Question

What is the main difference between the Symmetric-Key Cryptosystem and the Public-key cryptosystem? Please give the main differences of the following different encryption cryptosystems: the Block Ciphers DES and AES, Hash functions and the RSA cryptosystem and the EIGamal cryptosystem.

Answer 1

Difference between Symmetric Key and Public-Key Cryptosystems:-

Symmetric key cryptography is also known as shared key cryptography. As the name suggests, it involves 2 people using the same private key to both encrypt and decrypt information.

Public-key cryptography, on the other hand, is where 2 different keys are used – a public key for encryption and a private key for decryption.

Difference between Block Ciphers DES and AES:-

AES	DES
AES stands for Advanced Encryption Standard	DES stands for Data Encryption Standard
Key length can be of 128-bits, 192-bits and 256-bits.	Key length is 56 bits in DES.
Number of rounds depends on key length: 10(128-bits), 12(192-bits) or 14(256-bits)	DES involves 16 rounds of identical operations
The structure is based on a substitution-permutation network.	The structure is based in Feistel network.
AES is more secure than the DES cipher and is the de facto world standard.	DES can be broken easily as it has known vulnerabilities. 3DES(Triple DES) is a variation of DES which is secure than the usual DES.
The rounds in AES are: Byte Substitution, Shift Row, Mix Column and Key Addition	The rounds in DES are: Expansion, XOR operation with round key, Substitution and Permutation
AES can encrypt 128 bits of plaintext.	DES can encrypt 64 bits of plaintext.
AES cypher is derived from the square cipher.	DES cipher is derived from Lucifer cipher.
AES was designed by Vincent Rijmen and Joan Daemen.	DES was designed by IBM.
No known crypt-analytical attacks against AES but side-channel attacks against AES implementations possible. Biclique attack has better complexity than brute-force but still ineffective.	Known attacks against DES include Brute-force, Linear crypt-analysis and Differential crypt-analysis.

Difference between RSA and ElGamal:-

• Underlying assumption: RSA is eventually based on factoring (recovering p, q from n=pq), where ElGamal is eventually based on the discrete logarithm problem in cyclic groups (recover x from h=g^x).

• Both algorithms require similar key sizes, and can (theoretically) be broken using similar approaches.

• ElGamal can be implemented using elliptic curves, drastically increasing efficiency and decreasing the required key sizes. RSA cannot be made more efficient.

• RSA is thoroughly standardized, and practically every implementation is mutually compatible.
  ElGamal has a wide range of implementations, using different representations and algebraic groups, most of which are mutually incompatible. Some of these are actually standardized.

• There exist many advanced cryptographic schemes (e.g. identity-based encryption) that are ElGamal-like, but very few that are RSA-like.

• RSA used to be patented (expired long since);

• RSA is a deterministic algorithm.

• ElGamal is a probabilistic (randomized) algorithm.

• RSA only provides onewayness.
  ElGamal provides semantic security.

• Both are group-homomorphic and thus malleable.

• In RSA every key is independent (unique p and q).
  ElGamal has a system parameter (the group) that is shared by many keys.
• As a result:
  RSA can have weak keys (badly generated p and q).
  ElGamal can have bad system parameters (weak group), but every key using that group is equally secure.
• Both are implemented using modular arithmetic, but:
  RSA uses a different arithmetic structure for every key (mod n),
  ElGamal uses the same arithmetic structure for every key within the system (mod p).