Electric Power Resource Shuffling and Subnational Carbon Regulation: Looking Upstream for a Solution

The potential for shuffling in wholesale power markets thwarts California’s ability to meet its AB 32 GHG emission reduction goals, and may even lead to emissions increases. Yet, as California’s efforts illustrate, resource shuffling is extremely difficult to regulate at the state level. Short of California aggressively reducing its emissions limits to reflect the leakage problem of shuffling, the state is incapable of solving the problem on its own. As states follow California’s lead in crafting their own approaches to regulating GHG emissions, national solutions will be necessary to address the problem of resource shuffling, given interstate markets in wholesale electric power. Undoubtedly EPA can play a role, but its flexible approach to state carbon regulation suggests it is likely to leave the management of shuffling largely to states. Moreover, without some ability to preempt states the EPA too is ill-equipped to address shuffling. This Article has argued that the superior solution to resource shuffling lies upstream, in the electric power markets managed by FERC. For subnational carbon emissions regulation to meet its goals, it must be recognized that shuffling is a problem created by pricing practices in upstream interstate power markets. The ultimate solution to this problem lies with the federal regulators who manage these markets, not with individual states

CacheShuffle: A Family of Oblivious Shuffles

We consider oblivious two-party protocols where a client outsources N blocks of private data to a server. The client wishes to access the data to perform operations in such a way that the access pattern does not leak information about the data and the operations. In this context, we consider oblivious shuffling with a focus on bandwidth efficient protocols for clients with small local memory. In the shuffling problem, the N outsourced blocks, B_1,...,B_N, are stored on the server according to an initial permutation pi. The client wishes to reshuffle the blocks according to permutation sigma. Oblivious shuffling is a building block in several applications that hide patterns of data access. In this paper, we introduce a generalization of the oblivious shuffling problem, the K-oblivious shuffling problem, and provide bandwidth efficient algorithms for a wide range of client storage requirements. The task of a K-oblivious shuffling algorithm is to shuffle N encrypted blocks that were previously randomly allocated on the server in such a way that an adversarial server learns nothing about either the new allocation of blocks or the block contents. The security guarantee must hold when an adversary has partial information on the initial placement of a subset of K <=N revealed blocks. The notion of oblivious shuffling is obtained for K=N. We first study the N-oblivious shuffling problem and start by presenting CacheShuffleRoot, that is tailored for clients with O(sqrt{N}) blocks of memory and uses approximately 4N blocks of bandwidth. CacheShuffleRoot is a 4x improvement over the previous best known N-oblivious shuffle for practical sizes of N. We then generalize CacheShuffleRoot to CacheShuffle that can be instantiated for any client memory size S and requires O(N log_S N) blocks of bandwidth. Next, we present K-oblivious shuffling algorithms that require 2N + f(K,S) blocks of bandwidth for all K and a wide range of S. Any extra bandwidth above the 2N lower bound depends solely on K and S. Specifically, for clients with O(K) blocks of memory, we present KCacheShuffleBasic that uses exactly 2N blocks of bandwidth. For clients with memory S <= K, we present KCacheShuffle, that requires 2N + O(K log_S K) blocks of bandwidth. Finally, motivated by applications to ORAMs, we consider the case where the server stores D dummy blocks whose contents are irrelevant in addition to the N real blocks. For this case, we design algorithm KCacheShuffleDummy that shuffles N+D blocks with K revealed blocks using O(K) blocks of client storage and approximately D+2N blocks of bandwidth

Progressive Randomization of a Deck of Playing Cards: Experimental Tests and Statistical Analysis of the Riffle Shuffle

The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal theoretical approaches to the problem, which differed in how each defined randomness, has led to statistically different threshold numbers of shuffles. This paper reports a comprehensive experimental analysis of the card randomization problem for the purposes of determining 1) which of the two theoretical approaches made the more accurate prediction, 2) whether different statistical tests yield different threshold numbers of randomizing shuffles, and 3) whether manual or mechanical shuffling randomizes a deck more effectively for a given number of shuffles. Permutations of 52-card decks, each subjected to sets of 19 successive riffle shuffles executed manually and by an auto-shuffling device were recorded sequentially and analyzed in respect to 1) the theory of runs, 2) rank ordering, 3) serial correlation, 4) theory of rising sequences, and 5) entropy and information theory. Among the outcomes, it was found that: 1) different statistical tests were sensitive to different patterns indicative of residual order; 2) as a consequence, the threshold number of randomizing shuffles could vary widely among tests; 3) in general, manual shuffling randomized a deck better than mechanical shuffling for a given number of shuffles; and 4) the mean number of rising sequences as a function of number of manual shuffles matched very closely the theoretical predictions based on the Gilbert-Shannon-Reed (GSR) model of riffle shuffles, whereas mechanical shuffling resulted in significantly fewer rising sequences than predicted

Random planar trees and the Jacobian conjecture

We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F\colon \mathbb{C}^n \to \mathbb{C}^n$ whose Jacobian determinant is a nonzero constant) has a compositional inverse which is also a polynomial. The Jacobian conjecture may be formulated in terms of a problem involving labellings of rooted trees; we give a new probabilistic derivation of this formulation using multi-type branching processes. Thereafter, we develop a simple and novel approach to the Jacobian conjecture in terms of a problem about shuffling subtrees of $d$-Catalan trees, i.e. planar $d$-ary trees. We also show that, if one can construct a certain Markov chain on large $d$-Catalan trees which updates its value by randomly shuffling certain nearby subtrees, and in such a way that the stationary distribution of this chain is uniform, then the Jacobian conjecture is true. Finally, we show that the subtree shuffling conjecture is true in a certain asymptotic sense, and thereafter use our machinery to prove an approximate version of the Jacobian conjecture, stating that inverses of Keller maps have small power series coefficients for their high degree terms.Comment: 36 pages, 4 figures. Section 2.5 added, Section 3 expanded, further minor edit

Performance Evaluation and Modeling of HPC I/O on Non-Volatile Memory

HPC applications pose high demands on I/O performance and storage capability. The emerging non-volatile memory (NVM) techniques offer low-latency, high bandwidth, and persistence for HPC applications. However, the existing I/O stack are designed and optimized based on an assumption of disk-based storage. To effectively use NVM, we must re-examine the existing high performance computing (HPC) I/O sub-system to properly integrate NVM into it. Using NVM as a fast storage, the previous assumption on the inferior performance of storage (e.g., hard drive) is not valid any more. The performance problem caused by slow storage may be mitigated; the existing mechanisms to narrow the performance gap between storage and CPU may be unnecessary and result in large overhead. Thus fully understanding the impact of introducing NVM into the HPC software stack demands a thorough performance study. In this paper, we analyze and model the performance of I/O intensive HPC applications with NVM as a block device. We study the performance from three perspectives: (1) the impact of NVM on the performance of traditional page cache; (2) a performance comparison between MPI individual I/O and POSIX I/O; and (3) the impact of NVM on the performance of collective I/O. We reveal the diminishing effects of page cache, minor performance difference between MPI individual I/O and POSIX I/O, and performance disadvantage of collective I/O on NVM due to unnecessary data shuffling. We also model the performance of MPI collective I/O and study the complex interaction between data shuffling, storage performance, and I/O access patterns.Comment: 10 page

Strongly Secure and Efficient Data Shuffle On Hardware Enclaves

Mitigating memory-access attacks on the Intel SGX architecture is an important and open research problem. A natural notion of the mitigation is cache-miss obliviousness which requires the cache-misses emitted during an enclave execution are oblivious to sensitive data. This work realizes the cache-miss obliviousness for the computation of data shuffling. The proposed approach is to software-engineer the oblivious algorithm of Melbourne shuffle on the Intel SGX/TSX architecture, where the Transaction Synchronization eXtension (TSX) is (ab)used to detect the occurrence of cache misses. In the system building, we propose software techniques to prefetch memory data prior to the TSX transaction to defend the physical bus-tapping attacks. Our evaluation based on real implementation shows that our system achieves superior performance and lower transaction abort rate than the related work in the existing literature.Comment: Systex'1