PPT-Cryptography Lecture 23 Cyclic groups

Let G be a finite group of order q written multiplicatively Let g be some element of G Consider the set ltggt g 0 g 1 We know g q 1 g 0 so the set has . Algorithms. Scott Chappell. What is Cryptography?. Definition: the art of writing or solving codes. Basic Encryption Methods. Caesar Shift. Simple Substitution Cipher. Fun to use, but are easily cracked by computers and even by humans. Josh Benaloh. Tolga Acar. Fall 2016. November 8, 2016. Practical Aspects of Modern Cryptography. 1. What is Money?. 106 billion people lived. 94% are dead. Most of the world’s wealth made after 1800. 1. Part I: Crypto. Chapter 2: Crypto Basics. MXDXBVTZWVMXNSPBQXLIMSCCSGXSCJXBOVQXCJZMOJZCVC. TVWJCZAAXZBCSSCJXBQCJZCOJZCNSPOXBXSBTVWJC. JZDXGXXMOZQMSCSCJXBOVQXCJZMOJZCNSPJZHGXXMOSPLH. JZDXZAAXZBXHCSCJXTCSGXSCJXBOVQX. Symmetric Encryption. Key exchange . Public-Key Cryptography. Key exchange. Certification . Why Cryptography. General Security Goal. - . Confidentiality . (. fortrolig. ). - . End-point Authentication . What is cryptography?. Ceasar. Cipher. Public key cryptography. What is cryptography?. Cryptography.  or . cryptology.  (from . Greek.  . κρυπτός.  . kryptós. , "hidden, secret"; and . Richard J. Blech. Chief Executive Officer. Secure Channels, Inc.. Is there anyone here who cannot parse and explain this equation?. 2. If not, that’s ok.. 3. Why Pre-Computer Cryptography?. If you understand pre-computer crypto, you understand crypto!. Introduction I. Electrochemical methods are used . To investigate . electron transfer processes and . kinetics. To . study redox processes in organic and organometallic . chemistry. To . investigate multi-electron transfer processes in . to’s. . u. sing . OpenSSL. In this session, we will cover cryptography basics and explore cryptographic functions, performance and examples using . OpenSSL. . . July 2012. LAB: . http://processors.wiki.ti.com/index.php/Sitara_Linux_Training:_Cryptography. Definition. If . G. 1. , . G. 2, ..., . G. n. are groups, then their . external direct product G. 1 .  . G. 2 . ... .  . G. n. . is simply the set of all ordered . n. -tuples of elements of the groups under component-wise operations.. 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. Steven M. Bellovin. https://www.cs.columbia.edu/~smb. What is Cryptography?. Literally: “hidden writing”. (Technical, the entire field is “cryptology”, but almost no one except the NSA and historians uses that word.). We have discussed two classes of cryptographic assumptions. Factoring-based (factoring, RSA assumptions). Dlog. -based (. dlog. , CDH, and DDH assumptions). In two classes of groups. A. ll these problems are believed to be “hard,” i.e., to have no polynomial-time algorithms. Cyclic group G of order q with generator g.  G.  . G = {g. 0. , g. 1. , …, g. q-1. }. For any h .  G, define . log. g. h .  {0, …, q-1} as. . log. g. h = x  . The . art and science of concealing the messages to introduce secrecy in . information security . is recognized as cryptography. .. The word ‘cryptography’ was coined by combining two Greek words, ‘Krypto’ .