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In recent work, Backendal, Haller, and Paterson identified several exploitable vulnerabilities in the cloud storage provider MEGA. They demonstrated an RSA key recovery attack in which a malicious server could recover a client’s private RSA key after 512 client login attempts. We show how to exploit additional information revealed by MEGA’s protocol vulnerabilities to give an attack that requires only six client logins to recover the secret key. Our optimized attack combines several cryptanalytic techniques. In particular, we formulate and give a solution to a variant of the hidden number problem with small unknown multipliers, which may be of independent interest. We show that our lattice construction for this problem can be used to give improved results for the implicit factorization problem of May and Ritzenhofen. 

Lattice-based algorithms in cryptanalysis often search for a target vector satisfying integer linear constraints as a shortest or closest vector in some lattice. In this work, we observe that these formulations may discard non-linear information from the underlying application that can be used to distinguish the target vector even when it is far from being uniquely close or short. We formalize lattice problems augmented with a predicate distinguishing a target vector and give algorithms for solving instances of these problems. We apply our techniques to lattice-based approaches for solving the Hidden Number Problem, a popular technique for recovering secret DSA or ECDSA keys in side-channel attacks, and demonstrate that our algorithms succeed in recovering the signing key for instances that were previously believed to be unsolvable using lattice approaches. We carried out extensive experiments using our estimation and solving framework, which we also make available with this work. 

The adversarial model presented by trusted execution environments (TEEs) has prompted researchers to investigate unusual attack vectors. One particularly powerful class of controlled-channel attacks abuses page-table modifications to reliably track enclave memory accesses at a page-level granularity. In contrast to noisy microarchitectural timing leakage, this line of deterministic controlled-channel attacks abuses indispensable architectural interfaces and hence cannot be mitigated by tweaking microarchitectural resources. We propose an innovative controlled-channel attack, named CopyCat, that deterministically counts the number of instructions executed within a single enclave code page. We show that combining the instruction counts harvested by CopyCat with traditional, coarse-grained page-level leakage allows the accurate reconstruction of enclave control flow at a maximal instruction-level granularity. CopyCat can identify intra-page and intra-cache line branch decisions that ultimately may only differ in a single instruction, underscoring that even extremely subtle control flow deviations can be deterministically leaked from secure enclaves. We demonstrate the improved resolution and practicality of CopyCat on Intel SGX in an extensive study of single-trace and deterministic attacks against cryptographic implementations, and give novel algorithmic attacks to perform single-trace key extraction that exploit subtle vulnerabilities in the latest versions of widely-used cryptographic libraries. Our findings highlight the importance of stricter verification of cryptographic implementations, especially in the context of TEEs.