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Haocong Luo

Publications and source records attributed to Haocong Luo.

At least 37 records · Page 2Linked to original sources

PIM-Opt: Demystifying Distributed Optimization Algorithms on a Real-World Processing-In-Memory System

Modern Machine Learning (ML) training on large-scale datasets is a very time-consuming workload. It relies on the optimization algorithm Stochastic Gradient Descent (SGD) due to its effectiveness, simplicity, and generalization performance. Processor-centric architectures (e.g., CPUs, GPUs) commonly used for modern ML training workloads based on SGD are bottlenecked by data movement between the processor and memory units due to the poor data locality in accessing large datasets. As a result, processor-centric architectures suffer from low performance and high energy consumption while executing ML training workloads. Processing-In-Memory (PIM) is a promising solution to alleviate the data movement bottleneck by placing the computation mechanisms inside or near memory. Our goal is to understand the capabilities of popular distributed SGD algorithms on real-world PIM systems to accelerate data-intensive ML training workloads. To this end, we 1) implement several representative centralized parallel SGD algorithms on the real-world UPMEM PIM system, 2) rigorously evaluate these algorithms for ML training on large-scale datasets in terms of performance, accuracy, and scalability, 3) compare to conventional CPU and GPU baselines, and 4) discuss implications for future PIM hardware and highlight the need for a shift to an algorithm-hardware codesign. Our results demonstrate three major findings: 1) The UPMEM PIM system can be a viable alternative to state-of-the-art CPUs and GPUs for many memory-bound ML training workloads, especially when operations and datatypes are natively supported by PIM hardware, 2) it is important to carefully choose the optimization algorithms that best fit PIM, and 3) the UPMEM PIM system does not scale approximately linearly with the number of nodes for many data-intensive ML training workloads. We open source all our code to facilitate future research.

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RowPress Vulnerability in Modern DRAM Chips

Memory isolation is a critical property for system reliability, security, and safety. We demonstrate RowPress, a DRAM read disturbance phenomenon different from the well-known RowHammer. RowPress induces bitflips by keeping a DRAM row open for a long period of time instead of repeatedly opening and closing the row. We experimentally characterize RowPress bitflips, showing their widespread existence in commodity off-the-shelf DDR4 DRAM chips. We demonstrate RowPress bitflips in a real system that already has RowHammer protection, and propose effective mitigation techniques that protect DRAM against both RowHammer and RowPress.

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An Experimental Characterization of Combined RowHammer and RowPress Read Disturbance in Modern DRAM Chips

DRAM read disturbance can break memory isolation, a fundamental property to ensure system robustness (i.e., reliability, security, safety). RowHammer and RowPress are two different DRAM read disturbance phenomena. RowHammer induces bitflips in physically adjacent victim DRAM rows by repeatedly opening and closing an aggressor DRAM row, while RowPress induces bitflips by keeping an aggressor DRAM row open for a long period of time. In this study, we characterize a DRAM access pattern that combines RowHammer and RowPress in 84 real DDR4 DRAM chips from all three major DRAM manufacturers. Our key results show that 1) this combined RowHammer and RowPress pattern takes significantly smaller amount of time (up to 46.1% faster) to induce the first bitflip compared to the state-of-the-art RowPress pattern, and 2) at the minimum aggressor row activation count to induce at least one bitflip, the bits that flip are different across RowHammer, RowPress, and the combined patterns. Based on our results, we provide a key hypothesis that the read disturbance effect caused by RowPress from one of the two aggressor rows in a double-sided pattern is much more significant than the other.

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SpyHammer: Understanding and Exploiting RowHammer under Fine-Grained Temperature Variations

RowHammer is a DRAM vulnerability that can cause bit errors in a victim DRAM row solely by accessing its neighboring DRAM rows at a high-enough rate. Recent studies demonstrate that new DRAM devices are becoming increasingly vulnerable to RowHammer, and many works demonstrate system-level attacks for privilege escalation or information leakage. In this work, we perform the first rigorous fine-grained characterization and analysis of the correlation between RowHammer and temperature. We show that RowHammer is very sensitive to temperature variations, even if the variations are very small (e.g., $\pm 1$ °C). We leverage two key observations from our analysis to spy on DRAM temperature: 1) RowHammer-induced bit error rate consistently increases (or decreases) as the temperature increases, and 2) some DRAM cells that are vulnerable to RowHammer exhibit bit errors only at a particular temperature. Based on these observations, we propose a new RowHammer attack, called SpyHammer, that spies on the temperature of DRAM on critical systems such as industrial production lines, vehicles, and medical systems. SpyHammer is the first practical attack that can spy on DRAM temperature. Our evaluation in a controlled environment shows that SpyHammer can infer the temperature of the victim DRAM modules with an error of less than $\pm 2.5$ °C at the 90th percentile of all tested temperatures, for 12 real DRAM modules (120 DRAM chips) from four main manufacturers.

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Simultaneous Many-Row Activation in Off-the-Shelf DRAM Chips: Experimental Characterization and Analysis

We experimentally analyze the computational capability of commercial off-the-shelf (COTS) DRAM chips and the robustness of these capabilities under various timing delays between DRAM commands, data patterns, temperature, and voltage levels. We extensively characterize 120 COTS DDR4 chips from two major manufacturers. We highlight four key results of our study. First, COTS DRAM chips are capable of 1) simultaneously activating up to 32 rows (i.e., simultaneous many-row activation), 2) executing a majority of X (MAJX) operation where X>3 (i.e., MAJ5, MAJ7, and MAJ9 operations), and 3) copying a DRAM row (concurrently) to up to 31 other DRAM rows, which we call Multi-RowCopy. Second, storing multiple copies of MAJX's input operands on all simultaneously activated rows drastically increases the success rate (i.e., the percentage of DRAM cells that correctly perform the computation) of the MAJX operation. For example, MAJ3 with 32-row activation (i.e., replicating each MAJ3's input operands 10 times) has a 30.81% higher average success rate than MAJ3 with 4-row activation (i.e., no replication). Third, data pattern affects the success rate of MAJX and Multi-RowCopy operations by 11.52% and 0.07% on average. Fourth, simultaneous many-row activation, MAJX, and Multi-RowCopy operations are highly resilient to temperature and voltage changes, with small success rate variations of at most 2.13% among all tested operations. We believe these empirical results demonstrate the promising potential of using DRAM as a computation substrate. To aid future research and development, we open-source our infrastructure at https://github.com/CMU-SAFARI/SiMRA-DRAM.

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ABACuS: All-Bank Activation Counters for Scalable and Low Overhead RowHammer Mitigation

We introduce ABACuS, a new low-cost hardware-counter-based RowHammer mitigation technique that performance-, energy-, and area-efficiently scales with worsening RowHammer vulnerability. We observe that both benign workloads and RowHammer attacks tend to access DRAM rows with the same row address in multiple DRAM banks at around the same time. Based on this observation, ABACuS's key idea is to use a single shared row activation counter to track activations to the rows with the same row address in all DRAM banks. Unlike state-of-the-art RowHammer mitigation mechanisms that implement a separate row activation counter for each DRAM bank, ABACuS implements fewer counters (e.g., only one) to track an equal number of aggressor rows. Our evaluations show that ABACuS securely prevents RowHammer bitflips at low performance/energy overhead and low area cost. We compare ABACuS to four state-of-the-art mitigation mechanisms. At a near-future RowHammer threshold of 1000, ABACuS incurs only 0.58% (0.77%) performance and 1.66% (2.12%) DRAM energy overheads, averaged across 62 single-core (8-core) workloads, requiring only 9.47 KiB of storage per DRAM rank. At the RowHammer threshold of 1000, the best prior low-area-cost mitigation mechanism incurs 1.80% higher average performance overhead than ABACuS, while ABACuS requires 2.50X smaller chip area to implement. At a future RowHammer threshold of 125, ABACuS performs very similarly to (within 0.38% of the performance of) the best prior performance- and energy-efficient RowHammer mitigation mechanism while requiring 22.72X smaller chip area. ABACuS is freely and openly available at https://github.com/CMU-SAFARI/ABACuS.

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Read Disturbance in High Bandwidth Memory: A Detailed Experimental Study on HBM2 DRAM Chips

We experimentally demonstrate the effects of read disturbance (RowHammer and RowPress) and uncover the inner workings of undocumented read disturbance defense mechanisms in High Bandwidth Memory (HBM). Detailed characterization of six real HBM2 DRAM chips in two different FPGA boards shows that (1) the read disturbance vulnerability significantly varies between different HBM2 chips and between different components (e.g., 3D-stacked channels) inside a chip, (2) DRAM rows at the end and in the middle of a bank are more resilient to read disturbance, (3) fewer additional activations are sufficient to induce more read disturbance bitflips in a DRAM row if the row exhibits the first bitflip at a relatively high activation count, (4) a modern HBM2 chip implements undocumented read disturbance defenses that track potential aggressor rows based on how many times they are activated. We describe how our findings could be leveraged to develop more powerful read disturbance attacks and more efficient defense mechanisms. We open source all our code and data to facilitate future research at https://github.com/CMU-SAFARI/HBM-Read-Disturbance.

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Functionally-Complete Boolean Logic in Real DRAM Chips: Experimental Characterization and Analysis

Processing-using-DRAM (PuD) is an emerging paradigm that leverages the analog operational properties of DRAM circuitry to enable massively parallel in-DRAM computation. PuD has the potential to reduce or eliminate costly data movement between processing elements and main memory. Prior works experimentally demonstrate three-input MAJ (MAJ3) and two-input AND and OR operations in commercial off-the-shelf (COTS) DRAM chips. Yet, demonstrations on COTS DRAM chips do not provide a functionally complete set of operations. We experimentally demonstrate that COTS DRAM chips are capable of performing 1) functionally-complete Boolean operations: NOT, NAND, and NOR and 2) many-input (i.e., more than two-input) AND and OR operations. We present an extensive characterization of new bulk bitwise operations in 256 off-the-shelf modern DDR4 DRAM chips. We evaluate the reliability of these operations using a metric called success rate: the fraction of correctly performed bitwise operations. Among our 19 new observations, we highlight four major results. First, we can perform the NOT operation on COTS DRAM chips with a 98.37% success rate on average. Second, we can perform up to 16-input NAND, NOR, AND, and OR operations on COTS DRAM chips with high reliability (e.g., 16-input NAND, NOR, AND, and OR with an average success rate of 94.94%, 95.87%, 94.94%, and 95.85%, respectively). Third, data pattern only slightly affects bitwise operations. Our results show that executing NAND, NOR, AND, and OR operations with random data patterns decreases the success rate compared to all logic-1/logic-0 patterns by 1.39%, 1.97%, 1.43%, and 1.98%, respectively. Fourth, bitwise operations are highly resilient to temperature changes, with small success rate fluctuations of at most 1.66% when the temperature is increased from 50C to 95C. We open-source our infrastructure at https://github.com/CMU-SAFARI/FCDRAM

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RowPress: Amplifying Read Disturbance in Modern DRAM Chips

Memory isolation is critical for system reliability, security, and safety. Unfortunately, read disturbance can break memory isolation in modern DRAM chips. For example, RowHammer is a well-studied read-disturb phenomenon where repeatedly opening and closing (i.e., hammering) a DRAM row many times causes bitflips in physically nearby rows. This paper experimentally demonstrates and analyzes another widespread read-disturb phenomenon, RowPress, in real DDR4 DRAM chips. RowPress breaks memory isolation by keeping a DRAM row open for a long period of time, which disturbs physically nearby rows enough to cause bitflips. We show that RowPress amplifies DRAM's vulnerability to read-disturb attacks by significantly reducing the number of row activations needed to induce a bitflip by one to two orders of magnitude under realistic conditions. In extreme cases, RowPress induces bitflips in a DRAM row when an adjacent row is activated only once. Our detailed characterization of 164 real DDR4 DRAM chips shows that RowPress 1) affects chips from all three major DRAM manufacturers, 2) gets worse as DRAM technology scales down to smaller node sizes, and 3) affects a different set of DRAM cells from RowHammer and behaves differently from RowHammer as temperature and access pattern changes. We demonstrate in a real DDR4-based system with RowHammer protection that 1) a user-level program induces bitflips by leveraging RowPress while conventional RowHammer cannot do so, and 2) a memory controller that adaptively keeps the DRAM row open for a longer period of time based on access pattern can facilitate RowPress-based attacks. To prevent bitflips due to RowPress, we describe and evaluate a new methodology that adapts existing RowHammer mitigation techniques to also mitigate RowPress with low additional performance overhead. We open source all our code and data to facilitate future research on RowPress.

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PULSAR: Simultaneous Many-Row Activation for Reliable and High-Performance Computing in Off-the-Shelf DRAM Chips

Data movement between the processor and the main memory is a first-order obstacle against improving performance and energy efficiency in modern systems. To address this obstacle, Processing-using-Memory (PuM) is a promising approach where bulk-bitwise operations are performed leveraging intrinsic analog properties within the DRAM array and massive parallelism across DRAM columns. Unfortunately, 1) modern off-the-shelf DRAM chips do not officially support PuM operations, and 2) existing techniques of performing PuM operations on off-the-shelf DRAM chips suffer from two key limitations. First, these techniques have low success rates, i.e., only a small fraction of DRAM columns can correctly execute PuM operations because they operate beyond manufacturer-recommended timing constraints, causing these operations to be highly susceptible to noise and process variation. Second, these techniques have limited compute primitives, preventing them from fully leveraging parallelism across DRAM columns and thus hindering their performance benefits. We propose PULSAR, a new technique to enable high-success-rate and high-performance PuM operations in off-the-shelf DRAM chips. PULSAR leverages our new observation that a carefully crafted sequence of DRAM commands simultaneously activates up to 32 DRAM rows. PULSAR overcomes the limitations of existing techniques by 1) replicating the input data to improve the success rate and 2) enabling new bulk bitwise operations (e.g., many-input majority, Multi-RowInit, and Bulk-Write) to improve the performance. Our analysis on 120 off-the-shelf DDR4 chips from two major manufacturers shows that PULSAR achieves a 24.18% higher success rate and 121% higher performance over seven arithmetic-logic operations compared to FracDRAM, a state-of-the-art off-the-shelf DRAM-based PuM technique.

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Spatial Variation-Aware Read Disturbance Defenses: Experimental Analysis of Real DRAM Chips and Implications on Future Solutions

Read disturbance in modern DRAM chips is a widespread phenomenon and is reliably used for breaking memory isolation, a fundamental building block for building robust systems. RowHammer and RowPress are two examples of read disturbance in DRAM where repeatedly accessing (hammering) or keeping active (pressing) a memory location induces bitflips in other memory locations. Unfortunately, shrinking technology node size exacerbates read disturbance in DRAM chips over generations. As a result, existing defense mechanisms suffer from significant performance and energy overheads, limited effectiveness, or prohibitively high hardware complexity. In this paper, we tackle these shortcomings by leveraging the spatial variation in read disturbance across different memory locations in real DRAM chips. To do so, we 1) present the first rigorous real DRAM chip characterization study of spatial variation of read disturbance and 2) propose Svärd, a new mechanism that dynamically adapts the aggressiveness of existing solutions based on the row-level read disturbance profile. Our experimental characterization on 144 real DDR4 DRAM chips representing 10 chip designs demonstrates a large variation in read disturbance vulnerability across different memory locations: in the part of memory with the worst read disturbance vulnerability, 1) up to 2x the number of bitflips can occur and 2) bitflips can occur at an order of magnitude fewer accesses, compared to the memory locations with the least vulnerability to read disturbance. Svärd leverages this variation to reduce the overheads of five state-of-the-art read disturbance solutions, and thus significantly increases system performance.

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Rethinking the Producer-Consumer Relationship in Modern DRAM-Based Systems

Generational improvements to commodity DRAM throughout half a century have long solidified its prevalence as main memory across the computing industry. However, overcoming today's DRAM technology scaling challenges requires new solutions driven by both DRAM producers and consumers. In this paper, we observe that the separation of concerns between producers and consumers specified by industry-wide DRAM standards is becoming a liability to progress in addressing scaling-related concerns. To understand the problem, we study four key directions for overcoming DRAM scaling challenges using system-memory cooperation: (i) improving memory access latencies; (ii) reducing DRAM refresh overheads; (iii) securely defending against the RowHammer vulnerability; and (iv) addressing worsening memory errors. We find that the single most important barrier to advancement in all four cases is the consumer's lack of insight into DRAM reliability. Based on an analysis of DRAM reliability testing, we recommend revising the separation of concerns to incorporate limited information transparency between producers and consumers. Finally, we propose adopting this revision in a two-step plan, starting with immediate information release through crowdsourcing and publication and culminating in widespread modifications to DRAM standards.

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Ramulator 2.0: A Modern, Modular, and Extensible DRAM Simulator

We present Ramulator 2.0, a highly modular and extensible DRAM simulator that enables rapid and agile implementation and evaluation of design changes in the memory controller and DRAM to meet the increasing research effort in improving the performance, security, and reliability of memory systems. Ramulator 2.0 abstracts and models key components in a DRAM-based memory system and their interactions into shared interfaces and independent implementations. Doing so enables easy modification and extension of the modeled functions of the memory controller and DRAM in Ramulator 2.0. The DRAM specification syntax of Ramulator 2.0 is concise and human-readable, facilitating easy modifications and extensions. Ramulator 2.0 implements a library of reusable templated lambda functions to model the functionalities of DRAM commands to simplify the implementation of new DRAM standards, including DDR5, LPDDR5, HBM3, and GDDR6. We showcase Ramulator 2.0's modularity and extensibility by implementing and evaluating a wide variety of RowHammer mitigation techniques that require different memory controller design changes. These techniques are added modularly as separate implementations without changing any code in the baseline memory controller implementation. Ramulator 2.0 is rigorously validated and maintains a fast simulation speed compared to existing cycle-accurate DRAM simulators. Ramulator 2.0 is open-sourced under the permissive MIT license at https://github.com/CMU-SAFARI/ramulator2

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An Experimental Analysis of RowHammer in HBM2 DRAM Chips

RowHammer (RH) is a significant and worsening security, safety, and reliability issue of modern DRAM chips that can be exploited to break memory isolation. Therefore, it is important to understand real DRAM chips' RH characteristics. Unfortunately, no prior work extensively studies the RH vulnerability of modern 3D-stacked high-bandwidth memory (HBM) chips, which are commonly used in modern GPUs. In this work, we experimentally characterize the RH vulnerability of a real HBM2 DRAM chip. We show that 1) different 3D-stacked channels of HBM2 memory exhibit significantly different levels of RH vulnerability (up to 79% difference in bit error rate), 2) the DRAM rows at the end of a DRAM bank (rows with the highest addresses) exhibit significantly fewer RH bitflips than other rows, and 3) a modern HBM2 DRAM chip implements undisclosed RH defenses that are triggered by periodic refresh operations. We describe the implications of our observations on future RH attacks and defenses and discuss future work for understanding RH in 3D-stacked memories.

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HiRA: Hidden Row Activation for Reducing Refresh Latency of Off-the-Shelf DRAM Chips

DRAM is the building block of modern main memory systems. DRAM cells must be periodically refreshed to prevent data loss. Refresh operations degrade system performance by interfering with memory accesses. As DRAM chip density increases with technology node scaling, refresh operations also increase because: 1) the number of DRAM rows in a chip increases; and 2) DRAM cells need additional refresh operations to mitigate bit failures caused by RowHammer, a failure mechanism that becomes worse with technology node scaling. Thus, it is critical to enable refresh operations at low performance overhead. To this end, we propose a new operation, Hidden Row Activation (HiRA), and the HiRA Memory Controller (HiRA-MC). HiRA hides a refresh operation's latency by refreshing a row concurrently with accessing or refreshing another row within the same bank. Unlike prior works, HiRA achieves this parallelism without any modifications to off-the-shelf DRAM chips. To do so, it leverages the new observation that two rows in the same bank can be activated without data loss if the rows are connected to different charge restoration circuitry. We experimentally demonstrate on 56% real off-the-shelf DRAM chips that HiRA can reliably parallelize a DRAM row's refresh operation with refresh or activation of any of the 32% of the rows within the same bank. By doing so, HiRA reduces the overall latency of two refresh operations by 51.4%. HiRA-MC modifies the memory request scheduler to perform HiRA when a refresh operation can be performed concurrently with a memory access or another refresh. Our system-level evaluations show that HiRA-MC increases system performance by 12.6% and 3.73x as it reduces the performance degradation due to periodic refreshes and refreshes for RowHammer protection (preventive refreshes), respectively, for future DRAM chips with increased density and RowHammer vulnerability.

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Understanding RowHammer Under Reduced Wordline Voltage: An Experimental Study Using Real DRAM Devices

RowHammer is a circuit-level DRAM vulnerability, where repeatedly activating and precharging a DRAM row, and thus alternating the voltage of a row's wordline between low and high voltage levels, can cause bit flips in physically nearby rows. Recent DRAM chips are more vulnerable to RowHammer: with technology node scaling, the minimum number of activate-precharge cycles to induce a RowHammer bit flip reduces and the RowHammer bit error rate increases. Therefore, it is critical to develop effective and scalable approaches to protect modern DRAM systems against RowHammer. To enable such solutions, it is essential to develop a deeper understanding of the RowHammer vulnerability of modern DRAM chips. However, even though the voltage toggling on a wordline is a key determinant of RowHammer vulnerability, no prior work experimentally demonstrates the effect of wordline voltage (VPP) on the RowHammer vulnerability. Our work closes this gap in understanding. This is the first work to experimentally demonstrate on 272 real DRAM chips that lowering VPP reduces a DRAM chip's RowHammer vulnerability. We show that lowering VPP 1) increases the number of activate-precharge cycles needed to induce a RowHammer bit flip by up to 85.8% with an average of 7.4% across all tested chips and 2) decreases the RowHammer bit error rate by up to 66.9% with an average of 15.2% across all tested chips. At the same time, reducing VPP marginally worsens a DRAM cell's access latency, charge restoration, and data retention time within the guardbands of system-level nominal timing parameters for 208 out of 272 tested chips. We conclude that reducing VPP is a promising strategy for reducing a DRAM chip's RowHammer vulnerability without requiring modifications to DRAM chips.

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A Case for Transparent Reliability in DRAM Systems

Today's systems have diverse needs that are difficult to address using one-size-fits-all commodity DRAM. Unfortunately, although system designers can theoretically adapt commodity DRAM chips to meet their particular design goals (e.g., by reducing access timings to improve performance, implementing system-level RowHammer mitigations), we observe that designers today lack sufficient insight into commodity DRAM chips' reliability characteristics to implement these techniques in practice. In this work, we make a case for DRAM manufacturers to provide increased transparency into key aspects of DRAM reliability (e.g., basic chip design properties, testing strategies). Doing so enables system designers to make informed decisions to better adapt commodity DRAM to meet modern systems' needs while preserving its cost advantages. To support our argument, we study four ways that system designers can adapt commodity DRAM chips to system-specific design goals: (1) improving DRAM reliability; (2) reducing DRAM refresh overheads; (3) reducing DRAM access latency; and (4) mitigating RowHammer attacks. We observe that adopting solutions for any of the four goals requires system designers to make assumptions about a DRAM chip's reliability characteristics. These assumptions discourage system designers from using such solutions in practice due to the difficulty of both making and relying upon the assumption. We identify DRAM standards as the root of the problem: current standards rigidly enforce a fixed operating point with no specifications for how a system designer might explore alternative operating points. To overcome this problem, we introduce a two-step approach that reevaluates DRAM standards with a focus on transparency of DRAM reliability so that system designers are encouraged to make the most of commodity DRAM technology for both current and future DRAM chips.

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A Deeper Look into RowHammer`s Sensitivities: Experimental Analysis of Real DRAM Chips and Implications on Future Attacks and Defenses

RowHammer is a circuit-level DRAM vulnerability where repeatedly accessing (i.e., hammering) a DRAM row can cause bit flips in physically nearby rows. The RowHammer vulnerability worsens as DRAM cell size and cell-to-cell spacing shrink. Recent studies demonstrate that modern DRAM chips, including chips previously marketed as RowHammer-safe, are even more vulnerable to RowHammer than older chips such that the required hammer count to cause a bit flip has reduced by more than 10X in the last decade. Therefore, it is essential to develop a better understanding and in-depth insights into the RowHammer vulnerability of modern DRAM chips to more effectively secure current and future systems. Our goal in this paper is to provide insights into fundamental properties of the RowHammer vulnerability that are not yet rigorously studied by prior works, but can potentially be $i$) exploited to develop more effective RowHammer attacks or $ii$) leveraged to design more effective and efficient defense mechanisms. To this end, we present an experimental characterization using 248~DDR4 and 24~DDR3 modern DRAM chips from four major DRAM manufacturers demonstrating how the RowHammer effects vary with three fundamental properties: 1)~DRAM chip temperature, 2)~aggressor row active time, and 3)~victim DRAM cell's physical location. Among our 16 new observations, we highlight that a RowHammer bit flip 1)~is very likely to occur in a bounded range, specific to each DRAM cell (e.g., 5.4% of the vulnerable DRAM cells exhibit errors in the range 70C to 90C), 2)~is more likely to occur if the aggressor row is active for longer time (e.g., RowHammer vulnerability increases by 36% if we keep a DRAM row active for 15 column accesses), and 3)~is more likely to occur in certain physical regions of the DRAM module under attack (e.g., 5% of the rows are 2x more vulnerable than the remaining 95% of the rows).

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