Question

What is a decryption exponent for an RSA public key (n,e)?

1) An integer d with the property that ade = a (mod n) for all integers a that are relatively prime to n.
2) An integer d with the property that ade = a (mod e) for all integers a that are relatively prime to e.
3) An integer d with the property that ade = a (mod n) for all integers a that are relatively prime to e.
4) An integer d with the property that ade = a (mod e) for all integers a that are relatively prime to n.

Answer 1

The decryption exponent for an RSA public key is an integer d that satisfies the equation a^de = a (mod n) for integers a relatively prime to n. It is part of the private key in the RSA algorithm and allows for decryption of data encrypted with the public key.

Step-by-step explanation:

The decryption exponent for an RSA public key (n,e) is a crucial part of the RSA algorithm, which is used for secure data transmission. The correct decryption exponent is option 1: An integer d with the property that ade = a (mod n) for all integers a that are relatively prime to n. This means that for any integer a that does not share any common factors with n other than 1, raising a to the power of d and then to the power of e will result in a when taken modulo n.

The formula reflects the nature of the RSA encryption and decryption process, where e is the encryption exponent used in the public key, and d is the decryption exponent used in the private key. These exponents are related mathematically and are part of the key pair in the RSA algorithm. The ciphertext is created by raising the plaintext to the power of e and taking modulo n, and it is decrypted by raising the ciphertext to the power of d and again taking modulo n.