Braid Cryptology

Braid Cryptology - Braid Cryptography An application of...

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Unformatted text preview: Braid Cryptography An application of knot theory. Really. Click to edit Master subtitle style 5/7/09 Braids ied in class i {AB1AE0E6-E0A3-4EC4-9F31-95B6960AD0E3} {77708AED-AEB8-414D-851E-777C87841A09} {E3618BC3-66F2-4934-9139-3A25EE1D4B6E} Conjugation {1832B76F-8539-4949-9234-275A3A8E77AA} {235E8AF1-9432-4815-96AB-AD12DF5BB856} {0DA53C54-A8B3-4E6D-A5FA-C49BE21243E9} Bn Artin Generators {D8B45C69-5790-4F25-AEF1-1E3FD8BDA9B1} ult to solve (no polynomial timeand its + r = n at Set of braids - index n Add a crossing yet) l inverse either end Bl, Br, 5/7/09 Cryptography ousKnot Theory inproduct offorce e to brute primes odular arithmetic {4028CFF5-AE39-4320-AFAD-70DD9E33A008} {631DA2B7-F4DE-4788-817A-04BCBE2FC5E3} {4C74D88E-DA43-4BB7-B3C9-8EE7E697BDA3} Implement the algorithm Information to keep private problem to solve (one-w Find a hard {D0D1FB84-3AF5-42EB-BD65-BCF1BABBC8E7} {8B777D90-9094-4CB5-86F7-9787CCEBDFDE} Ensure minimal security hazards Finances 5/7/09 RSA Theory RSA - Ron Rivest, Adi Shamir, and Leonard Adleman 1. Choose large primes, (p,q), N = p*q, = (p-1)(q-1) Choose e | 1<e<, compute d | de1 (mod ) Encrypt: m = (int) Message => c = me mod N 2. 3. 5/7/09 RSA Example: Preparation N ==89 d = 1207 e 8448 7 p==8633 {B9F1B0FE-D132-4C1B-A074-BDCEA9FE4A83} {17DC09E0-7F68-42FC-BB78-385CA245B819} {AFA27FA3-82D0-4D9C-8D28-FB3456A10E48} {A0CA8644-83DA-4AAF-8C78-0224E6FD6F45} Choose {276F4CF3-8154-48FC-9138-AAE48ED519B0} Compute Compute Choose q = 97 5/7/09 RSA Example: Encryption and Decryption 46721207 mod 8633 = 81 {CE15F54D-ED93-47BC-81F9-82B7E163CEBC} {C7775337-E33D-46AB-9507-EFE98D1210F3} Decryption {9E86310F-F466-4E53-B4B3-AC498619A8D2} {0EEF6040-EA91-45D5-BE5F-75DA730025DB} Encryption {32B7A5F3-1ED2-4708-8017-46CAC79B8882} 81 => "Hi" "Hi" => 8+1= 81 c = 817 mod 8633 = 4672 5/7/09 Cryptographic Protocols e on key such that all influence the outcome {CB365AF7-C122-4FBC-A35B-9B67CD2F7F69} {2714C5E3-2056-4733-A85E-F30578208F74} Key Agreement Public Key Cryptosystems {7F873F2E-1F22-4853-BF99-66E2D03EFEAE} Asymmetric system, where anyone can encrypt. Only holder of p 5/7/09 Braid Problems y' such that x = y'p {FBD0A655-C680-4C1E-B8CE-408B56246659} {9F77BA89-005E-4113-8EC2-64625525D34E} General Conjugate Search Problem {A95B7287-4067-4C00-95EF-799D2F311359} Pth Root Problem x axa-1, find a 5/7/09 5/7/09 References http://www.cmis.brighton.ac.uk/staff/agf/ http://www.springerlink.com/content/hre5 http://www.ccs.neu.edu/home/riccardo/co http://www-cs.engr.ccny.cuny.edu/~csmm The Knot Book, by Colin C. Adams 2001 5/7/09 http://www.math.wisc.edu/~boston/bolst ...
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