Chapter 9 - Public-Key Cryptography and RSA
What third property does a Trapdoor OWF add?
Given y and a secret(the trapdoor), x is easy to compute
Why do we not know if P = NP but we believe P != NP
It is possible that P = NP, however nobody has proved it yet. The longer we go without proof, the more confident we are that P != NP
PK encryption is mostly used for
Key exchange and digital signatures
What class of algorithm is the Merkle-Hellman Knapsack problem?
NP-Complete
Asymmetric key cryptography is used when the secret is
Personal (not shared)
With Symmetric Crypto, because both entities have their own shared secret, each message has both
Privacy and authenticity
Asymmetric Cryptography uses what kind of keys?
Public-key
Symmetric Cryptography uses what kind of keys?
Secret-key
What is a Superincreasing (SI) sequence?
Sequences such that each number is greater than the sum of the preceding numbers.
What provides the foundation for RSA?
The Merkle-Hellman approach
What is the Algorithm class NP?
The class of all algorithms for which we can verify a magically guessed solution bounded by polynomial time.
In Merkle-Hellman Knapsack, which key is Superincreasing?
The public key is S and the private key is the corresponding SI knapsack
In Symmetric cryptography, if we used only n keys for n entities we could keep a message within a group. What does this lack?
There is no authentication this way (no ability to tell which member of the group sent it)
Why do we need to use both keys in PK crypto?
We need to use both to give us secrecy AND authentication
When is a boolean expression said to be in Conjunctive Normal form?
When it is a conjunction of clauses, each of which is a disjunction.
What is a function?
a rule that maps one element form the domain onto one element in the range
In PK Crypto, the public and private keys are each others
inverse
What is the weakness of Merkle-Hellman?
it is vulnerable to numerical analysis
In asymmetric encryption how many keys are required for n entities
n keys
What is the Algorithm class P?
the class of all algorithm for which there is a solution that runs in time bounded by some polynomial of n
What is the Algorithm class EXP?
the class of all algorithms for which a solution can be bounded by time c^n, for some constant c
Two numbers are said to be relatively prime if
they share no factors other than 1
In symmetric encryption how many keys are required for n entities
(n^2-n)/2 keys
If (w*x)mod(n)=r then
(w*(x+n))mod(n)=r AND (w*(x+2n))mod(n)=r
What are the characteristics of a NP-Complete problem?
- Each problem is solvable and by a relatively simple method. - There are O(2^n) cases to consider if we enumerate all possible cases - The problems are seemingly unrelated - If we could magically guess the correct answer, we could verify that it was the correct answer quickly.
What is a clique?
A fully-connected set of vertices in a graph.
What is an invertible function?
A function that also associates each element in the range with exactly one element in the domain
What is a one way function (OWF)?
A function that: -Given x, y=f(x) is easy to compute - Computing f^-1 is intractable (given y, computing x=f^-1(y) is not feasable)
