Computer Networks

Need for layered designing :
1. The first computer networks were designed with the hardware as the main concern and the software as an afterthought.
2. This strategy no longer works.
3. Network software is now highly structured.
4. To reduce their design complexity, most networks are organized as a stack of layers or levels, each one built upon the one below it.
5. The number of layers, the name of each layer, the contents of each layer, and the function of each layer differ from network to network.
6. The purpose of each layer is to offer certain services to the higher layers while hiding those layers from the details of how the offered services are actually implemented.
7. In a sense, each layer is a kind of virtual machine, offering certain services to the layer above it.
8. Therefore Layered Architecture provides Flexibility to modify and develop network services.
9. Let us consider the example: Given below is a three-layer network. When layer n on one machine carries on a conversation with layer n on another machine, the rules and conventions used in this conversation are collectively known as the layer n protocol.

By caching data, operating systems want to minimize delay to fetch next data or instruction. Cache mechanisms use principle of locality to bring in data which may be accessed next, based on currently accessed data, for faster access. There are two locality principles:
Temporal locality:  data which is used recently may be used again in near future.
Spatial locality:  data near to current accessed data may be accessed in near future.
There are three mapping techniques : Direct mapping, fully associative and set associative mapping.
Direct mapping:
In a direct mapped cache, lower order line address bits are used to access the directory. Since multiple line addresses map into the same location in the cache directory, the upper line address bits (tag bits) must be compared with the directory address to ensure a hit. If a comparison is not valid, the result is a cache miss, or simply a miss. The address given to the cache by the processor actually is subdivided into several pieces, each of which has a different role in accessing data.

Fully associative:
In fully associative mapping, when a request is made to the cahce, the requested address is compared in a directory against all entries in the directory. If the requested address is found (a directory hit), the corresponding location in the cache is fetched and returned to the processor; otherwise, a miss occurs. 

Set associative mapping:
The set associative cache operates in a fashion somewhat similar to the direct-mapped cache. Bits from the line address are used to address a cache directory. However, now there are multiple choices: two, four, or more complete line addresses may be present in the directory. Each of these line addresses corresponds to a location in a sub-cache. The collection of these sub-caches forms the total cache array. In a set associative cache, as in the direct-maped cache, all of these sub-arrays can be accessed simultaneously, together with the cache directory. If any of the entries in the cache directory match the reference address, and there is a hit, the particular sub-cache array is selected and outgated back to the processor. 

RSA Cryptosystem
 The system was invented by three scholars Ron Rivest, Adi Shamir, and Len Adleman and hence, it is termed as RSA cryptosystem.
Generation of RSA Key Pair
Each person or a party who desires to participate in communication using encryption needs to generate a pair of keys, namely public key and private key. The process followed in the generation of keys is described below −

• Generate the RSA modulus (n)

  • Select two large primes, p and q.

  • Calculate n=p*q. For strong unbreakable encryption, let n be a large number, typically a minimum of 512 bits.

• Find Derived Number (e)

  • Number e must be greater than 1 and less than (p − 1)(q − 1).

  • There must be no common factor for e and (p − 1)(q − 1) except for 1. In other words two numbers e and (p – 1)(q – 1) are coprime.

• Form the public key

  • The pair of numbers (n, e) form the RSA public key and is made public.

  • Interestingly, though n is part of the public key, difficulty in factorizing a large prime number ensures that attacker cannot find in finite time the two primes (p & q) used to obtain n. This is strength of RSA.

• Generate the private key

  • Private Key d is calculated from p, q, and e. For given n and e, there is unique number d.

  • Number d is the inverse of e modulo (p - 1)(q – 1). This means that d is the number less than (p - 1)(q - 1) such that when multiplied by e, it is equal to 1 modulo (p - 1)(q - 1).

  • This relationship is written mathematically as follows −

ed = 1 mod (p − 1)(q − 1)

The Extended Euclidean Algorithm takes p, q, and e as input and gives d as output.

Example:
An example of generating RSA Key pair is given below. (For ease of understanding, the primes p & q taken here are small values. Practically, these values are very high).

• Let two primes be p = 7 and q = 13. Thus, modulus n = pq = 7 x 13 = 91.

• Select e = 5, which is a valid choice since there is no number that is common factor of 5 and (p − 1)(q − 1) = 6 × 12 = 72, except for 1.

• The pair of numbers (n, e) = (91, 5) forms the public key and can be made available to anyone whom we wish to be able to send us encrypted messages.

• Input p = 7, q = 13, and e = 5 to the Extended Euclidean Algorithm. The output will be d = 29.

• Check that the d calculated is correct by computing −

de = 29 × 5 = 145 = 1 mod 72

• Hence, public key is (91, 5) and private keys is (91, 29).

Encryption and Decryption

Once the key pair has been generated, the process of encryption and decryption are relatively straightforward and computationally easy.

Interestingly, RSA does not directly operate on strings of bits as in case of symmetric key encryption. It operates on numbers modulo n. Hence, it is necessary to represent the plaintext as a series of numbers less than n.

RSA Encryption

• Suppose the sender wish to send some text message to someone whose public key is (n, e).

• The sender then represents the plaintext as a series of numbers less than n.

• To encrypt the first plaintext P, which is a number modulo n. The encryption process is simple mathematical step as −

C = Pe mod n

• In other words, the ciphertext C is equal to the plaintext P multiplied by itself e times and then reduced modulo n. This means that C is also a number less than n.

• Returning to our Key Generation example with plaintext P = 10, we get ciphertext C −

C = 105 mod 91

RSA Decryption

• The decryption process for RSA is also very straightforward. Suppose that the receiver of public-key pair (n, e) has received a ciphertext C.

• Receiver raises C to the power of his private key d. The result modulo n will be the plaintext P.

Plaintext = Cd mod n

• Returning again to our numerical example, the ciphertext C = 82 would get decrypted to number 10 using private key 29 −

Plaintext = 8229 mod 91 = 10