorphism Problem (LIP) as a foundation for cryptography that focuses on simplicity. This simplicity stems from LIP, which allows the use of lattices such as , leading to signature algorithms with no floats, no rejection sampling, and compact precomputed distributions. Such design features are desirable for constrained devices, and when computing signatures inside FHE or MPC. The most significant change from recent LIP proposals is the use of module lattices, reusing algorithms and ideas from NTRUSign and Falcon. Its simplicity makes Hawk competitive. We provide cryptanalysis with experimental evidence for the design of Hawk and implement two parameter sets, Hawk-512 and Hawk-1024. Signing using Hawk-512 and Hawk-1024 is four times faster than Falcon on x86 architectures, produces signatures that are about 15% more compact, and is slightly more secure against forgeries by lattice reduction attacks. When floating-points are unavailable, Hawk signs 15 times faster than Falcon. We provide a worst case to average case reduction for module LIP. For certain parametrisations of Hawk this applies to secret key recovery and we reduce signature forgery in the random oracle model to a new problem called the one more short vector problem

Lattice-based digital signature and discrete gaussian sampling

Lattice-based cryptography has generated considerable interest in the last two decades due toattractive features, including conjectured security against quantum attacks, strong securityguarantees from worst-case hardness assumptions and constructions of fully homomorphicencryption schemes. On the other hand, even though it is a crucial part of many lattice-basedschemes, Gaussian sampling is still lagging and continues to limit the effectiveness of this newcryptography. The first goal of this thesis is to improve the efficiency of Gaussian sampling forlattice-based hash-and-sign signature schemes. We propose a non-centered algorithm, with aflexible time-memory tradeoff, as fast as its centered variant for practicable size of precomputedtables. We also use the Rényi divergence to bound the precision requirement to the standarddouble precision. Our second objective is to construct Falcon, a new hash-and-sign signaturescheme, based on the theoretical framework of Gentry, Peikert and Vaikuntanathan for latticebasedsignatures. We instantiate that framework over NTRU lattices with a new trapdoor sampler

Heuristically secure threshold lattice-based cryptography schemes

In public-key encryption, a long-term private key can be an easy target for hacking and deserves extra protection. One way to enhance its security is to share the long-term private key among multiple (say n) distributed servers; any threshold number (t, t ≤ n) of these servers are needed to collectively use the shared private key without reconstructing it. As a result, an attacker who has compromised less than t servers will still not be able to reconstruct the shared private key. In this thesis, we studied threshold decryption schemes for lattice-based public-key en- cryption, which is one of the most promising post-quantum public-key encryption schemes. We developed threshold decryption schemes for Stinson’s, the standard NTRU, and NTRU with Ring Learning with Errors (R-LWE) cryptosystems. Prototype implementations were developed for validating the functionality of these threshold decryption schemes. Our de- signs achieve heuristic security, and its security is supported by mechanisms similar to that of R-LWE