Cryptography Basics Quiz

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Questions and Answers

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?

  • 128 bits
  • 256 bits (correct)
  • 64 bits
  • 512 bits

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?

<p>By replacing them with a fixed other letter (A)</p> Signup and view all the answers

What type of attack involves trying every possible substitution table?

<p>Exhaustive Key Search (A)</p> Signup and view all the answers

What primary technique does a substitution cipher utilize?

<p>Letter replacement (B)</p> Signup and view all the answers

What is one of the major types of ciphers used in symmetric cryptography?

<p>Block Ciphers (B)</p> Signup and view all the answers

Which statement about key length and security is accurate?

<p>Long key space is ineffective if social engineering is possible. (A)</p> Signup and view all the answers

Which innovation in cryptography was proposed in 1976?

<p>Public-key cryptography (D)</p> Signup and view all the answers

What term is used to describe encryption schemes that use the same key for both encryption and decryption?

<p>Symmetric Ciphers (C)</p> Signup and view all the answers

What is the security life time of a key length of 128 bits without quantum computers?

<p>Long-term (several decades) (D)</p> Signup and view all the answers

Which of the following is NOT a type of cryptographic technique classified under symmetric ciphers?

<p>Public-key Algorithms (B)</p> Signup and view all the answers

What did early forms of encryption, like the Caesar cipher, primarily rely on?

<p>Letter-based systems (C)</p> Signup and view all the answers

What is the primary characteristic of hybrid cryptographic schemes?

<p>They combine both symmetric and asymmetric techniques. (D)</p> Signup and view all the answers

Which cipher is recognized as an example of a substitution cipher?

<p>Caesar Cipher (A)</p> Signup and view all the answers

What does the term 'cryptanalysis' refer to in the field of cryptology?

<p>The art of breaking ciphers (A)</p> Signup and view all the answers

What is necessary for Alice and Bob to prevent Oscar from understanding their communication?

<p>Encrypting their messages with a symmetric cipher (D)</p> Signup and view all the answers

What does the ciphertext 'y' represent after Alice encrypts her plaintext 'x'?

<p>A unintelligible version of the plaintext (B)</p> Signup and view all the answers

What must Alice and Bob ensure to maintain the security of their communication?

<p>The key must be transmitted via a secure channel (C)</p> Signup and view all the answers

What operation does 'dK(y)' perform in the proposed communication model?

<p>It decrypts the ciphertext to reveal the original plaintext (D)</p> Signup and view all the answers

What is the role of the key generator in this model of symmetric cryptography?

<p>To generate keys for encryption and decryption (D)</p> Signup and view all the answers

In the equation 'y = eK(x)', what does the 'e' signify?

<p>It denotes an encryption method (A)</p> Signup and view all the answers

What happens if an attacker learns the key 'K' used in the encryption process?

<p>The attacker can decipher the messages (A)</p> Signup and view all the answers

Which of the following best describes the relationship between encryption and decryption in symmetric cryptography?

<p>They are inverse operations using the same key (B)</p> Signup and view all the answers

How many substitution tables (keys) are there in a substitution cipher?

<p>26! (approximately 288) (C)</p> Signup and view all the answers

Why cannot we conclude that the substitution cipher is secure solely based on the infeasibility of a brute-force attack?

<p>Because other types of attacks, like letter frequency analysis, still exist. (C)</p> Signup and view all the answers

What is the frequency of the letter 'e' in typical English texts?

<p>13% (B)</p> Signup and view all the answers

Which of the following is NOT a technique used in breaking substitution ciphers?

<p>Using random number generation (A)</p> Signup and view all the answers

What is the significance of letter pair frequencies in breaking ciphers?

<p>They highlight patterns in the plaintext that are preserved in ciphertext. (D)</p> Signup and view all the answers

After replacing the letter 'q' with 'E' in the ciphertext, what is the resulting partial plaintext reflected?

<p>E WILL MEET IN THE MIDDLE OF THE LIBRARY AT NOON (A)</p> Signup and view all the answers

Which letter is the second most common in English texts?

<p>T (D)</p> Signup and view all the answers

Which statement about letter frequency analysis in breaking substitution ciphers is correct?

<p>Letter pair and letter triple frequencies can also be exploited. (A)</p> Signup and view all the answers

What is the modulus in the expression 12 ≡ 3 mod 9?

<p>9 (B)</p> Signup and view all the answers

Which of the following is a valid remainder for the expression 12 mod 9?

<p>3 (B), -6 (D)</p> Signup and view all the answers

Why do we usually choose the smallest positive integer as a remainder?

<p>It simplifies the representation of numbers. (B)</p> Signup and view all the answers

How can you perform modular division according to the given content?

<p>By multiplying by the inverse of the divisor. (D)</p> Signup and view all the answers

What is a correct statement regarding remainders in modular arithmetic?

<p>There are infinitely many valid remainders. (C)</p> Signup and view all the answers

What is the result of 5 / 7 mod 9 if calculated correctly?

<p>4 (A)</p> Signup and view all the answers

In the division operation a / b ≡ a x b^{-1} mod m, what does b^{-1} represent?

<p>The inverse of b modulo m. (C)</p> Signup and view all the answers

Which of the following statements is true regarding the operation a ≡ r mod m?

<p>The value of r is always less than m. (D)</p> Signup and view all the answers

Which statement accurately reflects the properties of addition in modulo arithmetic?

<p>Addition has a neutral element and is commutative. (A)</p> Signup and view all the answers

What condition must be true for an element a in Zm to have a multiplicative inverse?

<p>The greatest common divisor of a and m must be 1. (C)</p> Signup and view all the answers

Which of the following elements in Z9 has no multiplicative inverse?

<p>3 (A)</p> Signup and view all the answers

What does the distributive law in modular arithmetic state?

<p>a × (b + c) = (a × b) + (a × c) (A)</p> Signup and view all the answers

What is the neutral element for multiplication in modulo arithmetic?

<p>1 (B)</p> Signup and view all the answers

In the context of cryptology, what type of cipher is commonly used that replaces each plaintext letter?

<p>Substitution Cipher (A)</p> Signup and view all the answers

In the ring Zm, what must be true about an element a for it to be coprime to m?

<p>It must share no factors with m other than 1. (A)</p> Signup and view all the answers

Which of the following expressions illustrates the additive inverse in modulo arithmetic?

<p>a + (-a) ≡ 0 mod m (B)</p> Signup and view all the answers

Flashcards

Cryptology

The study of secure communication techniques, encompassing both cryptography and cryptanalysis.

Cryptography

The art of designing and implementing methods to protect information, ensuring only authorized users can access it.

Cryptanalysis

The process of trying to break or decipher encrypted messages without knowing the secret key.

Symmetric Ciphers

Encryption schemes where both the sender and receiver use the same secret key to encrypt and decrypt messages.

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Asymmetric Ciphers

Encryption schemes using two separate keys: a public key for encryption and a private key for decryption.

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Hybrid Schemes

They combine the strengths of symmetric and asymmetric encryption.

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Substitution Cipher

It involves replacing characters with others based on a specific rule or mapping.

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Caesar Cipher

A method of encrypting messages by shifting letters in the alphabet by a fixed number of positions.

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Plaintext (x)

The intended message that Alice wants to send to Bob.

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Ciphertext (y)

The encrypted version of the plaintext, which should be unintelligible to Oscar.

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Key (K)

A secret code that is used by both Alice and Bob to encrypt and decrypt messages.

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Encryption

A process of transforming the plaintext into ciphertext using the key.

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Decryption

A process of transforming the ciphertext back into plaintext using the correct key.

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Secure Channel

A secure method to exchange the key between Alice and Bob, ensuring Oscar cannot intercept it.

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Shared Secret Key

A critical requirement for symmetric encryption, as the same key is used for both encryption and decryption.

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Key Space

The set of all possible keys that can be used for encryption and decryption.

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Security Lifetime

The amount of time a cryptographic algorithm is expected to remain secure. Longer is better.

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Brute-Force Attack

An attack that involves testing every possible key until the correct one is found.

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Cryptanalytic Attack

The method of breaking a cipher by analyzing encrypted messages to find patterns and weaknesses. .

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Statistical Analysis

A type of cryptanalysis that focuses on identifying the underlying statistical patterns in the ciphertext.

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Known Plaintext Attack

A type of cryptanalysis where an attacker attempts to exploit known information about the system or its users.

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Letter Frequency Analysis

The frequency analysis of letters is used to break substitution ciphers by identifying the most frequent ciphertext letters and mapping them to the most common letters in the corresponding language.

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Infeasibility of Brute-Force Attack

It is infeasible to break a substitution cipher with brute force due to the enormous number of potential keys.

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Secure Encryption Methods

Encryption methods that are still used today.

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Ciphertext

A message that has been encoded using a cipher, making it unreadable to unauthorized individuals.

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Plaintext

The original message before it is encrypted.

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Modulus Operation

A mathematical operation that finds the remainder after dividing one number by another. It's used to keep numbers within a set limit.

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Modulus (m)

The number that divides another number in a modulus operation. It defines the size of the set we're working with.

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Remainder (r)

The result of a modulus operation. It's the leftover amount after dividing.

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Non-Uniqueness of Remainders

A property of modular arithmetic stating that for any number and modulus, there are infinitely many remainders that satisfy the equation.

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Smallest Positive Remainder

The convention followed in modular arithmetic to use the smallest positive integer as the remainder.

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Modular Inverse

Used to perform division in modular arithmetic. It is another number that, when multiplied by the original number, results in a remainder of 1.

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Modular Division

A property of modular arithmetic that allows us to replace division with multiplication by the inverse.

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Inverse Property

An equation that states that when a number is multiplied by its inverse in modular arithmetic, the result is 1.

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Zm

In modular arithmetic, the set of integers from 0 to m-1, where operations are performed modulo m, meaning the result is the remainder after division by m.

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Coprime element in Zm

An element a in Zm is coprime to m if the greatest common divisor (GCD) of a and m is 1. This means they share no common factors except 1.

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Multiplicative Inverse in Zm

An element a in Zm has a multiplicative inverse if there exists another element a⁻¹ in Zm such that a × a⁻¹ ≡ 1 (mod m).

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Modular Arithmetic Operations

In modular arithmetic, operations like addition and multiplication follow the same rules as normal arithmetic, but the results are always reduced modulo m.

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Units in Zm

The set of elements in Zm for which multiplicative inverses exist. These elements are all the numbers in Zm that are coprime to m.

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Ring in Modular Arithmetic

A ring is a mathematical structure where addition and multiplication are defined, but division is only possible by elements that have a multiplicative inverse. Zm is a ring, where dividing by non-coprime elements is not possible.

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Distributive Law in Zm

The distributive law states that multiplying a number by the sum of two other numbers is equivalent to multiplying the number by each of the other numbers individually and then adding the products. This holds true in Zm.

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Neutral Element in Zm

The neutral element for addition in Zm is 0, as adding 0 to any element in Zm simply results in the same element. For multiplication, the neutral element is 1.

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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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