Podcast
Questions and Answers
What is the key space for a key length of 128 bits?
What is the key space for a key length of 128 bits?
- $2^{256}$
- $2^{128}$ (correct)
- $2^{512}$
- $2^{64}$
Which key length offers resistance against possible quantum computer attacks?
Which key length offers resistance against possible quantum computer attacks?
- 128 bits
- 256 bits (correct)
- 64 bits
- 512 bits
What is the expected security lifetime of a 64-bit key?
What is the expected security lifetime of a 64-bit key?
- Short term (few days or less) (correct)
- Several decades
- Indefinite lifetime
- Long-term (several decades)
In the substitution cipher, how are plaintext letters transformed?
In the substitution cipher, how are plaintext letters transformed?
What type of attack involves trying every possible substitution table?
What type of attack involves trying every possible substitution table?
What primary technique does a substitution cipher utilize?
What primary technique does a substitution cipher utilize?
What is one of the major types of ciphers used in symmetric cryptography?
What is one of the major types of ciphers used in symmetric cryptography?
Which statement about key length and security is accurate?
Which statement about key length and security is accurate?
Which innovation in cryptography was proposed in 1976?
Which innovation in cryptography was proposed in 1976?
What term is used to describe encryption schemes that use the same key for both encryption and decryption?
What term is used to describe encryption schemes that use the same key for both encryption and decryption?
What is the security life time of a key length of 128 bits without quantum computers?
What is the security life time of a key length of 128 bits without quantum computers?
Which of the following is NOT a type of cryptographic technique classified under symmetric ciphers?
Which of the following is NOT a type of cryptographic technique classified under symmetric ciphers?
What did early forms of encryption, like the Caesar cipher, primarily rely on?
What did early forms of encryption, like the Caesar cipher, primarily rely on?
What is the primary characteristic of hybrid cryptographic schemes?
What is the primary characteristic of hybrid cryptographic schemes?
Which cipher is recognized as an example of a substitution cipher?
Which cipher is recognized as an example of a substitution cipher?
What does the term 'cryptanalysis' refer to in the field of cryptology?
What does the term 'cryptanalysis' refer to in the field of cryptology?
What is necessary for Alice and Bob to prevent Oscar from understanding their communication?
What is necessary for Alice and Bob to prevent Oscar from understanding their communication?
What does the ciphertext 'y' represent after Alice encrypts her plaintext 'x'?
What does the ciphertext 'y' represent after Alice encrypts her plaintext 'x'?
What must Alice and Bob ensure to maintain the security of their communication?
What must Alice and Bob ensure to maintain the security of their communication?
What operation does 'dK(y)' perform in the proposed communication model?
What operation does 'dK(y)' perform in the proposed communication model?
What is the role of the key generator in this model of symmetric cryptography?
What is the role of the key generator in this model of symmetric cryptography?
In the equation 'y = eK(x)', what does the 'e' signify?
In the equation 'y = eK(x)', what does the 'e' signify?
What happens if an attacker learns the key 'K' used in the encryption process?
What happens if an attacker learns the key 'K' used in the encryption process?
Which of the following best describes the relationship between encryption and decryption in symmetric cryptography?
Which of the following best describes the relationship between encryption and decryption in symmetric cryptography?
How many substitution tables (keys) are there in a substitution cipher?
How many substitution tables (keys) are there in a substitution cipher?
Why cannot we conclude that the substitution cipher is secure solely based on the infeasibility of a brute-force attack?
Why cannot we conclude that the substitution cipher is secure solely based on the infeasibility of a brute-force attack?
What is the frequency of the letter 'e' in typical English texts?
What is the frequency of the letter 'e' in typical English texts?
Which of the following is NOT a technique used in breaking substitution ciphers?
Which of the following is NOT a technique used in breaking substitution ciphers?
What is the significance of letter pair frequencies in breaking ciphers?
What is the significance of letter pair frequencies in breaking ciphers?
After replacing the letter 'q' with 'E' in the ciphertext, what is the resulting partial plaintext reflected?
After replacing the letter 'q' with 'E' in the ciphertext, what is the resulting partial plaintext reflected?
Which letter is the second most common in English texts?
Which letter is the second most common in English texts?
Which statement about letter frequency analysis in breaking substitution ciphers is correct?
Which statement about letter frequency analysis in breaking substitution ciphers is correct?
What is the modulus in the expression 12 ≡ 3 mod 9?
What is the modulus in the expression 12 ≡ 3 mod 9?
Which of the following is a valid remainder for the expression 12 mod 9?
Which of the following is a valid remainder for the expression 12 mod 9?
Why do we usually choose the smallest positive integer as a remainder?
Why do we usually choose the smallest positive integer as a remainder?
How can you perform modular division according to the given content?
How can you perform modular division according to the given content?
What is a correct statement regarding remainders in modular arithmetic?
What is a correct statement regarding remainders in modular arithmetic?
What is the result of 5 / 7 mod 9 if calculated correctly?
What is the result of 5 / 7 mod 9 if calculated correctly?
In the division operation a / b ≡ a x b^{-1} mod m, what does b^{-1} represent?
In the division operation a / b ≡ a x b^{-1} mod m, what does b^{-1} represent?
Which of the following statements is true regarding the operation a ≡ r mod m?
Which of the following statements is true regarding the operation a ≡ r mod m?
Which statement accurately reflects the properties of addition in modulo arithmetic?
Which statement accurately reflects the properties of addition in modulo arithmetic?
What condition must be true for an element a in Zm to have a multiplicative inverse?
What condition must be true for an element a in Zm to have a multiplicative inverse?
Which of the following elements in Z9 has no multiplicative inverse?
Which of the following elements in Z9 has no multiplicative inverse?
What does the distributive law in modular arithmetic state?
What does the distributive law in modular arithmetic state?
What is the neutral element for multiplication in modulo arithmetic?
What is the neutral element for multiplication in modulo arithmetic?
In the context of cryptology, what type of cipher is commonly used that replaces each plaintext letter?
In the context of cryptology, what type of cipher is commonly used that replaces each plaintext letter?
In the ring Zm, what must be true about an element a for it to be coprime to m?
In the ring Zm, what must be true about an element a for it to be coprime to m?
Which of the following expressions illustrates the additive inverse in modulo arithmetic?
Which of the following expressions illustrates the additive inverse in modulo arithmetic?
Flashcards
Cryptology
Cryptology
The study of secure communication techniques, encompassing both cryptography and cryptanalysis.
Cryptography
Cryptography
The art of designing and implementing methods to protect information, ensuring only authorized users can access it.
Cryptanalysis
Cryptanalysis
The process of trying to break or decipher encrypted messages without knowing the secret key.
Symmetric Ciphers
Symmetric Ciphers
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Asymmetric Ciphers
Asymmetric Ciphers
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Hybrid Schemes
Hybrid Schemes
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Substitution Cipher
Substitution Cipher
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Caesar Cipher
Caesar Cipher
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Plaintext (x)
Plaintext (x)
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Ciphertext (y)
Ciphertext (y)
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Key (K)
Key (K)
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Encryption
Encryption
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Decryption
Decryption
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Secure Channel
Secure Channel
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Shared Secret Key
Shared Secret Key
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Key Space
Key Space
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Security Lifetime
Security Lifetime
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Brute-Force Attack
Brute-Force Attack
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Cryptanalytic Attack
Cryptanalytic Attack
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Statistical Analysis
Statistical Analysis
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Known Plaintext Attack
Known Plaintext Attack
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Letter Frequency Analysis
Letter Frequency Analysis
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Infeasibility of Brute-Force Attack
Infeasibility of Brute-Force Attack
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Secure Encryption Methods
Secure Encryption Methods
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Ciphertext
Ciphertext
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Plaintext
Plaintext
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Modulus Operation
Modulus Operation
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Modulus (m)
Modulus (m)
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Remainder (r)
Remainder (r)
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Non-Uniqueness of Remainders
Non-Uniqueness of Remainders
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Smallest Positive Remainder
Smallest Positive Remainder
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Modular Inverse
Modular Inverse
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Modular Division
Modular Division
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Inverse Property
Inverse Property
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Zm
Zm
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Coprime element in Zm
Coprime element in Zm
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Multiplicative Inverse in Zm
Multiplicative Inverse in Zm
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Modular Arithmetic Operations
Modular Arithmetic Operations
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Units in Zm
Units in Zm
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Ring in Modular Arithmetic
Ring in Modular Arithmetic
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Distributive Law in Zm
Distributive Law in Zm
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Neutral Element in Zm
Neutral Element in Zm
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Study Notes
Introduction to Cryptography
- The textbook, Understanding Cryptography, by Christof Paar and Jan Pelzl, is a resource for students and practitioners
- The book's version is dated October 28, 2010
- The slides were prepared by Christof Paar and Jan Pelzl
Terms of Use
- The slides can be used freely
- Copyrights remain with Christof Paar and Jan Pelzl
- The book title (“Understanding Cryptography”) and authors’ names must remain on each slide
- Modifications must maintain credits to the book authors and title
- Reproduction of slides in printed form is prohibited without written consent from the authors
Chapter Content
- Overview of cryptography
- Basics of symmetric cryptography
- Cryptanalysis
- Substitution Cipher
- Modular arithmetic
- Shift (or Caesar) Cipher and Affine Cipher
Further Reading
- Handbook of Applied Cryptography by A. Menezes, P. van Oorschot, S. Vanstone (CRC Press, 1996)
- Encyclopedia of Cryptography and Security by H.v. Tilborg (Springer, 2005)
- The Code Book: The Science of Secrecy, by S. Singh (Anchor, 2000)
- The Codebreakers: The Comprehensive History of Secret Communication, by D. Kahn (Scribner, 1996)
- Cryptool software (http://www.cryptool.de)
Classification of Cryptology
- Cryptology branches into Cryptography and Cryptanalysis
- Cryptography further branches into Symmetric Ciphers (Block Ciphers, Stream Ciphers) and Asymmetric Ciphers
- Protocols are also part of this classification
Basic Crypto Facts
- Early encryption signs were discovered in Egypt around 2000 B.C.
- Letter-based schemes (e.g., Caesar cipher) were common
- All encryption schemes before 1976 were symmetric
- Asymmetric cryptography was introduced in 1976 by Diffie, Hellman, and Merkle
- Modern protocols often use hybrid schemes combining symmetric and asymmetric ciphers
Symmetric Cryptography
- Also known as private-key, single-key, or secret-key cryptography
- Alice and Bob need to communicate securely over an insecure channel (e.g., internet, WLAN)
- Oscar (a malicious third party) might eavesdrop
- Encryption and decryption use the same key (K)
Symmetric Cryptography (Solution)
- Oscar only receives ciphertext (y) which should seem random
- Alice uses encryption (e(x)) to encrypt plaintext (x) with key (K) to create ciphertext (y)
- Bob applies decryption (d(y)) using the same key (K) to recover the plaintext (x)
- A secure channel (e.g., a physical courier, secure WiFi protocol) is needed to transmit the key
Symmetric Cryptography (Equations)
- Encryption equation: y = ek(x)
- Decryption equation: x = dk(y)
Symmetric Cryptography (Important Point)
- The security of the scheme depends on the secrecy of the key K, not the algorithm.
Cryptanalysis
- No mathematical proof exists for the security of most ciphers
- Cryptanalysis is needed to evaluate a cipher's security, testing its ability to resist attacks
- By understanding and analyzing a crypto-system, potential vulnerabilities can be discovered
Cryptanalysis Attacks
- Classical Attacks (mathematical analysis, Brute-force attack)
- Implementation Attacks (reverse engineering, power measurement)
- Social Engineering (tricking users into divulging information)
Brute-Force Attack
- The attacker tries every possible key until the correct one is found
- The key length determines the key space size, thus affects the time taken by a brute-force attack
- Security time greatly increases with key length
Substitution Cipher
- Replaces each plaintext letter with a fixed other letter
- Example: A becomes k, B becomes d, C becomes w
- A historically significant cipher
- Useful for understanding brute-force vs. analytical attacks
Attacks on Substitution Ciphers
- Exhaustive Key Search (Brute-Force): Testing all possible substitution tables until the correct one produces understandable plaintext
- Letter Frequency Analysis: Exploiting the consistent frequency patterns of letters in typical natural languages to identify plaintext letters from ciphertext.
Breaking Substitution Ciphers
- Finding the most frequent letter in the ciphertext, which in natural language is usually 'e'
- Using the calculated frequency to guess other characters and decipher the plaintext gradually leading to a full decryption
Modular Arithmetic
- Important for asymmetric cryptography (e.g., RSA, elliptic curves)
- Useful for describing historical ciphers (e.g., Caesar, affine ciphers)
Modular Arithmetic: Properties
- Remainder is not always unique
- By convention, the smallest positive integer 'r' is chosen as the remainder (0 ≤ r ≤ m-1)
- The inverse of a number 'a' exists in modulo m only if their Greatest Common Divisor (GCD) is 1 (gcd(a, m) = 1)
Shift (Caesar) Cipher
- An ancient cipher, likely used by Julius Caesar
- Shifts each letter in the plaintext by a fixed number of positions (k) in the alphabet
- The mathematical description uses modular arithmetic to handle wrapping around the end of the alphabet.
Affine Cipher
- An extension of the Shift cipher, adding multiplication to letter shifting
- The encryption formula employs modular arithmetic and necessitates the existence of a modular multiplicative inverse (a⁻¹) for efficient decryption
Lessons Learned
- Never develop your own encryption algorithm without experienced cryptanalysts' scrutiny.
- Avoid unsupported encryption algorithms and protocols
- Attackers target the weakest points and a large key space doesn't guarantee security
- Key lengths (e.g., 64-bit, 128-bit, 256-bit) affect security against exhaustive attacks
- Modular arithmetic facilitates the mathematical modeling of historical ciphers like the affine cipher.
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