Introduction to Cryptography

Christopher Martin

What is Cryptography?

“There are two kinds of cryptography in the world: the kind that will keep your kid sister from reading your files, and the kind that will keep major governments from reading your files” - Bruce Schneier, preface to Applied Cryptography

Cryptography is the science of keeping things secret, this is known formally as confidentiality.

Cryptography can be asked to do other things as well.

But what can crypto do for me?

AuthenticationProof of identity

IntegrityProof of content

NonrepudiationProof of transmission

Terminology

1. Plaintext or Cleartext• The message

2. Ciphertext• The encrypted message

3. Encryption or Enciphering• The process of turning plaintext into

ciphertext• E(M) = C

4. Decryption or Deciphering• The opposite of the above• D(C) = M or D(E(M)) = M

Son of Terminology

1. Cryptography• Art and science of keeping secrets secret• Practitioners are called Cryptographers

2. Cryptanalysis• The art and science of making secrets not.

Breaking Cryptography• Practitioners are called Cryptanalysts

3. Cryptology• The branch of mathematics that encompasses

both of the above.• Practitioners are called Cryptologists

Return of Son of Terminology1. Key

• The “shared secret” used to keep the message secret.

• Can be one value from any sized range, called the keyspace

2. Cryptographic Algorithm• The series of steps applied to the message and

the key• Also called a cipher

3. Cryptosystem• A single algorithm, plus all possible

plaintexts, ciphertexts, and keys

A brief digression on secrecy

All secrecy resides in the keyKerchoffs’ Law

Restricted Algorithms

Types of encryption algorithms

Asymmetric Also known as public key Uses two keys, public and private

Symmetric Uses one key that is shared between parties

Historical/Classical Substitution ciphers, polyalphabetic cipers, codes

Hash Not technically encryption algorithms but are part of cryptography

Symmetric Encryption

Ek(M) = C, Dk(C) = M, Dk(Ek(M)) = M The encryption key can be calculated from the decryption key, and vice versa Usually, however, there is only one key

The primary Achilles heel is that the key must be shared between n parties

DES, 3DES, Blowfish, Twofish, Serpent, IDEA, AES (Rijndael)

Can operate in two modes: stream and block, and most modern algorithms have variable key size

One Time Pads

Subset of Symmetric ciphersOffers theoretically perfect securityKey is comprised of a large sheet of truly random letters.

Each key is used only onceEncryption is the addition modulo 26 of the key letter, and the plaintext letter

Asymmetric Encryption

Ek-pub(M) = C, Dk-priv(C) = M,

Dk-priv(Ek-pub(M)) = M

Given the public key, it is computationally infeasible to calculate the private key

Can also be used for digital signaturesExamples: RSA, DSA, ElGamal,Diffe-Hellman

Hashing Algorithms

Hashing is about integrityThere is no key involved in hashing

Takes an arbitrary sized input, and produces a unique fixed size output

The smallest change in the input should produce a totally different output

The process is non reversibleExamples: MD4, MD5, SHA-1, SHA-128, SHA-256

Attacking Cryptography

CryptanalysisCiphertext Only AttackKnown Plaintext AttackChosen Plaintext Attack

Adaptive chosen plaintextChosen Ciphertext AttackChosen Key AttackRubber Hose Cryptanalysis

Where to use cryptography?Anywhere you want to have something remain secret SSL, TLS, IPv6, SSH, IPSec all keep information secure in transit

Any Symmetric Algorithm can keep your files safe in storage There are file systems available that will

encrypt your data on the fly. EncFS and Loop-AES for unix, EFS for windows, FileVault for Mac OS X

You can add encryption at the application level, or at the server level for storing database information securely

Where can I get cryptography?Your best bet it to have it bundled with the Operating System, or to buy supported add-on hardware that does what you want. OpenBSD is the de facto standard for operating system supported cryptography.

Add on libraries like OpenSSL and libTomCrypt are also available for most unix like platforms.

Roll Your Own Not really recommended unless you are an expert

Conclusions

Cryptography is only one part of a multi layered security system

It’s not a magic bulletIt’s fun

Sources

1.Applied Cryptography, Bruce Schneier1996, Wiley and Sons

2.Practical Cryptography, Bruce Schneier and Niels Ferguson2003, Wiley Publishing

3.Silence on the Wire, Michael Zalewski2005, No Starch Press