Sure, let's start with the encryption process:

1. First, we need to calculate the public key of the receiver. The public key is the result of the multiplication of the private key by the generator point G. In this case, the private key is 2 and G is (2,7). So, we need to perform the operation 2*(2,7) on the elliptic curve. The result is the public key of the receiver.

2. Next, we need to calculate the first part of the ciphertext. This is done by multiplying the random integer k by the generator point G. In this case, k is 3 and G is (2,7). So, we need to perform the operation 3*(2,7) on the elliptic curve. The result is the first part of the ciphertext.

3. The second part of the ciphertext is calculated by adding the message point to the result of the multiplication of the random integer k by the public key of the receiver. In this case, the message point is (3,5), k is 3, and the public key of the receiver is the result from step 1. So, we need to perform the operation (3,5) + 3*(public key) on the elliptic curve. The result is the second part of the ciphertext.

Now, let's move on to the decryption process:

1. The receiver can decrypt the message by subtracting the result of the multiplication of their private key by the first part of the ciphertext from the second part of the ciphertext. In this case, the private key is 2, the first part of the ciphertext is the result from step 2 of the encryption process, and the second part of the ciphertext is the result from step 3 of the encryption process. So, we need to perform the operation (second part of the ciphertext) - 2*(first part of the ciphertext) on the elliptic curve. The result is the original message point.

Please note that all the operations on the elliptic curve are performed modulo p, where p is the prime number defining the field of the curve. In this case, p is 11.

Question

Sure, let's start with the encryption process:

1. First, we need to calculate the public key of the receiver. The public key is the result of the multiplication of the private key by the generator point G. In this case, the private key is 2 and G is (2,7). So, we need to perform the operation 2*(2,7) on the elliptic curve. The result is the public key of the receiver.

2. Next, we need to calculate the first part of the ciphertext. This is done by multiplying the random integer k by the generator point G. In this case, k is 3 and G is (2,7). So, we need to perform the operation 3*(2,7) on the elliptic curve. The result is the first part of the ciphertext.

3. The second part of the ciphertext is calculated by adding the message point to the result of the multiplication of the random integer k by the public key of the receiver. In this case, the message point is (3,5), k is 3, and the public key of the receiver is the result from step 1. So, we need to perform the operation (3,5) + 3*(public key) on the elliptic curve. The result is the second part of the ciphertext.

Now, let's move on to the decryption process:

1. The receiver can decrypt the message by subtracting the result of the multiplication of their private key by the first part of the ciphertext from the second part of the ciphertext. In this case, the private key is 2, the first part of the ciphertext is the result from step 2 of the encryption process, and the second part of the ciphertext is the result from step 3 of the encryption process. So, we need to perform the operation (second part of the ciphertext) - 2*(first part of the ciphertext) on the elliptic curve. The result is the original message point.

Please note that all the operations on the elliptic curve are performed modulo p, where p is the prime number defining the field of the curve. In this case, p is 11.

Knowee AI · Accepted Answer

Sure, let's start with the encryption process:

1. First, we need to calculate the public key of the receiver. The public key is the result of the multiplication of the private key by the generator point G. In this case, the private key is 2 and G is (2,7). So, we need to perform the operation 2*(2,7) on the elliptic curve. The result is the public key of the receiver.

2. Next, we need to calculate the first part of the ciphertext. This is done by multiplying the random integer k by the generator point G. In this case, k is 3 and G is (2,7). So, we need to perform the operation 3*(2,7) on the elliptic curve. The result is the first part of the ciphertext.

3. The second part of the ciphertext is calculated by adding the message point to the result of the multiplication of the random integer k by the public key of the receiver. In this case, the message point is (3,5), k is 3, and the public key of the receiver is the result from step 1. So, we need to perform the operation (3,5) + 3*(public key) on the elliptic curve. The result is the second part of the ciphertext.

Now, let's move on to the decryption process:

1. The receiver can decrypt the message by subtracting the result of the multiplication of their private key by the first part of the ciphertext from the second part of the ciphertext. In this case, the private key is 2, the first part of the ciphertext is the result from step 2 of the encryption process, and the second part of the ciphertext is the result from step 3 of the encryption process. So, we need to perform the operation (second part of the ciphertext) - 2*(first part of the ciphertext) on the elliptic curve. The result is the original message point.

Please note that all the operations on the elliptic curve are performed modulo p, where p is the prime number defining the field of the curve. In this case, p is 11.

Choose the Elliptic curve with prime p = 11 , a = 1, b = 3 Generator G = (2, 7) and Message=(3,5), receiver private key is 2 and sender random integer k = 3 Compute the encryption anddecryption processes completely

Question

Solution

Similar Questions

Upgrade your grade with Knowee