Information and network security 32 principles of public key cryptosystems

Information and Network Security:32
Principles of Public-Key Cryptosystems
Prof Neeraj Bhargava
Vaibhav Khanna
Department of Computer Science
School of Engineering and Systems Sciences
Maharshi Dayanand Saraswati University Ajmer

• Stallings Figure “Public-Key Cryptosystems: Secrecy and Authentication”
illustrates the essential elements of a public-key encryption scheme.
• Note that public-key schemes can be used for either secrecy or authentication, or
both (as shown here). There is some source A that produces a message in
plaintext X The M elements of X are letters in some finite alphabet.
• The message is intended for destination B. B generates a related pair of keys: a
public key, PUb, and a private key, PRb. PRb is known only to B, whereas PUb is
publicly available and therefore accessible by A.
• With the message X and the encryption key PUb as input, A forms the ciphertext
Y = E(PUb, X) The intended receiver, in possession of the matching private key, is
able to invert the transformation: X = D(PRb, Y) An adversary, observing Y and
having access to PUb, but not having access to PRb or X, must attempt to recover
X and/or PRb.

• This provides confidentiality. Can also use a public-key encryption to
provide authentication: Y = E(PRa, X); X = D(PUa, Y) To provide both the
authentication function and confidentiality have a double use of the public-
key scheme (as shown here): Z = E(PUb, E(PRa, X)) X = D(PUa, D(PRb, Z))
• In this case, separate key pairs are used for each of these purposes. The
receiver owns and creates secrecy keys, sender owns and creates
authentication keys.
• In practice typically DO NOT do this, because of the computational cost of
public-key schemes. Rather encrypt a session key which is then used with a
block cipher to encrypt the actual message, and separately sign a hash of
the message as a digital signature - this will be discussed more later.

Public-Key Applications
• can classify uses into 3 categories:
• encryption/decryption (provide secrecy)
• digital signatures (provide authentication)
• key exchange (of session keys)
• some algorithms are suitable for all uses, others are
specific to one

• Public-key systems are characterized by the use of a cryptographic
type of algorithm with two keys.
• Depending on the application, the sender uses either the sender’s
private key or the receiver’s public key, or both, to perform some type
of cryptographic function.
• In broad terms, we can classify the use of public-key cryptosystems
into the three categories:
• • Encryption/decryption: The sender encrypts a message with the
recipient’s public key.

• Digital signature: The sender “signs” a message with its private key,
either to the whole message or to a small block of data that is a
function of the message.
• • Key exchange: Two sides cooperate to exchange a session key.
Several different approaches are possible, involving the private key(s)
of one or both parties.
• Some algorithms are suitable for all three applications, whereas
others can be used only for one or two of these applications.

Public-Key Requirements
• Public-Key algorithms rely on two keys where:
• it is computationally infeasible to find decryption key knowing only algorithm
& encryption key
• it is computationally easy to en/decrypt messages when the relevant
(en/decrypt) key is known
• either of the two related keys can be used for encryption, with the other used
for decryption (for some algorithms)
• these are formidable requirements which only a few algorithms have
satisfied

Public-Key Requirements
• need a trapdoor one-way function
• one-way function has
• Y = f(X) easy
• X = f–1(Y) infeasible
• a trap-door one-way function has
• Y = fk(X) easy, if k and X are known
• X = fk
–1(Y) easy, if k and Y are known
• X = fk
–1(Y) infeasible, if Y known but k not known
• a practical public-key scheme depends on a suitable
trap-door one-way function

Security of Public Key Schemes
like private key schemes brute force exhaustive
search attack is always theoretically possible
but keys used are too large (>512bits)
security relies on a large enough difference in
difficulty between easy (en/decrypt) and hard
(cryptanalyse) problems
more generally the hard problem is known, but is
made hard enough to be impractical to break
requires the use of very large numbers
hence is slow compared to private key schemes

Assignment
• Explain the Principles of Public-Key Cryptosystems.

Information and network security 32 principles of public key cryptosystems

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Information and network security 32 principles of public key cryptosystems