Showing papers by "Eran Tromer published in 2015"

Secure Sampling of Public Parameters for Succinct Zero Knowledge Proofs

Abstract: Non-interactive zero-knowledge proofs (NIZKs) are a powerful cryptographic tool, with numerous potential applications. However, succinct NIZKs (e.g., zk-SNARK schemes) necessitate a trusted party to generate and publish some public parameters, to be used by all provers and verifiers. This party is trusted to correctly run a probabilistic algorithm (specified by the the proof system) that outputs the public parameters, and publish them, without leaking any other information (such as the internal randomness used by the algorithm), violating either requirement may allow malicious parties to produce convincing "proofs" of false statements. This trust requirement poses a serious impediment to deploying NIZKs in many applications, because a party that is trusted by all users of the envisioned system may simply not exist. In this work, we show how public parameters for a class of NIZKs can be generated by a multi-party protocol, such that if at least one of the parties is honest, then the result is secure (in both aforementioned senses) and can be subsequently used for generating and verifying numerous proofs without any further trust. We design and implement such a protocol, tailored to efficiently support the state-of-the-art NIZK constructions with short and easy-to-verify proofs (Parno et al. IEEE SaP '13, Ben-Sasson et al. USENIX Sec '14, Danezis et al., ASIACRYPT '14). Applications of our system include generating public parameters for systems such as Zero cash (Ben-Sasson et al. IEEE SaP '13) and the scalable zero-knowledge proof system of (Ben-Sasson et al. CRYPTO '14).

Stealing Keys from PCs Using a Radio: Cheap Electromagnetic Attacks on Windowed Exponentiation

Abstract: We present new side-channel attacks on RSA and ElGamal implementations that use sliding-window or fixed-window (m-ary) modular exponentiation. The attacks extract decryption keys using a very low measurement bandwidth (a frequency band of less than 100 kHz around a carrier under 2 MHz) even when attacking multi-GHz CPUs.

Stealing Keys from PCs using a Radio: Cheap Electromagnetic Attacks on Windowed Exponentiation (extended version)

Abstract: We present new side-channel attacks on RSA and ElGamal implementations that use the popular sliding-window or xed-window ( m-ary) modular exponentiation algorithms. The attacks can extract decryption keys using a very low measurement bandwidth (a frequency band of less than 100 kHz around carrier under 2 MHz) even when attacking multi-GHz CPUs. We demonstrate the attacks’ feasibility by extracting keys from GnuPG, in a few seconds, using a nonintrusive measurement of electromagnetic emanations from laptop computers. The measurement equipment is cheap and compact, uses readily-available components (a Software Dened Radio USB dongle or a consumer-grade radio receiver), and can operate untethered while concealed, e.g., inside pita bread. The attacks use a few non-adaptive chosen ciphertexts, crafted so that whenever the decryption routine encounters particular bit patterns in the secret key, intermediate values occur with a special structure that causes observable uctuations in the electromagnetic eld. Through suitable signal processing and cryptanalysis, the bit patterns and eventually the whole secret key are recovered.

Get your hands off my laptop: physical side-channel key-extraction attacks on PCs

Abstract: We demonstrate physical side-channel attacks on a popular software implementation of RSA and ElGamal, running on laptop computers. Our attacks use novel side channels, based on the observation that the “ground” electric potential, in many computers, fluctuates in a computation-dependent way. An attacker can measure this signal by touching exposed metal on the computer’s chassis with a plain wire, or even with a bare hand. The signal can also be measured on the ground shield at the remote end of Ethernet, USB and display cables. Through suitable cryptanalysis and signal processing, we have extracted 4096-bit RSA keys and 3072-bit ElGamal keys from laptops, via each of these channels, as well as via power analysis and electromagnetic probing. Despite the GHz-scale clock rate of the laptops and numerous noise sources, the full attacks require a few seconds of measurements using Medium Frequency (MF) signals (around 2 MHz), or one hour using Low Frequency (LF) signals (up to 40 kHz).

Cluster Computing in Zero Knowledge.

Abstract: Large computations, when amenable to distributed parallel execution, are often executed on computer clusters, for scalability and cost reasons. Such computations are used in many applications, including, to name but a few, machine learning, webgraph mining, and statistical machine translation. Oftentimes, though, the input data is private and only the result of the computation can be published. Zero-knowledge proofs would allow, in such settings, to verify correctness of the output without leaking (additional) information about the input.

Cluster Computing in Zero Knowledge

Abstract: Large computations, when amenable to distributed parallel execution, are often executed on computer clusters, for scalability and cost reasons. Such computations are used in many applications, including, to name but a few, machine learning, webgraph mining, and statistical machine translation. Oftentimes, though, the input data is private and only the result of the computation can be published. Zero-knowledge proofs would allow, in such settings, to verify correctness of the output without leaking (additional) information about the input.

Path-quality monitoring in the presence of adversaries: the secure sketch protocols

Abstract: Edge networks connected to the Internet need effective monitoring techniques to inform routing decisions and detect violations of Service Level Agreements (SLAs). However, existing measurement tools, like ping, traceroute, and trajectory sampling, are vulnerable to attacks that can make a path look better than it really is. Here, we design and analyze a lightweight path-quality monitoring protocol that reliably raises an alarm when the packet-loss rate exceed a threshold, even when an adversary tries to bias monitoring results by selectively delaying, dropping, modifying, injecting, or preferentially treating packets. Our protocol is based on sublinear algorithms for sketching the second moment of stream of items and can monitor billions of packets using only 250--600 B of storage and the periodic transmission of a comparably sized IP packet. We also show how this protocol can be used to construct a more sophisticated protocol that allows the sender to localize the link responsible for the dropped packets. We prove that our protocols satisfy a precise definition of security, analyze their performance using numerical experiments, and derive analytic expressions for the tradeoff between statistical accuracy and system overhead. This paper contains a deeper treatment of results from earlier conference papers and several new results.

Circuits Resilient to Additive Attacks with Applications to Secure Computation.

Abstract: We study the question of protecting arithmetic circuits against additive attacks, which can add an arbitrary fixed value to each wire in the circuit. This extends the notion of algebraic manipulation detection (AMD) codes, which protect information against additive attacks, to that of AMD circuits which protect computation. We present a construction of such AMD circuits: any arithmetic circuit C over a finite field F can be converted into a functionally-equivalent randomized arithmetic circuit Ĉ of size O(|C|) that is fault-tolerant in the following sense. For any additive attack on the wires of Ĉ, its effect on the output of Ĉ can be simulated, up to O(|C|/|F|) statistical distance, by an additive attack on just the input and output. Given a small tamper-proof encoder/decoder for AMD codes, the input and output can be protected as well. We also give an alternative construction, applicable to small fields (for example, to protect Boolean circuits against wire-toggling attacks). It uses a small tamper-proof decoder to ensure that, except with negligible failure probability, either the output is correct or tampering is detected. Our study of AMD circuits is motivated by simplifying and improving protocols for secure multiparty computation (MPC). Typically, securing MPC protocols against active adversaries is much more difficult than securing them against passive adversaries. We observe that in simple MPC protocols that were designed to protect circuit evaluation only against passive adversaries, the effect of any active adversary corresponds precisely to an additive attack on the original circuit’s wires. Thus, to securely evaluate a circuit C in the presence of active adversaries, it suffices to apply the passivesecure protocol to Ĉ. We use this methodology to simplify feasibility results and attain efficiency improvements in several standard MPC models.

Secure Association for the Internet of Things

Abstract: Existing standards (ZigBee and Bluetooth Low Energy) for networked low-power wireless devices do not support secure association (or pairing) of new devices into a network: their association process is vulnerable to man-in-the-middle attacks. This paper addresses three essential aspects in attaining secure association for such devices.First, we define a user-interface primitive, oblivious comparison, that allows users to approve authentic associations and abort compromised ones. This distills and generalizes several existing approve/abort mechanisms, and moreover we experimentally show that OC can be implemented using very little hardware: one LED and one switch.Second, we provide a new Message Recognition Protocol (MRP) that allows devices associated using oblivious comparison to exchange authenticated messages without the use of publickey cryptography (which exceeds the capabilities of many IoT devices). This protocol improves upon previously proposed MRPs in several respects.Third, we propose a robust definition of security for MRPs that is based on universal composability, and show that our MRP protocol satisfies this definition.

Stealing Keys from PCs using a Radio: Cheap Electromagnetic Attacks on Windowed Exponentiation.

Abstract: We present new side-channel attacks on RSA and ElGamal implementations that use sliding-window or fixed-window (m-ary) modular exponentiation. The attacks extract decryption keys using a very low measurement bandwidth (a frequency band of less than 100 kHz around a carrier under 2 MHz) even when attacking multi-GHz CPUs.

Secure Association for the Internet of Things.

Abstract: Existing standards (ZigBee and Bluetooth Low Energy) for networked low-power wireless devices do not support secure association (or pairing) of new devices into a network: their association process is vulnerable to man-in-the-middle attacks. This paper addresses three essential aspects in attaining secure association for such devices. First, we de ne a user-interface primitive, oblivious comparison, that allows users to approve authentic associations and abort compromised ones. This distills and generalizes several existing approve/abort mechanisms, and moreover we experimentally show that OC can be implemented using very little hardware: one LED and one switch. Second, we provide a new Message Recognition Protocol (MRP) that allows devices associated using oblivious comparison to exchange authenticated messages without the use of public-key cryptography (which exceeds the capabilities of many IoT devices). This protocol improves upon previously proposed MRPs in several respects. Third, we propose a robust de nition of security for MRPs that is based on universal composability, and show that our MRP satis es this de nition.

Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture

Abstract: We build a system that provides succinct non-interactive zero-knowledge proofs (zk-SNARKs) for program executions on a von Neumann RISC architecture. The system has two components: a cryptographic proof system for verifying satisfiability of arithmetic circuits, and a circuit generator to translate program executions to such circuits. Our design of both components improves in functionality and efficiency over prior work, as follows. Our circuit generator is the first to be universal: it does not need to know the program, but only a bound on its running time. Moreover, the size of the output circuit depends additively (rather than multiplicatively) on program size, allowing verification of larger programs. The cryptographic proof system improves proving and verification times, by leveraging new algorithms and a pairing library tailored to the protocol. We evaluated our system for programs with up to 10,000 instructions, running for up to 32,000 machine steps, each of which can arbitrarily access random-access memory; and also demonstrated it executing programs that use just-in-time compilation. Our proofs are 230 bytes long at 80 bits of security, or 288 bytes long at 128 bits of security. Typical verification time is 5 milliseconds, regardless of the original program’s running time.