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Problem Brief

Encryption Validity

FULLTIMEINTERNOA

Encryption is the process of converting information algorithmically so that a valid recipient can read the information before it is no longer a valuable secret. This is its validity period. An attacker has limited processing power and can only test a certain number of keys per second. This is the instruction count. The size of the universe of keys divided by the instruction count gives the average time to find a message key. To achieve a balance between the processing power for encryption/ decryption and the strength of the encryption, the validity period of the message must be taken into consideration.

Given the number of keys, a hijacker can test per second, determine if the encrypted information should remain confidential throughout its validity period. Each test will return two items of information as integers:

  • Can a hijacker crack the code within the period? (1 if true, 0 if false)
  • The strength of the encryption, that is, the number of keys that must be tested to break the encryption.

    • The strength of the encryption is determined as follows:

  • Keys is a list of positive integers, keys[i], that act as keys.
  • The degree of divisibility of an element is the number of elements in the set keys that are greater than 1 and are divisors of the element, i.e element modulo divisor = 0.
  • The element m that has the maximum number of divisors (or degree of divisibility) in keys is used to determine the strength of the encryption.
  • The strength of the encryption is defined as (the degree of divisibility of m) * 10^5

    • Function Description

    Complete the function encryptionValidity.

    encryptionValidity has the following parameter(s):

  • int instructionCount: the number of keys the hijacker can test per second
  • int validityPeriod: the number of seconds the message must be protected.
  • int keys[n]: the keys for encryption/decryption

    • 1Example 1

    Input
    instructionCount = 1000, validityPeriod = 10000, keys = [2, 4, 8, 2]
    Output
    [1, 400000]
    Explanation
    The element m that has the maximum number of divisors is 8 ad its degree of divisibility is 4. The encryption strength is 4 * 10^5 = 400,000. The hijacker can perform instructionCount = 1,000 calculations per second. During the total validityPeriod = 10,000 seconds, the hijacker can test 1000 * 1000 = 1000000 = 10^7 keys. Thus, there is sufficient time for the key to be determined and the message decrypted before its validity expires. The first value in the return array is 1 because the message can be decrypted. The return array is [1, 400000] because the hijacker can decrypt the message in time, and the strength of the encryption is 400000.

    Constraints

    Limits and guarantees your solution can rely on.

  • 1 <= instructionCount, validityPeriod <= 10^8
  • 1 <= 1 <= n <= 105
  • 1 <= 1<= keys[i] <= 105
    • public int[] encryptionValididy(int instructionCount, int validityPeriod, int[] keys) {
  // write your code here
}
    Input

    instructionCount

    1000

    validityPeriod

    10000

    keys

    [2, 4, 8, 2]

    Output

    [1, 400000]

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