Public Key Property Page

Public key cryptography is based upon the RSA algorithm, which was invented in 1977 by Ronald L. Rivest, Adi Shamir, and Leonard M. Adleman. The RSA algorithm works by taking two large prime numbers, p and q, and finding their product n = pq; n is known as the modulus. Additionally, a public value, e, is selected when the key pair is created; e is known as the exponent. An encrypted message c is computed by raising a message m to the e power, modulo n, as described below:

c = m^e mod n

To decrypt c and retrieve the original message m, the encrypted message is raised to the d power modulo n; d is known as the private key, as described below:

m = c^d mod n

The mathematical relationship between e and d ensures that the algorithm correctly recovers the original message m, since

c^d = (m^e)^d = m^1 = m mod n

The modulus n is chosen so that it is less than m, thus

m mod n = m, so that
c^d = m

The RSA algorithm works because if you know p, q, and e, it is easy to compute d, but if you know only n and e it is more difficult to determine d. The private key d is actually the inverse of e, modulo the product of (p-1) and (q-1) as described below:

ed = 1 mod (p-1)(q-1)

Thus, the private key is constructed using a modulus of (p-1)(q-1), but encryption and decryption is performed using a modulus of n = pq.

A description of each of the fields in this property page follows. None of the fields are editable.

Key Type
This field identifies the type of key. The Certificate Server utilizes public key cryptography based on the RSA algorithm, of which the key type is RSA Encryption.

Key Size
This field displays the size in bits of the modulus for the key pair.

Exponent
The public value that a plaintext message is raised to, modulo the modulus that produces the encrypted message. The Certificate Server uses a public key value of 65537, or 10001 in hexidecimal notation.

Modulus
The value n in the above discussion. See above.

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