PPT-China Summer School on Lattices and Cryptography

Craig Gentry and Shai Halevi June 4 2014 Homomorphic Encryption over Polynomial Rings The Ring LWE Problem RLWE Recall LWE LWE traditional formulation Hard to distinguish between A b . However computational aspects of lattices were not investigated much until the early 1980s when they were successfully employed for breaking several proposed cryptosystems among many other applications It was not until the late 1990s that lattices w CS 465. Last Updated. : . Aug 25, 2015. Outline. Provide a brief historical background of cryptography. Introduce definitions and high-level description of four cryptographic primitives we will learn about this semester. Sixth Edition. by William Stallings . Chapter 10. Other Public-Key Cryptosystems. “Amongst the tribes of Central Australia every man, woman, and child has a secret or sacred name which is bestowed by the older men upon him or her soon after birth, and which is known to none but the fully initiated members of the group. This secret name is never mentioned except upon the most solemn occasions; to utter it in the hearing of men of another group would be a most serious breach of tribal custom. When mentioned at all, the name is spoken only in a whisper, and not until the most elaborate precautions have been taken that it shall be heard by no one but members of the group. The native thinks that a stranger knowing his secret name would have special power to work him ill by means of magic.”. Minkowski’s. Theorem. Chapter 2. Preface. A lattice point is a point in R. d . with integer coordinates.. Later we will talk about general lattice point.. Lattice Point. Let C ⊆ R. d. be symmetric around the origin, convex, bounded and suppose that volume(C)>2. China Summer School on Lattices and Cryptography, June 2014. Starting Point: Linear Equations. Easy to solve a linear system of equations. Given . A. , . b. , find . s. S. olved using Gaussian elimination, Cramer rule, etc.. Craig Gentry. and . Shai. . Halevi. June 3, 2014. Somewhat . Homomorphic. Encryption. Part 1: . Homomorphic. Encryption: Background, Applications, Limitations. Computing on Encrypted Data. Can we delegate the . Neil Conway. UC Berkeley. Joint work with:. Peter Alvaro, Peter . Bailis. ,. David Maier, Bill Marczak,. Joe Hellerstein, . Sriram. . Srinivasan. Basho Chats #004. June 27, 2012. Programming. Distributed Programming. CS. . 111. Operating . Systems . Peter Reiher. . Outline. Basic concepts in computer security. Design principles for security. Important security tools for operating systems. Access control. Cryptography and operating systems. Josh Benaloh. Tolga Acar. Fall 2016. October 25, 2016. 2. The wiretap channel. Key (K. 1. ). Key (K. 2. ). Eavesdropper. Plaintext. (P). Noisy insecure. channel. Encrypt. Decrypt. Alice. Bob. Plaintext. CSE3002 – History of Computing. Group A: Daniel . Bownoth. , Michael Feldman, Dalton Miner, Ashley Sanders. Encryption. The process of securing information by transforming it into code.. Encrypted data must be deciphered, or . Symmetric Encryption. Key exchange . Public-Key Cryptography. Key exchange. Certification . Why Cryptography. General Security Goal. - . Confidentiality . (. fortrolig. ). - . End-point Authentication . Vadim . Lyubashevsky. Cryptography. Allows for secure communication in the presence of malicious parties. 2. Cryptography. Allows for secure communication in the presence of malicious parties. 3. Cryptography. Research by. B. rianne Power,. E. rin Brush, and . K. endra Johnson-Tesch. Supervised by Jill Dietz at St. Olaf College. Chermak and Delgado (1989) were . interested in finding families of . characteristic subgroups. They . DMR 1905920. 2021 Intellectual Merit. Oleg Gang, Columbia University. Assembly of designed and bioactive protein arrays. Encapsulation of ferritin inside designed DNA octahedra is followed by assembly of these DNA-ferritin voxels into prescribed 2D and 3D lattices. Ferritins preserve their bioactivity when assembled into designed arrays..