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Computer and Network Security: MIT 6.857 Class Notes

The use and disclosure of patient medical information originally was protected by a patchwork of state laws, leaving gaps in the protection of patients’ privacy and confidentiality. The U.S. Congress recognized the need for national patient record privacy standards in 1996 when they enacted the Health Insurance Portability and Accountability Act of 1996 (HIPAA). This law encouraged electronic transactions to lower health care costs, but also required new safeguards to protect the security and confidentiality of that information. All medical records and other individually identifiable health information used or disclosed by a covered entity in any form, whether electronically, on paper, or orally, are covered | MIT 6.857 Computer and Network Security Class Notes File http theory.lcs.mit.edu rivest notes notes.pdf 1 Revision December 2 2002 Computer and Network Security MIT 6.857 Class Notes by Ronald L. Rivest December 2 2002 1 Copyright 2002 Ronald L. Rivest. All rights reserved. May be freely reproduced for educational or personal use. MIT 6.857 Computer and Network Security Class Notes File http theory.lcs.mit.edu rivest notes ntintro.pdf 2 Revision December 2 2002 Introduction to Number Theory Elementary number theory provides a rich set of tools for the implementation of cryptographic schemes. Most public-key cryptosystems are based in one way or another on number-theoretic ideas. The next pages provide a brief introduction to some basic principles of elementary number theory. 1 Copyright 2002 Ronald L. Rivest. All rights reserved. May be freely reproduced for educational or personal use. MIT 6.857 Computer and Network Security Class Notes File http theory.lcs.mit.edu rivest notes bignum.pdf 3 Revision December 2 2002 Bignum computations Many cryptographic schemes such as RSA work with large integers also known as bignums or multiprecision integers. Here large may mean 160-4096 bits 49-1233 decimal digits with 1024-bit integers 308 decimal digits typical. We briefly overview of some implementation issues and possibilities. When RSA was invented efficiently implementing it was a problem. Today standard desktop CPU s perform bignum computations quickly. Still for servers doing hundreds of SSL connections per second a hardware assist may be needed such as the SSL accelerators produced by nCipher www.ncipher.com . A popular C C software subroutine library supporting multi-precision operations is GMP GNU Multiprecision package www.swox.com gmp . A more elaborate package based on GMP is Shoup s NTL Number Theory Library www.shoup.net ntl . For a survey see https www.cosic.esat.kuleuven.ac.be nessie call mplibs.html. Java has excellent support for multiprecision operations