Public-Key Cryptography - Topic 4 Flashcards
Problems with symmetric cryptography
non-repudiation cannot be achieved without the involvement of a third trusted party
A different key is required for each pair of users, or even per encryption - session key
- An n user system requires n*(n-1)/2 keys - the n^2 problem
- Generating and distributing is hard
- Maintaining security for keys already distributed also a challenge
What is public key cryptography (PKC)?
Keys come in pairs - one public, one private; it is infeasible to generate one key from the other; encryption produced by using one of the keys could only be reversed by the other key in the pair.
Easy to generate keys (public and private)
Hard to compute private key from public key
Easy to encrypt and decrypt if the right key is known
Hard to recover plaintext from ciphertext without the right key
What is a one-way function?
C = f(M) “Easy”
C = f-1(M) “Infeasible”
Trap-door one way function
C = f(K,M) “Easy” if K & M known
M = f-1(K, C) “Easy” if K & C known
M = f-1(K, C) “Infeasible” if K not know, C known
What are some commonly used one-way functions?
Integer factorisation (used in RSA)
- Finding prime factors of a large integer: n=p*q
- n is known
- find p and q
Discrete logarithm (Used in DSS/DSA (Digital Signature Standard/Digital Signature Algorithm) and DH (Diffie-Helman))
- a^x = b mod p
- a, b and p are known
- finding an integer, x, satisfying the equation
Which three algorithms work for both encryption and decryption signatures
RSA, ElGamal and Rabin
How can you achieve confidentiality (Secrecy) with PKC
Encrypted with a public key and decrypted with a private key, should only be used for short messages, like secure transportation of a symmetrical key
How can you achieve authenticity with PKC?
Signature is signed on the hash value of M, i.e. H(M), and a timestamp should be included
Message is encoded with a private key and signed with the hash of M, then decoded with a public key and M to verified signedH(M)
What is RSA commonly used for?
Confidentiality
- Encrypt the plaintext M using recipient’s public key;
- As only the recipient has the corresponding private key, so M can only be read by the recipient
Digital Signature
- message authenticity (message origin authenticity and content integrity) and non-repudiation of message origin
- Sign M (actually the hash of M) using sender’s private key;
- As only the sender has this private key, so the message must have been signed by the sender
What type of cipher is RSA?
A block cipher
What are the three functions of RSA?
Key generation
Encryption
Decryption
Encryption and decryption use the same function with different keys
