Announcements
Introduction
Objectives
Symmetric Key
Encryption
Ciphertext IND
IND-KPA
IND-CPA
IND-CCA1
IND-CCA2
Achieve IND-CPA
One Time Pad
AES Block Cipher
Summary
Introduction to Encryption
Ruta Jawale
July 1, 2019
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Introduction to Encryption, Exercises of Cryptography and System Security
We phrase security of encryption schemes as a game between a challenger and an adversary. If no adversary can win the game.
Typology: Exercises
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Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Introduction to Encryption
Ruta Jawale
July 1, 2019
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Announcements
Homework 1 due in a week (7/8)
Project 1 due in about a week (7/11)
Midterm 1 in two weeks (7/15)
Attend lecture and discussion sections to learn material to
appear on Midterm 1
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Alice’s security specifications
We want CIA. (No, not the Central Intelligence Agency.)
Confidentiality
only Alice and Bob should know the message
Integrity
Alice’s message was not modified or tampered with
Authentication
Bob should be able to verify Alice sent the message
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Meet Alice’s adversaries
Eve the Eavesdropper
Likes: Reading messages
Dislikes: Confidentiality
Mallory the Manipulator
Likes: Altering messages
Dislikes: Integrity/Authenticity
For now, we’ll focus on giving Eve a hard time.
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Types of encryption
Encryption key Decryption key
Symmetric key encryption =
same private key for encryption and decryption
Asymmetric key encryption 6 =
separate public encryption key and private decryption key
Both types of encryption achieve confidentiality, necessary to
annoy Eve. For now, we’ll focus on symmetric encryption.
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Learning objectives
Learn how to make formal security arguments
Specifically prove or disprove that a scheme is IND-KPA or
IND-CPA secure
Build intuition from formal security proofs
For example, understand what it means to be IND-CPA
secure
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
Symmetric key encryption
How do we know that our encryption works?
∀m, k Dec(k, Enc(k, m)) = m
We call this the correctness property!
Is the correctness property enough for encryption to be
confidential? No, we need a security guarantee.
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
How do establish security? Games!
We phrase security of encryption schemes as a game between a
challenger and an adversary. If no adversary can win the game
with probability greater than random chance, then we consider
the scheme secure.
Challenger
Photo Credit: lichess
Adversary
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
IND-KPA Secure
Phases Challenger C Adversary A
setup k ← Gen(1n^ )
challenge cipher
m∗ 0 , m∗ 1
b
c∗^ ← Enc(k, m b∗ )
c∗
send bit
b′
determine win If b = b
′
, A wins.
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
IND-KPA Secure
Phases Challenger C Adversary A
setup k ← Gen(1n^ )
challenge cipher
m∗ 0 , m∗ 1
b
c∗^ ← Enc(k, m b∗ )
c
∗
send bit
b′
determine win If b = b′, A wins.
∀ adversaries A, Pr[A wins game] ≤
+ negligible
Why
? Some adversary A could guess bit b. They have
probability
2 to succeed. We don’t consider this an “attack”
on our encryption scheme.
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
IND-CPA secure
Phases Challenger C Adversary A setup k ← Gen( n )
encrypt plaintext
mi ←−−−−−−−−−−− for i ∈ poly(n)
ci ← Enc(k, mi )
ci −−−−−−−−−−−→
challenge cipher
m∗ 0 , m∗ 1 ←−−−−−−−−−−−
b
c∗^ ← Enc(k, m∗ b )
c∗ −−−−−−−−−−−→
encrypt plaintext
m′ i ←−−−−−−−−−−− for i ∈ poly(n)
ci ← Enc(k, m i′ )
c i′ −−−−−−−−−−−→
send bit
b′ ←−−−−−−−−−−− determine win If b = b′, A wins.
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
IND-CPA secure
Phases Challenger C Adversary A setup k ← Gen(1n^ )
encrypt plaintext
mi ←−−−−−−−−−−− for i ∈ poly(n)
ci ← Enc(k, mi )
ci −−−−−−−−−−−→
challenge cipher
m∗ 0 , m∗ 1 ←−−−−−−−−−−−
b
c∗^ ← Enc(k, m∗ b )
c∗ −−−−−−−−−−−→
encrypt plaintext
m′ i ←−−−−−−−−−−− for i ∈ poly(n)
ci ← Enc(k, m i′ )
c i′ −−−−−−−−−−−→
send bit
b′ ←−−−−−−−−−−− determine win If b = b′, A wins.
∀ adversaries A, Pr[A wins game] ≤
+ negligible
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
IND-CCA1 secure
Phases Challenger C Adversary A setup k ← Gen(1n^ )
decrypt ciphertext and
ci , mj ←−−−−−−−−−−− for i, j ∈ poly(n) encrypt plaintext mi ← Dec(k, ci )
cj ← Enc(k, mj )
mi , cj −−−−−−−−−−−→
challenge cipher
m 0 ∗ , m∗ 1 ←−−−−−−−−−−−
b
c∗^ ← Enc(k, m∗ b )
c∗ −−−−−−−−−−−→
encrypt plaintext
m′ j ←−−−−−−−−−−− for j ∈ poly(n)
c j′ ← Enc(k, m′ j )
c j′ −−−−−−−−−−−→
send bit
b′ ←−−−−−−−−−−− determine win If b = b′, A wins.
∀ adversaries A, Pr[A wins game] ≤
2 +^ negligible
Announcements Introduction Objectives Symmetric Key Encryption Ciphertext IND IND-KPA IND-CPA IND-CCA IND-CCA Achieve IND-CPA One Time Pad AES Block Cipher Summary
IND-CCA2 secure
Phases Challenger C Adversary A setup k ← Gen(1n^ )
decrypt ciphertext and
ci , mj ←−−−−−−−−−−− for i, j ∈ poly(n) encrypt plaintext mi ← Dec(k, ci )
cj ← Enc(k, mj )
mi , cj −−−−−−−−−−−→
challenge cipher
m∗ 0 , m∗ 1 ←−−−−−−−−−−− b ← {$ 0 , 1 }
c∗^ ← Enc(k, m∗ b )
c∗ −−−−−−−−−−−→
decrypt ciphertext and
c′ i , m′ j ←−−−−−−−−−−− for i, j ∈ poly(n), where c′ i 6 = c∗ encrypt plaintext m′ i ← Dec(k, c′ i )
c′ j ← Enc(k, m′ j )
m′ i , c j′ −−−−−−−−−−−→
send bit
b′ ←−−−−−−−−−−− determine win If b = b′, A wins.