Applied Cryptography - Public Key Cryptography

Front 1

What are the two main advantages of public key cryptography compared with symmetric techniques?

Back 1

1) In asymmetric encryption, there is no secret channel necessary for the exchange of the public key

2) Asymmetric ciphers creates lesser-key management problems than symmetric ciphers

Front 2

What are the two limitations of public key cryptography compared with symmetric techniques?

Back 2

1) Asymmetric ciphers takes about 1000 times more CPU time to process an asymmetric encryption or decryption than a symmetric encryption or decryption

2) Data can only be encrypted using the public key and only decrypted using the private key

Front 3

Using an example, explain both of the major limitations of symmetric encryption

Back 3

1) Key Distribution Problem - How do we reach a point where both parties have the same key

2) Not suitable for authentication since receiver can forge message and claim it came from the sender

Front 4

Many communications systems use a combination of public key encryption and symmetric encryption. Why is this the case and how does it work?

Back 4

This type of hybrid cryptosystem takes advantage of the convenience of asymmetric encryption and the efficiency of symmetric encryption.

Symmetric encryption is efficient but does not provide a convenient way of sharing a key.

Asymmetric encryption in the other hand provides a convenient key sharing mechanism but encryption is not as efficient as symmetric encryption.

Thus by using symmetric encryption to encrypt only the session key and asymmetric encryption for the rest of the communication, this hybrid cryptosystem leverage the best of both encryption methods

Front 5

If two numbers are relatively prime, what does this mean? Give an example.

Back 5

Two numbers a,b are relatively prime if they have no common divisors apart from 1

Front 6

If x is a "primitive root" of y, what does this mean

Back 6

This means that

x mod y, x^2 mod y^2, x^n mod y^n

has the set of numbers in {0,1,...,q-1} that are relatively prime to q

Front 7

What is the discrete logarithm problem?

Back 7

The inverse problem to exponentiation is to find x such that y = g^x (mod p)

Front 8

Explain why the security of RSA depends on the difficulty of factoring large numbers

Back 8

RSA uses the large number obtained from factorizing as part of its public key. Therefore the private key of RSA are the two prime numbers specified which only the owner should know. The public key should be difficult to break hence the need for the difficulty of factoring large numbers

Front 9

What is the purpose of the Diffie-Hellmann public key technique? Briefly describe it

Back 9

A public key technique for exchanging secret keys.

The secret key is calculated by both parties.

Requires some global public parameters

Based on difficulty in solving for x where a = b^x (mod c) ... a,b,c are known

Front 10

Briefly outline ElGamal encryption

Back 10

An asymmetric key encryption algorithm for public-key crytography which is based on the Diffie-Hellman key exchange.

Front 11

Give a reason why Elliptic Curve Cryptography is sometimes chosen for use instead of RSA

Back 11

RSA uses integer or polynomial arithmetic with very large numbers/polynomials. This imposes a significant load in storing and processing keys and messages.

ECC however offers the same security as RSA with smaller bit sizes and lower processing and memory overhead.

Front 12

Discuss the significance of key size in cryptography? In your answer, comment on both symmetric and public key encryption

Back 12

Key length is directly proportional to security. In modern cryptosystems, key length is measured in bits and each bit of a key increases the difficulty of a brute-force attack exponentially.

Public key encryption requires rather long keys around 1024 bits whereas symmetric encryptions, both block and stream, are able to use shorter keys around 256 bits.