A kilobit hidden SNFS discrete logarithm computation

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime $p$ looks random, and $p--1$ has a 160-bit prime factor, in line with recommended parameters for the Digital Signature Algorithm. However, our p has been trapdoored in such a way that the special number field sieve can be used to compute discrete logarithms in $\mathbb{F}\_p^*$ , yet detecting that p has this trapdoor seems out of reach. Twenty-five years ago, there was considerable controversy around the possibility of back-doored parameters for DSA. Our computations show that trapdoored primes are entirely feasible with current computing technology. We also describe special number field sieve discrete log computations carried out for multiple weak primes found in use in the wild. As can be expected from a trapdoor mechanism which we say is hard to detect, our research did not reveal any trapdoored prime in wide use. The only way for a user to defend against a hypothetical trapdoor of this kind is to require verifiably random primes

Analysis of RSA based on Quantitating Key Security Strength

AbstractRSA is an asymmetric crypto algorithm which is applied widely in the information security of E-Commerce and Internet-Bank. Its security has been withstanding tests since several decades ago. But the key security isn’t equal to that of algorithm, which is often neglected by most of users and scholars. As to most constructions, they lack definite recognition to the safety of the RSA key. As a result, even some strong crypto-algorithms used it still meets the security predicament. In this paper, start with the known plaintext attack to RSA public key crypto scheme, we pioneer the mechanism of quantitation of the RSA key security strength, the concept of key security coefficient, the evaluation model of security coefficient and the algorithm to extract security strength. Further more, an innovative method of generating secure keys is proposed. After some experimentations, the security performance of key and distribution of secure key-amount, and their key security coefficient are surveyed and analyzed in detail. The theoretic analysis and statistics demonstrate that our mechanism could elevate security of RSA in effect

Software Grand Exposure: SGX Cache Attacks Are Practical

Side-channel information leakage is a known limitation of SGX. Researchers have demonstrated that secret-dependent information can be extracted from enclave execution through page-fault access patterns. Consequently, various recent research efforts are actively seeking countermeasures to SGX side-channel attacks. It is widely assumed that SGX may be vulnerable to other side channels, such as cache access pattern monitoring, as well. However, prior to our work, the practicality and the extent of such information leakage was not studied. In this paper we demonstrate that cache-based attacks are indeed a serious threat to the confidentiality of SGX-protected programs. Our goal was to design an attack that is hard to mitigate using known defenses, and therefore we mount our attack without interrupting enclave execution. This approach has major technical challenges, since the existing cache monitoring techniques experience significant noise if the victim process is not interrupted. We designed and implemented novel attack techniques to reduce this noise by leveraging the capabilities of the privileged adversary. Our attacks are able to recover confidential information from SGX enclaves, which we illustrate in two example cases: extraction of an entire RSA-2048 key during RSA decryption, and detection of specific human genome sequences during genomic indexing. We show that our attacks are more effective than previous cache attacks and harder to mitigate than previous SGX side-channel attacks

Caveat Implementor! Key Recovery Attacks on MEGA

MEGA is a large-scale cloud storage and communication platform that aims to provide end-to-end encryption for stored data. A recent analysis by Backendal, Haller and Paterson (IEEE S&P 2023) invalidated these security claims by presenting practical attacks against MEGA that could be mounted by the MEGA service provider. In response, the MEGA developers added lightweight sanity checks on the user RSA private keys used in MEGA, sufficient to prevent the previous attacks. We analyse these new sanity checks and show how they themselves can be exploited to mount novel attacks on MEGA that recover a target user’s RSA private key with only slightly higher attack complexity than the original attacks. We identify the presence of an ECB encryption oracle under a target user’s master key in the MEGA system; this oracle provides our adversary with the ability to partially overwrite a target user’s RSA private key with chosen data, a powerful capability that we use in our attacks. We then present two distinct types of attack, each type exploiting different error conditions arising in the sanity checks and in subsequent cryptographic processing during MEGA’s user authentication procedure. The first type appears to be novel and exploits the manner in which the MEGA code handles modular inversion when recomputing u = q−1 mod p. The second can be viewed as a small subgroup attack (van Oorschot and Wiener, EUROCRYPT 1996, Lim and Lee, CRYPTO 1998). We prototype the attacks and show that they work in practice. As a side contribution, we show how to improve the RSA key recovery attack of Backendal-Haller-Paterson against the unpatched version of MEGA to require only 2 logins instead of the original 512. We conclude by discussing wider lessons about secure implementation of cryptography that our work surfaces.ISSN:0302-9743ISSN:1611-334

Internet security for mobile computing

Mobile devices are now the most dominant computer platform. Every time a mobile web application accesses the internet, the end user’s data is susceptible to malicious attacks. For instance, when paying a bill at a store with NFC mobile payment, navigating through a city operating GPS on a smartphone, or dictating the temperature at a household with a home automation device. These activities seem routine, yet, when vulnerabilities are present they can leave holes for hackers to access bank accounts, pinpoint a user’s recent location, or tell when someone is not at home. The awareness of the end user cannot be trusted. Device vendors and developers must provide safeguards. An ongoing issue is that the present security standards are outdated and were never envisioned with mobile devices in mind. It can be suggested that security is only idling the progress of mobile computing. Still, many application developers and IT professionals do not adopt security standards fast enough to keep up-to-date with known vulnerabilities. The main goals of the next generation of security standards, TLS, will provide developers with greater security efficiency and improved mobile throughput. These proposed capabilities of the TLS protocol will streamline mobile computing into the forefront of security practices. The analysis of this report demonstrates concepts on the direction mobile security, usability, and performance from a development standpoint.Electrical and Computer Engineerin

A Unified Method for Private Exponent Attacks on RSA using Lattices

International audienceLet (n = pq, e = n^β) be an RSA public key with private exponent d = n^δ , where p and q are large primes of the same bit size. At Eurocrypt 96, Coppersmith presented a polynomial-time algorithm for finding small roots of univariate modular equations based on lattice reduction and then succussed to factorize the RSA modulus. Since then, a series of attacks on the key equation ed − kφ(n) = 1 of RSA have been presented. In this paper, we show that many of such attacks can be unified in a single attack using a new notion called Coppersmith's interval. We determine a Coppersmith's interval for a given RSA public key (n, e). The interval is valid for any variant of RSA, such as Multi-Prime RSA, that uses the key equation. Then we show that RSA is insecure if δ < β + 1/3 α − 1/3 √ (12αβ + 4α^2) provided that we have approximation p0 ≥ √ n of p with |p − p0| ≤ 1/2 n^α , α ≤ 1/2. The attack is an extension of Coppersmith's result

A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

A distributed public key creation system for ad-hoc groups

Ad-hoc networks are on the forefront of technological advances as more embedded devices allow for wireless communications without necessarily requiring a network infrastructure to connect to. One of the larger problems associated with such ad-hoc networks is the lack of being able to access a PKI to create individual secure sessions for these groups being created. For this project, an implementation generating the public and private keys for an RSA public-key protocol has been created on top of the M2MI middleware developed at RIT. In this implementation, as originally described by Dan Boneh, all parties help contribute to the generation of the RSA public modulus, N, without explicitly knowing the factorization of it. It has been shown that this implementation requires, on average, 32689 rounds of the protocol to create a 1024-bit RSA modulus for the group, and has an approximate growth of log2(N) 25 rounds per bit

Smooth Number Message Authentication Code in the IoT Landscape

This paper presents the Smooth Number Message Authentication Code (SNMAC) for the context of lightweight IoT devices. The proposal is based on the use of smooth numbers in the field of cryptography, and investigates how one can use them to improve the security and performance of various algorithms or security constructs. The literature findings suggest that current IoT solutions are viable and promising, yet they should explore the potential usage of smooth numbers. The methodology involves several processes, including the design, implementation, and results evaluation. After introducing the algorithm, provides a detailed account of the experimental performance analysis of the SNMAC solution, showcasing its efficiency in real-world scenarios. Furthermore, the paper also explores the security aspects of the proposed SNMAC algorithm, offering valuable insights into its robustness and applicability for ensuring secure communication within IoT environments.Comment: 19 pages, 7 figure