Thanks to relatively small public and secret keys, the Supersingular Isogeny Key Encapsulation (SIKE) protocol made it into the third evaluation round of the post-quantum standardization project of the National Institute of Standards and Technology (NIST). Even though a large body of research has been devoted to the efficient implementation of SIKE, its latency is still undesirably long for many real-world applications. Most existing implementations of the SIKE protocol use the Montgomery representation for the underlying field arithmetic since the corresponding reduction algorithm is considered the fastest method for performing multiple-precision modular reduction. In this paper, we propose a new data representation for supersingular isogeny-based Elliptic-Curve Cryptography (ECC), of which SIKE is a sub-class. This new representation enables significantly faster implementations of modular reduction than the Montgomery reduction, and also other finite-field arithmetic operations used in ECC can benefit from our data representation. We implemented all arithmetic operations in C using the proposed representation such that they have constant execution time and integrated them to the latest version of the SIKE software library. Using four different parameters sets, we benchmarked our design and the optimized generic implementation on a 2.6 GHz Intel Xeon E5-2690 processor. Our results show that, for the prime of SIKEp751, the proposed reduction algorithm is approximately 2.61 times faster than the currently best implementation of Montgomery reduction, and our representation also enables significantly better timings for other finite-field operations. Due to these improvements, we were able to achieve a speed-up by a factor of about 1.65, 2.03, 1.61, and 1.48 for SIKEp751, SIKEp610, SIKEp503, and SIKEp434, respectively, compared to state-of-the-art generic implementations.

Immersive authoring is an increasingly popular technique to design AR/VR scenes because design and testing can be done concurrently. Most existing systems, however, are single-user and limited to either AR or VR, thus constrained in the interaction techniques. We present XRDirector, a role-based collaborative immersive authoring system that enables designers to freely express interactions using AR and VR devices as puppets to manipulate virtual objects in 3D physical space. In XRDirector, we adapt roles known from filmmaking to structure the authoring process and help coordinate multiple designers in immersive authoring tasks. We study how novice AR/VR creators can take advantage of the roles and modes in XRDirector to prototype complex scenes with animated 3D characters, light effects, and camera movements, and also simulate interactive system behavior in a Wizard of Oz style. XRDirector's design was informed by case studies around complex 3D movie scenes and AR/VR games, as well as workshops with novice AR/VR creators. We show that XRDirector makes it easier and faster to create AR/VR scenes without the need for coding, characterize the issues in coordinating designers between AR and VR, and identify the strengths and weaknesses of each role and mode to mitigate the issues.