FORESEC Academy FORESEC Academy Security Essentials (IV)

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Presentation transcript:

FORESEC Academy FORESEC Academy Security Essentials (IV)

FORESEC Academy Why do I Care about Crypto?

FORESEC Academy Concepts in Cryptography

FORESEC Academy Concepts in Cryptography (2) Tractable ProblemsIntractable Problems “Easy” problems. Can be solved in polynomial time (i.e., “quickly”) for certain inputs Examples : constant problems linear problems quadratic problems cubic problems “Hard” problems. Cannot be solved in polynomial time (i.e., “quickly”) Examples : exponential or super-polynomial problems factoring large integers into primes (RSA) solving the discrete logarithm problem(ElGamal) computing elliptic curves in a finite field (ECC) Computational Complexity deals with time and space requirements for the execution of algorithms. Problems can be classified as tractable or intractable.

FORESEC Academy Concepts in Cryptography (3) An Example of an Intractable Problem... Difficulty of factoring a large integer into its two prime factors  A “hard” problem  Years of intense public scrutiny suggest intractability  No mathematical proof so far Example: RSA based on difficulty of factoring a large integer into its prime factors ~1000 times slower than DES considered “secure” de facto standard patent expired in 2000

FORESEC Academy Concepts in Cryptography (4)  A “hard” problem  Years of intense public scrutiny suggest intractability  No mathematical proof so far  The discrete logarithm problem is as difficult as the problem of factoring a large integer into its prime factors Another Intractable Problem… Difficulty of solving the discrete logarithm problem --for finite fields Examples El Gamal encryption and signature schemes Diffie-Hellman key agreement scheme Schnorr signature scheme NIST.s Digital Signature Algorithm (DSA)

FORESEC Academy Concepts in Cryptography (5)  A “hard” Problem  Years of intense public scrutiny suggest intractability  No mathematical proof so far  In general, elliptic curve cryptosystems (ECC) offer higher speed, lower power consumption, and tighter code Yet Another Intractable Problem... Difficulty of solving the discrete logarithm problem--as applied to elliptic curves Examples Elliptic curve El Gamal encryption and signature schemes Elliptic curve Diffie-Hellman key agreement scheme Schnorr signature scheme NIST.s Digital Signature Algorithm (DSA)

FORESEC Academy Voila! We Can Now Build...

FORESEC Academy DES: Data Encryption Standard  Released March 17, 1975  Rather fast encryption algorithm  Widely used; a de facto standard  Symmetric-key, 64 -bit block cipher  56 -bit key size ! Small 256 keyspace  Today, DES is not considered secure

FORESEC Academy DES Weaknesses  DES is considered non-secure for very sensitive encryption. It is crackable in a short period of time.  See the Cracking DES book by O’Reilly.  Multiple encryptions and key size will increase the security.  Double DES is vulnerable to the meet-in-the- middle attack and only has an effective key length of 57 bits.  Triple DES is preferred.

FORESEC Academy DES  In 1992 it was proven that DES is not a group. This means that multiple DES encryptions are not equivalent to a single encryption. THIS IS A GOOD THING.  If something is a group then - E(K 2,E(K,M)) = E(K 3,M)  Since DES is not a group, multiple encryptions will increase the security.

FORESEC Academy Meet-in-the-middle Attack

FORESEC Academy Triple DES USAGEVULNERABILITIES Supported in latest releases of Web clients, such as Microsoft Internet Explorer & Netscape Communicator Prefer Triple DES over DES (which is. officially. No longer considered to be secure) Cracking Triple DES means examining all possible pairs of crypto-variables (a task considered to be beyond today’s technology) So far, there have been no public reports claiming to have cracked Triple DES...

FORESEC Academy Triple DES (2)

FORESEC Academy AES THE FIVE “AES” FINALISTS !  MARS IBM  RC6 tm RSA Laboratories  Rijndael Joan Daemen, Vincent Rijmen  Serpent Ross Anderson, Eli Biham, Lars Knudsen  Twofish Bruce Schneier, John Kelsey, Doug Whiting, David Wagner, Chris Hall, Niels Ferguson Significance Developing “good” cryptographic algorithms that can be trusted is hard. The only practical way to develop such algorithms is to perform the development process in an open manner, and under intense public scrutiny of the global cryptographic community. Can you think of a recent example in which this was not followed? Advanced Encryption Standard AES is a new encryption algorithm(s) that is being designed to be effective well into the 21st century Countdown to AES ! 1/2/1997, the quest for AES begins... 8/9/1999, five finalist algorithms announced Announced winner – Rijndeal 12/26/2001 – AES approved!

FORESEC Academy AES Algorithm