Question

Considering the additive homomorphic encryption scheme, which is shown below:

• Encryption

o Suppose k be the random key in range [0, M]

o Represent data x as an integer in range [0, M]

o Compute ciphertext c= (x+k) mod M

• Decryption

o Compute plaintext m=(c-k) mod M

If we change the scheme to the following:

• Encryption

o Suppose k be the random key in range [0, M]

o Represent data x as an integer in range [0, M]

o Compute ciphertext c= x+k

• Decryption

o Compute plaintext m=c-k

What will the problem be?

Answer 1

Answer:

Decryption

o Compute plaintext m=(c-k) mod M

If we change the scheme to the following:

• Encryption

o Suppose k be the random key in range [0, M]

o Represent data x as an integer in range [0, M]

o Compute ciphertext c= x+k

• Decryption

o Compute plaintext m=c-k

What will the problem be?