What is Asymmetric Cryptography?
- Some algorithms use a pair of keys
- If one key is used for encryption, the other is used for decryption
- You can generate a pair of keys, but one key cannot be obtained from the other in reasonable computation time
- One key is kept private, one key is made public (K- and K+
What kind of arithmetic does RSA encryption rely on?
Modular Arithmetic
Why is RSA Secure?
- If you know the public key (n, e) and want to determine d, you would have to compute factors of n which is a hard problem
What is the purpose of creating a signature by computing a message digest instead of encryption with a private / public key?
Computation of a signature by applying a private key to a long message is computationally expensive
How is a fixed-length “fingerprint” computed?
Hash function H is applied to message m, giving a fixes size message digest H(m)
How does a signed message digest work?
- Instead of signing entire message, sign only hash result
- Bob sends message and signed digest
- Alice received message and computes message digest
- Alice received signed message digest and computed message digest
- If signed digest and calculated digest are equal, message is considered signed
What properties does a secure hash function have?
- Given x, it is computationally infeasible to find m such that H(m) = x
- Given m, it is computationally infeasible to find m’ != m such that H(m) = H(m’)
Provide some examples of Hash Function Algorithms
- MD5 (compute 128-bit message digest in 4-step process)
- SHA1 (160 bit digest), SHA-256, SHA-512
What is the main benefit of using a Message Authentication Code (MAC)?
- It is faster, since no encryption is necessary
What is a Message Authentication Code (MAC)?
- Alternative to signed message digest
- Shared secret s used between parties
- Hash is computed on m + s
- Bob sends message m and h = H(m+s)
- Alice receives (m, h) and computes H(m+s)
- If h=H(m+s) message is considered signed
Provide three examples of authentication encryption
- MAC-then-Encrypt (IPSec)
- Encrypt-then-MAC (SSL)
- Encrypt-and-MAC (SSH)
What is a Certification Authority (CA)?
- Entity registers public key with CA and provides some proof of identity
- Certification Authority provides a certificate:
- Binds public key to particular entity
- Signed by CA’s private key
- CA’s public key is know (trusted) to public
Describe how a certificate is checked
When Alice wants Bob’s public key:
- Bob provides a certificate
- Certificate is signed by CA
- Alice applies CA’s public key to confirm certificate’s authenticity
- Certificate contains Bob’s public key
