Lecture Notes on Computer Security - Cryptography - Fall 2006 | CSE 543, Study notes of Computer Science

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CSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

CSE 543 - Computer Security

Lecture 4 - Cryptography

September 14, 2006

URL: http://www.cse.psu.edu/~tjaeger/cse543-f06/ 1

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

Review: secret vs. public key crypto.

• Secret key cryptography
  • Symmetric keys, where A single key (k) is used is used for E and D
  • D( E( p, k ), k ) = p
• All (intended) receivers have access to key
• Note: Management of keys determines who has access to encrypted data - E.g., password encrypted email
• Also known as symmetric key cryptography - Public key cryptography - Each key pair consists of a public and private component: k+ (public key), k- (private key) D( E(p, k+), k- ) = p D( E(p, k-), k+ ) = p - Public keys are distributed (typically) through public key certificates - Anyone can communicate secretly with you if they have your certificate - E.g., SSL-base web commerce

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

Hash Algorithms

• Hash algorithm
  • Compression of data into a hash value
  • E.g., h(d) = parity(d)
  • Such algorithms are generally useful in programs
• … as used in cryptosystems
  • One-way - (computationally) hard to invert h() , i.e., compute h - (y), where y=h(d)
  • Collision resistant^ hard to find two data x 1 and x 2 such that h(x 1 ) == h(x 2 )
• Q: What can you do with these constructs?

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

• HMAC
  • Authenticates integrity for data d
  • Uses some key k and hash algorithm h
  • To simplify, hmac(k,d) = h( k+d )
• Why does this provide authenticity?
  • Cannot produce hmac(k,d) unless you know k, d
  • If you could, then can break h
  • Exercise for class: prove the previous statement
• Used in protocols to authenticate content

Hashed Message Authentication Code

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

Digital Signatures

• Models physical signatures in digital world
  • Association between private key and document
  • … and indirectly identity and document.
  • Asserts that document is authentic and non- reputable
• To sign a document
  • Given document d, private key k-
  • Signature S(d) = E( k -, h(d) )
• Validation
  • Given document d, signature S(d), public key k+
  • Validate D(k +, S(d)) = H(d)

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

Basic truths of cryptography …

• Cryptography is not frequently the source of

security problems

• Algorithms are well known and widely studied
  • Use of crypto commonly is … (e.g., WEP)
• Vetted through crypto community
• Avoid any “proprietary” encryption
• Claims of “new technology” or “perfect security” are almost assuredly snake oil

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger

Building systems with cryptography

• Use quality libraries
  • SSLeay, lim (from Lenstra), Victor Shoup’s library, RSAREF, cryptolib
  • Find out what cryptographers think of a package before using it
• Code review like crazy
• Educate yourself on how to use library
  • Caveats by original designer and programmer

CSE543 Computer (and Network) Security - Fall 2005 - Professor McDanielCSE543 Computer (and Network) Security - Fall 2006 - Professor Jaeger Common issues that lead to pitfalls

• Generating randomness
• Storage of secret keys
• Virtual memory (pages secrets onto disk)
• Protocol interactions
• Poor user interface
• Poor choice of key length, prime length, using parameters from one algorithm in another