Page 50 - DCAP516_COMPUTER_SECURITY

Computer Security

Notes RSA parameters:
(i) Choose two large primes, and, (typically greater than).
(ii) Compute and.
(iii) Choose a number relatively prime to and call it.

(iv) Find such that mod z.
RSA encryption and decryption: Divide the plaintext (regarded as a bit string) into blocks, so
that each plaintext message, falls in the interval.

To encrypt, computer mod n. So the public encryption key consists of the pair (e, n).
To decrypt, computer mod n. So the private decryption key consists of the pair (d, n).
If the cryptanalyst could factor the (publicly known), he could then find and, and from these.
With knowledge of and, and hence the private key can be found.
The security of the RSA method is based on the difficulty of factoring large numbers. Using best
known algorithm and a computer with a 1-sec instruction time:

Factoring a 200-digit number requires 4 billion years of computer time.
Factoring a 500-digit number requires years of computer time.

!
Caution In practice, RSA is too slow for actually encrypting large volumes of data.
So most RSA-based systems use public-key cryptography primarily for distributing
one-time session keys for use with DES, IDEA, or similar algorithms.

Other Ppublic-key Algorithms

The three major categories are those based on the difficulty of:

factoring large numbers,
computing discrete logarithms, and
determining the contents of a knapsack from its weight.

4.6 Uses of Encryption

Encryption can be used in several different ways as summarized below. In addition to the
characteristics of a particular encryption algorithm that are required to support a given use, the
algorithm itself is generally integrated into a larger system that handles other aspects of the
area to which encryption is being applied to ensure correct use and to minimize the visibility of
the use of encryption. For example, if encryption is used for file protection, directories may also
be protected and keys are managed on behalf of users so that normal file access does not change
much.

Message Encryption: This is the traditional use of cryptography. Blocks of text are encrypted
as units. This is the normal way in which email is encrypted.

Digital Signatures: Authenticating who sent a message is often useful. In the public key
scheme, the secret decryption key can be used to encrypt, allowing the non-secret encryption
key to be used to decrypt. Since only the secret key holder is presumed to have the secret
key, only he could have encrypted/signed the message. Anyone can check the digital

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