Tianji: Securing a Practical Asynchronous Multi-User ORAM

Oblivious Random Access Machines (ORAMs) allow cloud users to access remote data without leaking access patterns. Current ORAM solutions achieve this goal at expense of either increasing bandwidth consumption by a factor of <inline-formula><tex-math notation="LaTeX">$O(\log N)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mo form="prefix">log</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq1-3241184.gif"/></alternatives></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$N$</tex-math><alternatives><mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq2-3241184.gif"/></alternatives></inline-formula> is the number of data blocks, or relying on homomorphic encryption for bandwidth amplification reduction to <inline-formula><tex-math notation="LaTeX">$O(1)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq3-3241184.gif"/></alternatives></inline-formula>. Furthermore, most ORAMs are only effective for a single user, while the solutions for multi-user scenarios often induce security or performance problems. This article introduces <italic>Tianji</italic> — an asynchronous multi-user Shamir-based ORAM system — which supports asynchronous network access scenarios for multiple users with improved security and performance. <italic>Tianji</italic> is implemented on top of <italic>S<inline-formula><tex-math notation="LaTeX">$^{3}$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>3</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="wang-ieq4-3241184.gif"/></alternatives></inline-formula>ORAM<inline-formula><tex-math notation="LaTeX">$^+$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mo>+</mml:mo></mml:msup></mml:math><inline-graphic xlink:href="wang-ieq5-3241184.gif"/></alternatives></inline-formula></italic>—an extension of the state-of-the-art Shamir-based S<inline-formula><tex-math notation="LaTeX">$^{3}$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>3</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="wang-ieq6-3241184.gif"/></alternatives></inline-formula>ORAM with a new non-eviction data write-back scheme to achieve <inline-formula><tex-math notation="LaTeX">$O(1)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq7-3241184.gif"/></alternatives></inline-formula> consumption in both bandwidth amplification and storage capacity. Our experimental results show that the proposed <italic>Tianji</italic> with <italic>S<inline-formula><tex-math notation="LaTeX">$^{3}$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>3</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="wang-ieq8-3241184.gif"/></alternatives></inline-formula>ORAM<inline-formula><tex-math notation="LaTeX">$^+$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mo>+</mml:mo></mml:msup></mml:math><inline-graphic xlink:href="wang-ieq9-3241184.gif"/></alternatives></inline-formula></italic> can significantly outperform the state-of-the-art multi-user <italic>TaoStore</italic> in terms of access latency and client scalability. Additionally, its average response time is relatively stable when client loads increase.