• Keine Ergebnisse gefunden

Prof. Martin Hofmann Ludwig-Maximilians-Universit¨ at M¨ unchen

N/A
N/A
Info
Herunterladen
Protected

Academic year: 2021

Aktie "Prof. Martin Hofmann Ludwig-Maximilians-Universit¨ at M¨ unchen"

Copied!
1
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Jetzt herunterladen ( 1 Seite )

Volltext

(1)

Prof. Martin Hofmann Ludwig-Maximilians-Universit¨ at M¨ unchen

Dr. Ulrich Sch¨ opp Institut f¨ ur Informatik

Summer 2017

Cryptography

Exercise Sheet 2

Exercise 1-4 was not finished in the first Tutorial and will be discussed in Tutorial 2.

Exercise 2-1

• Prove or disprove P (A) ≤ P (A | B) + P (B) for arbitrary A and B.

• In a lecture that has been given in 2015 and 2016, the exam results were as follows:

2015 2016 very good 7% 10%

good 19% 21%

satisfactory 14% 22%

pass 23% 18%

fail 37% 27%

Suppose you meet two students who took the lecture in the past two years, but not in the same year. The first student tells you that she achieved ‘good’ result. The second student only managed a ‘satisfactory’ result. What is the probability that the first student took the course in 2015?

Exercise 2-2 In the lectures, perfect secrecy was defined by means of an indistinguishabilily experiment. An encryption scheme Π is perfectly secret if and only if P (PrivK

eavA,Π

) = 1/2 for any adversary A.

It was then stated in a Proposition that this definition is equivalent to requiring P (M = m|C = c) = P (M = m) for all m and c that satisfy P(C = c|M = m) 6= 0.

In the lectures, only one direction of the proof of this equivalence was spelled out: that the definition with the indistinguishability experiment implies the other definition. Prove the implication in the other direction to complete the proof that the two definitions are equivalent.

Exercise 2-3 Assume given an arbitrary encryption scheme Π with |K| < |M|. Construct

an adversary A for the indistinguishability experiment that satisfies P (PrivK

eavA,Π

) > 1/2.

Referenzen

Jetzt herunterladen ( PDF - 1 Seite - 96.51 KB )

ÄHNLICHE DOKUMENTE

Ludwig-Maximilians-Universit¨at M¨unchen

(b) Begr¨ unden Sie kurz, warum {¬·} nicht funktional vollst¨ andig ist.. (c) Begr¨ unden Sie kurz, warum {¬·} funktional vollst¨ andig f¨ ur einstellige

Ludwig-Maximilians-Universit¨at M¨unchen

Zeigen Sie, dass es zu jeder Formel ϕ eine ¨ aquivalente termreduzierte Formel gibt, dessen Gr¨ oße linear in der Gr¨ oße von ϕ beschr¨ ankt ist..

Ludwig-Maximilians-Universit¨at M¨unchen

eine Formel- menge Γ eine Eigenschaft des Universum ausdr¨ uckt, wenn f¨ ur jede Menge U gilt: Die Eigenschaft trifft auf U zu gdw.. es ein Modell von

Ludwig-Maximilians-Universit¨at M¨unchen

Wenn ja, begr¨ unden Sie dies, wenn nicht, dann geben Sie jeweils ein k an, so dass der Duplikator das Spiel G N,A i n f¨ ur alle i ≤ k, aber der Spoiler das Spiel G N k+1 ,A

Prof. Martin Hofmann Ludwig-Maximilians-Universit¨ at M¨ unchen

Assume for simplicity that a transaction consists just of the amount x of money to be transferred (and ignore account numbers and the like). The amount x is encoded by the group

Prof. Martin Hofmann Ludwig-Maximilians-Universit¨ at M¨ unchen

Exercise 10-2 The RSA hardness assumption states that P (RSA-inv A (n) = 1) ≤ negl(n) for any probilistic polynomial time adversary A. Show that the RSA hardness assumption implies

Prof. Martin Hofmann Ludwig-Maximilians-Universit¨ at M¨ unchen

The distinguisher D is a probabilistic polynomial time algorithm, so it can make at most polynomially many different requests to the oracle function, say with arguments x

Exercise 2 Show that the class

In this exercise we want to show that the model construction for FO 2 -formulae from the lecture is optimal in the following sense: in general it does not suffice to take only