Breaking A Message Encrypted With Private-Key Cryptography: Lab Analysis
To break a message encrypted with private-key cryptography, it requires either to exploit a weakness in the encryption algorithm, or to try an exhaustive search of all possible keys (brute force method). Increase in key size is an e ective remedy for this. If the key is large enough (e.g., 128 bits), such a search would take a very long time (few years), even with very powerful computers. Private-key methods are ecient and dicult to break[21].
However, one major drawback is that the key must be exchanged between the sender and recipient beforehand, raising the issue of how to protect the secrecy of the key.
When the President of the United States exchanges launch codes with a nuclear weapons site under his command, the key is accompanied …show more content…
Because it is a one way function, the only way to reverse the process is to use one of the two original numbers. However, assuming the two original numbers are very large, their product is even bigger; it would be impractical for an adversary to try every possibility to determine what the two original numbers were.
3.0.2 Galois Field
Galois Field, which is named after Evariste Galois, otherwise called nite eld, is the eld in which there exists nitely numerous components. It is especially valuable in translating machine information because they are represented in binary structures.
Computer information consists of two binary numbers, 0 and 1, They are the segments in Galois eld whose number of element is two. Representing to information as a vector in a Galois Field permits scienti c operations to scramble information e ectively. [2].
There are many cryptographic algorithms using GF among them, the AES algorithm uses the GF(2
8
). The data byte can be characterized using a polynomial representation of GF(2
8
) .
Arithmetic operation are implemented di erently in eld, an addition can be im- plementedas bit-wise XOR operation. In Galois eld, the multiplication product of
However, one major drawback is that the key must be exchanged between the sender and recipient beforehand, raising the issue of how to protect the secrecy of the key.
When the President of the United States exchanges launch codes with a nuclear weapons site under his command, the key is accompanied …show more content…
Because it is a one way function, the only way to reverse the process is to use one of the two original numbers. However, assuming the two original numbers are very large, their product is even bigger; it would be impractical for an adversary to try every possibility to determine what the two original numbers were.
3.0.2 Galois Field
Galois Field, which is named after Evariste Galois, otherwise called nite eld, is the eld in which there exists nitely numerous components. It is especially valuable in translating machine information because they are represented in binary structures.
Computer information consists of two binary numbers, 0 and 1, They are the segments in Galois eld whose number of element is two. Representing to information as a vector in a Galois Field permits scienti c operations to scramble information e ectively. [2].
There are many cryptographic algorithms using GF among them, the AES algorithm uses the GF(2
8
). The data byte can be characterized using a polynomial representation of GF(2
8
) .
Arithmetic operation are implemented di erently in eld, an addition can be im- plementedas bit-wise XOR operation. In Galois eld, the multiplication product of