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What is the definition of a computationally hard problem and how does it relate to the field of cryptography?

A computationally hard problem is a task that is difficult for a computer to solve quickly. In the field of cryptography, computationally hard problems are used to create secure encryption methods. By using algorithms that are difficult for computers to crack, cryptography ensures that sensitive information remains protected from unauthorized access.


What requirement must a public key cryptosystems fulfill to be a secure algorithm?

1. It is computationally easy for a party B to generate a pair(Public key KUb, Private key KRb) 2. It is computationally easy for a sender A, knowing the public key and the message to be encrypted , M, to generate the corresponding ciphertext: C=EKUb(M) 3. It is computationally easy for the receiver B to decrypt the resulting ciphertext using the private key to recover the original message : M=DKRb(C)=DKRb[EKUb(M)] 4. It is computationally infeasible for an opponent , knowing the public key,KUb,to determine the private key,KRb. 5. It is computationally infeasible for an opponent , knowing the public key,KUb, and a ciphertext, C, to recover the original message,M. 6. The encryption and decryption functions can be applied in either order: M=EKUb[DKRb(M)]=DKUb [EKRb(M)]


What requirements must a public key cryptosystems fulfill to be a secure algorithm?

1. It is computationally easy for a party B to generate a pair(Public key KUb, Private key KRb) 2. It is computationally easy for a sender A, knowing the public key and the message to be encrypted , M, to generate the corresponding ciphertext: C=EKUb(M) 3. It is computationally easy for the receiver B to decrypt the resulting ciphertext using the private key to recover the original message : M=DKRb(C)=DKRb[EKUb(M)] 4. It is computationally infeasible for an opponent , knowing the public key,KUb,to determine the private key,KRb. 5. It is computationally infeasible for an opponent , knowing the public key,KUb, and a ciphertext, C, to recover the original message,M. 6. The encryption and decryption functions can be applied in either order: M=EKUb[DKRb(M)]=DKUb [EKRb(M)]


What the computer was made for?

Solving computationally intensive problems that were beyond the capability of human computers to solve.


Is the problem of determining the polynomial reducibility of a given function computationally feasible?

Determining the polynomial reducibility of a given function is computationally feasible, but it can be complex and time-consuming, especially for higher-degree polynomials. Various algorithms and techniques exist to tackle this problem, but it may require significant computational resources and expertise to efficiently solve it.


How are fractals apart of math?

Fractals are generated from recursive mathematical equations, this is why you can zoom-in on them infinitely and they will continue to repeat themselves (this is also why they are so computationally intensive)


What characteristic are needed to secure hash function?

1. H can be applied to a block of data of any size. 2. H produces a fixed-length output. 3. H(x) is relatively easy to compute for any given x, making both hardware and software implementations practical. 4. For any given value h, it is computationally infeasible to find x such that H(x) = h. This is sometimes referred to in the literature as the one-way property. 5. For any given block x, it is computationally infeasible to find y ≠ x with H(y) = H(x). 6. It is computationally infeasible to find any pair (x, y) such that H(x) = H(y).


What is the difference between an unconditionally secure cipher and a computationally secure cipher?

unconditional security no matter how much computer power or time is available, the cipher cannot be broken since the ciphertext provides insufficient information to uniquely determine the corresponding plaintext computational security given limited computing resources (eg time needed for calculations is greater than age of universe), the cipher cannot be broken


What does it mean for a system to be Turing complete?

A system is considered Turing complete if it can simulate any algorithm or computation that a Turing machine can perform. This means that the system has the ability to solve any problem that is computationally solvable.


The efficiency of using recursive function rather than using ordinary function?

For some algorithms recursive functions are faster, and there are some problems that can only be solved through recursive means as iterative approaches are computationally infeasible.


What is soft computer?

Soft computing is a term applied to a field within computer science which is characterized by the use of inexact solutions to computationally hard tasks. Soft computing covers similar topics of computational intelligence, natural computing, and organic computing.


What is soft computing methodology?

Soft computing is a term applied to a field within computer science which is characterized by the use of inexact solutions to computationally hard tasks. Soft computing covers similar topics of computational intelligence, natural computing, and organic computing.