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1. Computationally Data-Independent Memory Hard Functions

   https://doi.org/10.4230/LIPIcs.ITCS.2020.36  

   Ameri, M ; Blocki, J ; Zhou, S. ( January 2020 , Leibniz international proceedings in informatics)

   null (Ed.)

   Memory hard functions (MHFs) are an important cryptographic primitive that are used to design egalitarian proofs of work and in the construction of moderately expensive key-derivation functions resistant to brute-force attacks. Broadly speaking, MHFs can be divided into two categories: data-dependent memory hard functions (dMHFs) and data-independent memory hard functions (iMHFs). iMHFs are resistant to certain side-channel attacks as the memory access pattern induced by the honest evaluation algorithm is independent of the potentially sensitive input e.g., password. While dMHFs are potentially vulnerable to side-channel attacks (the induced memory access pattern might leak useful information to a brute-force attacker), they can achieve higher cumulative memory complexity (CMC) in comparison than an iMHF. In particular, any iMHF that can be evaluated in N steps on a sequential machine has CMC at most 𝒪((N^2 log log N)/log N). By contrast, the dMHF scrypt achieves maximal CMC Ω(N^2) - though the CMC of scrypt would be reduced to just 𝒪(N) after a side-channel attack. In this paper, we introduce the notion of computationally data-independent memory hard functions (ciMHFs). Intuitively, we require that memory access pattern induced by the (randomized) ciMHF evaluation algorithm appears to be independent from the standpoint of a computationally bounded eavesdropping attacker - even if the attacker selects the initial input. We then ask whether it is possible to circumvent known upper bound for iMHFs and build a ciMHF with CMC Ω(N^2). Surprisingly, we answer the question in the affirmative when the ciMHF evaluation algorithm is executed on a two-tiered memory architecture (RAM/Cache). We introduce the notion of a k-restricted dynamic graph to quantify the continuum between unrestricted dMHFs (k=n) and iMHFs (k=1). For any ε > 0 we show how to construct a k-restricted dynamic graph with k=Ω(N^(1-ε)) that provably achieves maximum cumulative pebbling cost Ω(N^2). We can use k-restricted dynamic graphs to build a ciMHF provided that cache is large enough to hold k hash outputs and the dynamic graph satisfies a certain property that we call "amenable to shuffling". In particular, we prove that the induced memory access pattern is indistinguishable to a polynomial time attacker who can monitor the locations of read/write requests to RAM, but not cache. We also show that when k=o(N^(1/log log N)) , then any k-restricted graph with constant indegree has cumulative pebbling cost o(N^2). Our results almost completely characterize the spectrum of k-restricted dynamic graphs. 

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2. TPM-FAIL: TPM meets Timing and Lattice Attacks

   Moghimi, Daniel ; Sunar, Berk ; Eisenbarth, Thomas ; Heninger, Nadia ( January 2020 , Proceedings of the 29th USENIX Security Symposium)

   null (Ed.)

   Trusted Platform Module (TPM) serves as a hardware based root of trust that protects cryptographic keys from privileged system and physical adversaries. In this work, we perform a black-box timing analysis of TPM 2.0 devices deployed on commodity computers. Our analysis reveals that some of these devices feature secret-dependent execution times during signature generation based on elliptic curves. In particular, we discovered timing leakage on an Intel firmware based TPM as well as a hardware TPM. We show how this information allows an attacker to apply lattice techniques to recover 256-bit private keys for ECDSA and ECSchnorr signatures. On Intel fTPM, our key recovery succeeds after about 1,300 observations and in less than two minutes. Similarly, we extract the private ECDSA key from a hardware TPM manufactured by STMicroelectronics, which is certified at Common Criteria (CC) EAL 4+, after fewer than 40,000 observations. We further highlight the impact of these vulnerabilities by demonstrating a remote attack against a StrongSwan IPsec VPN that uses a TPM to generate the digital signatures for authentication. In this attack, the remote client recovers the server’s private authentication key by timing only 45,000 authentication handshakes via a network connection. The vulnerabilities we have uncovered emphasize the difficulty of correctly implementing known constant-time techniques, and show the importance of evolutionary testing and transparent evaluation of cryptographic implementations. Even certified devices that claim resistance against attacks require additional scrutiny by the community and industry, as we learn more about these attacks. 

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3. TPM-Fail:TPM meets Timing and Lattice Attacks

   Moghimi, Daniel ; Sunar, Berk ; Eisenbarth, Thomas ; Heninger, Nadia ( January 2020 , 29th USENIX Security Symposium (USENIX Security 20))

   null (Ed.)

   Trusted Platform Module (TPM) serves as a hardwarebased root of trust that protects cryptographic keys from privileged system and physical adversaries. In this work, we perform a black-box timing analysis of TPM 2.0 devices deployed on commodity computers. Our analysis reveals that some of these devices feature secret-dependent execution times during signature generation based on elliptic curves. In particular, we discovered timing leakage on an Intel firmwarebased TPM as well as a hardware TPM. We show how this information allows an attacker to apply lattice techniques to recover 256-bit private keys for ECDSA and ECSchnorr signatures. On Intel fTPM, our key recovery succeeds after about 1,300 observations and in less than two minutes. Similarly, we extract the private ECDSA key from a hardware TPM manufactured by STMicroelectronics, which is certified at Common Criteria (CC) EAL 4+, after fewer than 40,000 observations. We further highlight the impact of these vulnerabilities by demonstrating a remote attack against a StrongSwan IPsec VPN that uses a TPM to generate the digital signatures for authentication. In this attack, the remote client recovers the server’s private authentication key by timing only 45,000 authentication handshakes via a network connection. The vulnerabilities we have uncovered emphasize the difficulty of correctly implementing known constant-time techniques, and show the importance of evolutionary testing and transparent evaluation of cryptographic implementations. Even certified devices that claim resistance against attacks require additional scrutiny by the community and industry, as we learn more about these attacks. 

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4. A Hybrid Approach to Secure Function Evaluation using SGX

   https://doi.org/10.1145/3321705.3329835  

   Choi, Joseph I. ; Tian, Dave ; Hernandez, Grant ; Patton, Christopher ; Mood, Benjamin ; Shrimpton, Thomas ; Butler, Kevin R. ; Traynor, Patrick ( July 2019 , ACM Asia Conference on Computer and Communications Security)

   A protocol for two-party secure function evaluation (2P-SFE) aims to allow the parties to learn the output of function f of their private inputs, while leaking nothing more. In a sense, such a protocol realizes a trusted oracle that computes f and returns the result to both parties. There have been tremendous strides in efficiency over the past ten years, yet 2P-SFE protocols remain impractical for most real-time, online computations, particularly on modestly provisioned devices. Intel's Software Guard Extensions (SGX) provides hardware-protected execution environments, called enclaves, that may be viewed as trusted computation oracles. While SGX provides native CPU speed for secure computation, previous side-channel and micro-architecture attacks have demonstrated how security guarantees of enclaves can be compromised. In this paper, we explore a balanced approach to 2P-SFE on SGX-enabled processors by constructing a protocol for evaluating f relative to a partitioning of f. This approach alleviates the burden of trust on the enclave by allowing the protocol designer to choose which components should be evaluated within the enclave, and which via standard cryptographic techniques. We describe SGX-enabled SFE protocols (modeling the enclave as an oracle), and formalize the strongest-possible notion of 2P-SFE for our setting. We prove our protocol meets this notion when properly realized. We implement the protocol and apply it to two practical problems: privacy-preserving queries to a database, and a version of Dijkstra's algorithm for privacy-preserving navigation. Our evaluation shows that our SGX-enabled SFE scheme enjoys a 38x increase in performance over garbled-circuit-based SFE. Finally, we justify modeling of the enclave as an oracle by implementing protections against known side-channels. 

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5. On the Security of Homomorphic Encryption on Approximate Numbers

   https://doi.org/10.1007/978-3-030-77870-5_23  

   Li, B. ; Micciancio, D. ( October 2021 , Advances in Cryptology – EUROCRYPT 2021)

   Canteaut, A. ; Standaert, F. (Ed.)

   We present passive attacks against CKKS, the homomorphic encryption scheme for arithmetic on approximate numbers presented at Asiacrypt 2017. The attack is both theoretically efficient (running in expected polynomial time) and very practical, leading to complete key recovery with high probability and very modest running times. We implemented and tested the attack against major open source homomorphic encryption libraries, including HEAAN, SEAL, HElib and PALISADE, and when computing several functions that often arise in applications of the CKKS scheme to machine learning on encrypted data, like mean and variance computations, and approximation of logistic and exponential functions using their Maclaurin series. The attack shows that the traditional formulation of IND-CPA security (or indistinguishability against chosen plaintext attacks) achieved by CKKS does not adequately capture security against passive adversaries when applied to approximate encryption schemes, and that a different, stronger definition is required to evaluate the security of such schemes. We provide a solid theoretical basis for the security evaluation of homomorphic encryption on approximate numbers (against passive attacks) by proposing new definitions, that naturally extend the traditional notion of IND-CPA security to the approximate computation setting. We propose both indistinguishability-based and simulation-based variants, as well as restricted versions of the definitions that limit the order and number of adversarial queries (as may be enforced by some applications). We prove implications and separations among different definitional variants, and discuss possible modifications to CKKS that may serve as a countermeasure to our attacks. 

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