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AbstractSupersingular Isogeny Graphs were introduced as a source of hard problems in cryptography by Charles, Goren, and Lauter [6] for the construction of cryptographic hash functions and have been used for key exchange SIKE. The security of such systems depends on the difficulty of finding a path between two random vertices. In this article, we study several aspects of the structure of these graphs. First, we study the subgraph given by j-invariants in , using the related isogeny graph consisting of only -rational curves and isogenies. We prove theorems on how the connected components thereof attach, stack, and foldwhen mapped into the full graph. The -rational vertices are fixed by the Frobenius involution on the graph, and we call the induced graph the spine. Finding paths to the spine is relevant in cryptanalysis. Second, we present numerous computational experiments and heuristics relating to the position of the spine within the whole graph. These include studying the distance of random vertices to the spine, estimates of the diameter of the graph, how often paths are preserved under the Frobenius involution, and what proportion of vertices are conjugate. We compare some of the heuristics with known results on other Ramanujan graphs.

In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary octics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of primes of bad reduction for the associated hyperelliptic curves. We illustrate our theorem with explicit computations. This work is motivated by the study of the values of these modular functions at CM points of the Siegel upper half-space, which, if their denominators are known, can be used to effectively compute models of (hyperelliptic, in our case) curves with CM.

Artificial Intelligence (AI) is increasingly incorporated into the cloud businessin order to improve the functionality (e.g., accuracy) of the service. The adoption of AI as a cloud service raises serious privacy concerns in applications where the risk of data leakageis not acceptable. Examples of such applications include scenarios where clients hold potentially sensitive private information such as medical records, financial data, and/or location. This article proposes ReDCrypt, the first reconfigurablehardware-accelerated framework that empowers privacy-preserving inference of deep learning models in cloud servers. ReDCrypt is well-suited for streaming (a.k.a., real-time AI)settings where clients need to dynamically analyze their data as it is collected over time without having to queue the samples to meet a certain batch size. Unlike prior work, ReDCrypt neither requires to change how AI models are trained nor relies on two non-colluding servers to perform. The privacy-preserving computation in ReDCrypt is executed using Yao’s Garbled Circuit(GC) protocol. We break down the deep learning inference task into two phases: (i) privacy-insensitive (local) computation, and (ii) privacy-sensitive (interactive) computation. We devise a high-throughput and power-efficient implementation of GC protocol on FPGA for the privacy-sensitive phase. ReDCrypt’s accompanying API provides support for seamless integration of ReDCrypt into any deep learning framework. Proof-of-concept evaluations for different DL applications demonstrate up to 57-fold higher throughput per core compared to the best prior solution with no drop in the accuracy.

'Moore's Outlaws' (July/August 2010) highlights the danger posed by attackers in cyberspace and makes the case for deploying stronger cyber security measures. As researchers at Microsoft Research, we believe machines [...]

This paper presents a practical digital signature scheme to be used in conjunction with network coding. Furthermore, the authors' idea simultaneously provides authentication and detects malicious nodes that intentionally corrupt content on the network.

Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S=(2P+ Q) from given points Pand Qon an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication.Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S=(2P+ Q) from given points Pand Qon an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication.

We show that for all finite fields Fq, there exists a curve C over Fq of genus 3 such that the number of rational points on C is within 3 of the Serre–Weil upper or lower bound. For some q, we also obtain improvements on the upper bound for the number of rational points on a genus 3 curve over Fq.

Genotype imputation is a fundamental step in genomic data analysis, where missing variant genotypes are predicted using the existing genotypes of nearby “tag” variants. Although researchers can outsource genotype imputation, privacy concerns may prohibit genetic data sharing with an untrusted imputation service. Here, we developed secure genotype imputation using efficient homomorphic encryption (HE) techniques. In HE-based methods, the genotype data are secure while it is in transit, at rest, and in analysis. It can only be decrypted by the owner. We compared secure imputation with three state-of-the-art non-secure methods and found that HE-based methods provide genetic data security with comparable accuracy for common variants. HE-based methods have time and memory requirements that are comparable or lower than those for the non-secure methods. Our results provide evidence that HE-based methods can practically perform resource-intensive computations for high-throughput genetic data analysis. The source code is freely available for download at https://github.com/K-miran/secure-imputation.

Abstract:: We give ray class field descriptions of the function fields of the Hermitian, Suzuki and Ree curves.

An interview with principal researcher Kristin Lauter is presented. When asked on the difference of the homomorphic encryption from other encryption technologies, Lauter mentions the ability of the former to upload data to cloud. She says that the focus of practical homomorphic encryption is on the computation of certain high value functions. She adds that the health care providers are also considering the privacy issues of medical records.

Several letters to the editor are presented in response to articles in previous issues including "Can AIDS Be Cured?" by Jon Cohen in the July/August 2010 issue, "Solar's Great Leap Forward" and "The German Experiment," in the July/August 2010 issue and "Moore's Outlaws" in the July/August 2010.