The concept of public key cryptography evolved from an attempt to attack two of themost difficult problems associated with symmetric encryption.

**PRINCIPLES OF PUBLIC KEY
CRYPTOGRAPHY**

The
concept of public key cryptography evolved from an attempt to attack two of
themost difficult problems associated with symmetric encryption.

·
Key distribution under symmetric key encryption
requires either (1) that two communicants already share a key, which someone
has been distributed to them or (2) the use of a key distribution center.

·
Digital signatures.

**1. Public key cryptosystems**

Public
key algorithms rely on one key for encryption and a different but related key
for decryption.

These
algorithms have the following important characteristics:

·
It is computationally infeasible to determine the
decryption key given only the knowledge of the cryptographic algorithm and the
encryption key.

In
addition, some algorithms, such as RSA, also exhibit the following
characteristic:

· Either of
the two related keys can be used for encryption, with the other used for
decryption.

The
essential steps are the following:

·
Each user generates a pair of keys to be used for
encryption and decryption of messages.

·
Each user places one of the two keys in a public
register or other accessible file. This is the public key. The companion key is
kept private.

·
If A wishes to send a confidential message to B, A
encrypts the message using B‟s public key.

·
When B receives the message, it decrypts using its
private key. No other recipient can decrypt the message because only B knows
B‟s private key.

With this
approach, all participants have access to public keys and private keys are
generated locally by each participant and therefore, need not be distributed.
As long as a system controls its private key, its incoming communication is
secure.

Let the
plaintext be X=[X1, X2, X3, …,Xm] where m is the number of letters in some
finite alphabets. Suppose A wishes to send a message to B. B generates a pair
of keys: a public key KU_{b} and a private key KR_{b}. KR_{b}
is known only to B, whereas KU_{b} is publicly available and therefore
accessible by A.

With the
message X and encryption key KU_{b} as input, A forms the cipher text

**Y=[Y1, Y2, Y3, … Yn]., i.e., Y=E
KU _{b}(X)**

The
receiver can decrypt it using the private key KR_{b}. i.e., X=D KR_{b}().
The encrypted message serves as a **digital
signature.**

It is
important to emphasize that the encryption process just described does not
provide confidentiality. There is no protection of confidentiality because any
observer can decrypt the message by using the sender‟s public key.

It is however,
possible to provide both the authentication and confidentiality by a double use
of the public scheme.

Initially,
the message is encrypted using the sender‟s private key. This provides the
digital signature. Next, we encrypt again, using the receiver‟s public key. The
final ciphertext can be decrypted only by the intended receiver, who alone has
the matching private key. Thus confidentiality is provided.

**2 Requirements for public key
cryptography**

It is
computationally easy for a party B to generate a pair [KU_{b} , KR_{b}].

It is
computationally easy for a sender A, knowing the public key and the message to
be encrypted M, to generate the corresponding ciphertext: C=EKU_{b}(M).

It is
computationally easy for the receiver B to decrypt the resulting ciphertext
using the private key to recover the original message: M = DKR_{b} (C)
= DKR_{b} [EKU_{b} (M)]

It is
computationally infeasible for an opponent, knowing the public key KU_{b},
to determine the private key KR_{b}.

It is
computationally infeasible for an opponent, knowing the public key KU_{b},
and a ciphertext C, to recover the original message M.

The
encryption and decryption functions can be applied in either order: M = EKU_{b} [DKR_{b} (M) = DKU_{b}
[EKR_{b} (M)]

**Public key cryptanalysis**

Public
key encryption scheme is vulnerable to a brute force attack. The counter
measure is to use large keys.

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Cryptography and Network Security : Principles of Public Key Cryptography |

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