chapter 12
DESCRIPTION
Chapter 12. Cryptography Explained. Search Problems. Specified by an algorithm C Two inputs I is the instance. S is the solution. Must complete in polynomial time I. S is a solution to I if and only if C(I,S) is True. NP-Complete Problems. A class of search problems - PowerPoint PPT PresentationTRANSCRIPT
Search ProblemsSearch ProblemsSpecified by an algorithm CTwo inputs
◦I is the instance.◦S is the solution.◦Must complete in polynomial time I.
S is a solution to I if and only if C(I,S) is True.
NP-Complete ProblemsNP-Complete Problems
A class of search problems◦Traveling salesman problem
Time limited.
◦Rudrata: Knight’s Tour on a chess board. Cover all 64 squares?
◦Euler: Graph Theory Cross a bridge only once.
◦Knapsack Add maximum items below a limit.
GoalsGoalsComplexity
◦Difficult to solve.◦Number of possible solutions large.◦Brute force solution expected to be
infeasible.Satisfiable
◦Assign values to a formula so that it is true.◦(V1) && (v2 || v3) && (!v3 || !v1)
Solvable◦Simple approach to solve problem.
Figure 12-1 Clique Subgraphs in a Graph.Clique: every vertex connected to every other vertex.v1, v2, v7, v8 form clique size = 4.
Figure 12-3 Hierarchies of Complexity Classes.Problem space. Some solvable in polynomial time (P).Some are beyond Polynomial time (EXP).Class NP between P and EXP.
Diffusion, Confusion, Diffusion, Confusion, Substitution, PermutationSubstitution, PermutationDiffusion
◦ Spread the effect of a change to plaintext throughout the cipher text.
Confusion◦ Relationship between plain and cipher text
should be as random and not apparent.
Substitution (Confusion) S-Boxes◦ Replace one character with another.
Permutation (transposition) P-Boxes◦ Provide confusion by rearranging the
characters in the text.
Figure 12-6 Distribution Center for Encrypted Information.
Key Clearinghouse, centralize key distribution.
Figure 12-7 Cycles of Substitution and PermutationDES: strength from repeating substitution and permutations.
Figure 12-8 Product Ciphers.
Two weak but complementary ciphers can be made more secure by being applied together, the product of the two ciphers.
Elliptical Curve Elliptical Curve CryptographyCryptographyOffers considerably greater security for a given
key sizeThe smaller key size also makes possible much
more compact implementations for a given level of security, which means faster cryptographic operations, running on smaller chips or more compact software. This means less heat production and less power consumption — all of which is of particular advantage in constrained devices, but of some advantage anywhere.
There are extremely efficient, compact hardware implementations available for ECC exponentiation operations, offering potential reductions in implementation footprint even beyond those due to the smaller key length alone.
Quantum CryptographyQuantum Cryptography
Instead of depending on the computational difficulty of cracking one-way functions, quantum encryption creates uncrackable codes that employ the laws of physics to guarantee security.
Different quantum states, such as photon polarization, can be used to represent 1s and 0s in a manner that cannot be observed without the receiver's discovering it.
For instance, if hackers observe a polarized photon, then 50 percent of the time they will scramble the result, making it impossible to hide the eavesdropping attempt from the receiver.