The given text is a decryption process using the Knapsack cipher. The number 74 is encrypted using the public key 7 and modulo 59, resulting in the cipher text 46.

The superincreasing sequence (2,3,7,15,29) is then used to decrypt the cipher text.

First, the largest number in the sequence that is less than or equal to the cipher text is subtracted from the cipher text. This is done repeatedly until the cipher text is reduced to 0.

In this case, 29 is subtracted from 46 to get 17. Then, 15 is subtracted from 17 to get 2.

The positions in the sequence of the numbers that were subtracted form the decrypted message. In this case, the positions are 5 (for 29) and 4 (for 15).

So, the decrypted message is (5,4).

Question

The given text is a decryption process using the Knapsack cipher. The number 74 is encrypted using the public key 7 and modulo 59, resulting in the cipher text 46.

The superincreasing sequence (2,3,7,15,29) is then used to decrypt the cipher text.

First, the largest number in the sequence that is less than or equal to the cipher text is subtracted from the cipher text. This is done repeatedly until the cipher text is reduced to 0.

In this case, 29 is subtracted from 46 to get 17. Then, 15 is subtracted from 17 to get 2.

The positions in the sequence of the numbers that were subtracted form the decrypted message. In this case, the positions are 5 (for 29) and 4 (for 15).

So, the decrypted message is (5,4).

Knowee AI · Accepted Answer

The given text is a decryption process using the Knapsack cipher. The number 74 is encrypted using the public key 7 and modulo 59, resulting in the cipher text 46.

The superincreasing sequence (2,3,7,15,29) is then used to decrypt the cipher text.

First, the largest number in the sequence that is less than or equal to the cipher text is subtracted from the cipher text. This is done repeatedly until the cipher text is reduced to 0.

In this case, 29 is subtracted from 46 to get 17. Then, 15 is subtracted from 17 to get 2.

The positions in the sequence of the numbers that were subtracted form the decrypted message. In this case, the positions are 5 (for 29) and 4 (for 15).

So, the decrypted message is (5,4).

Decrypt 74: 𝐶 ′ = 74 ⋅ 7 ( mod 59 ) = 518 ( mod 59 ) = 46 C ′ =74⋅7 (mod 59)=518 (mod 59)=46 Using the superincreasing sequence ( 2 , 3 , 7 , 15 , 29 ) (2,3,7,15,29): 46 − 29 = 17 17 − 15 = 2 46−29=17 17−15=2

Question

𝐶 ′

74 ⋅ 7 ( mod 59 )

518 ( mod 59 )

46 − 29

17 17 − 15

Solution

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