Quiz 2 answers

Question I •

Question 1 •

Question 2 •

Question 3 •

Question 4 •

Show that encryption from PRG is secure m c m c

m Repeat as many times as the distinguisher wants

Show that PRF construction of encryption is secure

Show that PRF construction of encryption is secure

Show that PRF construction of encryption is secure

MAC forgery game •

Mac example exercise •

Security of macs from PRF via hybrid games

Mac forgery example •

Collision resistance hash function •

Collision-resistant hash function exercises •

Collision-resistant hash function exercises •

Collision-resistant hash function exercises •

Collision-resistant hash function exercises •

Collision-resistant hash function exercises •

Computational assumptions

Types of computational assumptions • Decisional: distinguish between two distributions (or games) • Search: trying to find an element which fulfills certain properties

Discrete logarithm assumption •

Examples of hardness reduction •

Decisional Diffie Hellman problem •

Reduction •

Quadratic Residuosity •

Quadratic Residuosity •

Quadratic Residuosity •

Equivalence for quadratic residuosity problem •

If x is even return 0; If x is odd return 1;

Factoring assumption •

Polynomial recovery •

Learning with errors •

Example of LWE problem •