Many terpene glycosides exhibit contrasteric patterns of 1,2-diol glycosylation in which the more hindered alcohol bears a sugar; protection of the less hindered alcohol only increases steric repulsion. Here, we report a method for contrasteric glycosylation using a new sugar-linker that forms a cleavable, 10-membered ring with high efficiency, leading to syntheses of cotylenin E, J, and ISIR-050. Linker selection was aided by DFT calculations of side reactions and stereoselectivity, as well as conformational analyses using autoDFT, a Python script that converts SMILES strings to DFT-optimized conformational ensembles.
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Long Polynomial Modular Multiplication Using Low-Complexity Number Theoretic Transform [Lecture Notes]
This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and the discrete Fourier transform (DFT). The main goal is to extend the well-known theory of the DFT in signal processing (SP) to other applications involving polynomials in a ring, such as homomorphic encryption (HE).
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- Award ID(s):
- 2243053
- PAR ID:
- 10501324
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Signal Processing Magazine
- Volume:
- 41
- Issue:
- 1
- ISSN:
- 1053-5888
- Page Range / eLocation ID:
- 92 to 102
- Subject(s) / Keyword(s):
- Number Theoretic Transform , Discrete Fourier Transform , Fast Fourier Transform , Root Of Unity , Point-wise Multiplication Polynomial Modular Multiplication Negative Wrapped Convolution Twiddle Shifting Low-Complexity NTT
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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