Symmetric Schemes

• Process of protection and deprotection uses the same key;
• Keys are usually used during a short period of time;
• Keys are established after a negotiation process between who encrypts and who decrypts;
• Used in:
  • Symmetric cipher;
  • MAC.

Symmetric Cipher

Algorithms (G, E, D):

• G - probabilistic function for key generation;
  • G :-> Keys;
• E - probabilistic function for cipher;
  • E: Keys -> {0, 1}* -> {0, 1}*;
• D - deterministic function for decipher;
  • D: Keys -> {0, 1}* -> {0, 1}*.

Properties

• Keys: D(k)(E(k)(m)) = m;
• Security property: is computationally infeasible to find m (plain text) from c (ciphered text), without knowing the key k;
• Symmetric scheme: use of the same key k in the functions E and D;
• Message m and ciphered text c are byte sequences with variable dimension ({0,1}*);
• Does not guarantee data integrity;
• Examples: DES-CBC-PKCS5Padding, AES-CBC-PKCS5Padding, etc.

MAC (Message Authentication Code) Scheme

Algorithms (G, T, V):

• G - probabilistic function for key generation;
  • G :-> Keys;
• T - probabilistic function for tag generation;
  • T: Keys -> {0, 1}* -> Tags;
• V - deterministic function for tag verification;
  • V: Keys -> ( Tags x {0, 1}* ) -> {true, false}.

Properties

• Keys: V(k)(T(k)(m), m) = true;
• Security property: is computationally infeasible to find m (plain text) from t (tag), without knowing the key k;
• Symmetric Scheme: use of the same key k in the functions T and V;
• Message m and tag t are byte sequences with variable dimension ({0,1}*);
• Tag t has fixed dimension (e.g. 160, 256 bits);
• Code detectors and error correctors do not serve for MAC schemes;
• Examples: HMAC-SHA1, HMAC-SHA256, etc.

Symmetric Cipher Primitives

• To use symmetric cipher schemes, we need to choose a symmetric cipher primitive;
• Examples: DES, AES, Blowfish, etc;
• Block cipher primitive:
  • n - block dimension;
  • l - key dimension;
  • Function E: {0, 1}^l -> {0, 1}^n -> {0, 1}^n;
  • Function D: {0, 1}^l -> {0, 1}^n -> {0, 1}^n.

Features

• The block dimension n must be sufficiently high to prevent attacks based on the statistics of the plain text;
• The key dimension l must be sufficiently high to prevent attacks based on brute force.

Operation Modes

• Plain text patterns should not be evident in the ciphered text;
• The efficiency of the used method should be higher than the efficiency of the cipher primitive;
• Ciphered text dimension should be approximately equal to plain text dimension;
• The decipher should be capable of error detection and correction;
• Random access - ability to decipher and change only part of the ciphered text.

ECB (Electronic Code Book) Mode

• Plain text blocks equal, ciphered with the same key, imply ciphered text blocks equal;
• Interdependence in the cipher - The cipher is performed independently in each block;
• Error propagation - Error occurrence in a ciphered text block affects only the decipher of that block;
• Random access.

CBC (Cipher Block Chaining) Mode

• Under the same key and under the same initialization vector (IV), two equal messages imply equal ciphered texts;
• Interdependence in the cipher - The cipher is performed independently in each block;
• Error propagation - Error occurrence in a ciphered text block cj affects the decipher of that block and the next block cj+1;
  • The decipher of the block cj+1 will have errors in the same positions as the block cj;
• Reordering the ciphered text blocks affects the decipher;
• It is relatively easy to manipulate a given plain text block.

IV - Initialization Vector

• Should be stored and transmitted in plain;
• Should not be reused - uniqueness;
• Should not be predictable - unpredictability.

Padding

• Padding is a way to take data that may or may not be a multiple of the block size for a cipher and extend it out so that it is;
• X is the bytes count to add to the message dimension to make it a multiple of the block dimension;
• Example: PKCS#5 and PKCS#7 padding.

Stream Operation Modes

Modes like CBC need different algorithms to cipher and decipher.

CTR (Counter) Mode

• Under the same key and under the same initialization vector (IV), two equal messages imply equal ciphered texts;
• Error propagation - Error occurrence in a ciphered text block cj affects only the decipher of that block;
  • The decipher of the block cj will have errors in the same positions as the block cj;
• Random access;
• It is relatively easy to manipulate a given plain text block.

Authenticated Cipher

• To guarantee confidentiality and simultaneously authenticity, it is necessary to use a combination of the Cipher and MAC schemes;
• There are two approaches:
  • Encrypt-then-MAC - The tag indicates whether there was a change or not in the ciphered text;
  • MAC-then-Encrypt - The tag is generated over the message, and is then all encrypted;
• There are operation modes whose objective is to produce an authenticated cipher by combining the operations in a single algorithm:
  • Galois/Counter Mode (GCM);
  • Offset Codebook Mode (OCB);
  • Counter with CBC-MAC (CCM).