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Introduction to Cryptography: Goals, Principles, and Applications

This lecture provides a high-level survey of cryptography, discussing its goals, principles, and applications. It covers private-key and public-key settings, emphasizing the importance of understanding threat models and security guarantees.

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Introduction to Cryptography: Goals, Principles, and Applications

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  1. CMSC 414Computer and Network SecurityLecture 2 Jonathan Katz

  2. JCE tutorial • In class next Wednesday • HW1 will use it

  3. Assigned readings from lecture 1 • “Inside the Twisted Mind of the Security Professional” • “We are All Security Customers” • “Information Security and Externalities” • Comments?

  4. A high-level survey of cryptography

  5. Caveats • Everything I present will be (relatively) informal • I may simplify, but I will not say anything that is an outright lie… • Cryptography offers formal definitions and rigorous proofs of security (neither of which we will cover here) • For more details, take CMSC 456 in the Fall (or read my book)! • If you think you already know cryptography from somewhere else (CMSC456, CISSP, your job, the news), you are probably mistaken

  6. Goals of cryptography • Crypto deals primarily with three goals: • Confidentiality • Integrity (of data) • Authentication (of resources, people, systems) • Other goals also considered • E.g., non-repudiation • E-cash (e.g., double spending) • General secure multi-party computation • Anonymity • …

  7. Private- vs. public-key settings • For the basic goals, there are two settings: • Private-key / shared-key / symmetric-key / secret-key • Public-key • The private-key setting is the “classical” one (thousands of years old) • The public-key setting dates to the 1970s

  8. Private-key cryptography • The communicating parties share some information that is random and secret • This shared information is called a key • Key is not known to an attacker • This key must be shared (somehow) in advance of their communication

  9. To emphasize • Alice and Bob share a key K • Must be shared securely • Must be completely random • Must be kept completely secret from attacker • We don’t discuss (for now) how they do this • You can imagine they meet on a dark street corner and Alice hands a USB device (with a key on it) to Bob

  10. Private-key cryptography • For confidentiality: • Private-key (symmetric-key) encryption • For data integrity: • Message authentication codes

  11. Canonical applications • Two (or more) distinct parties communicating over an insecure network • E.g., secure communication • A single party who is communicating “with itself” over time • E.g., secure storage

  12. Bob Bob Alice Alice K K K shared info K

  13. Bob Bob K K

  14. Security? • We will specify the exact threat model being addressed • We will also specify the security guarantees that are ensured, within this threat model • Here: informally; CMSC 456: formally • Crucial to understand these issues before crypto can be successfully deployed! • Make sure the stated threat model matches your application • Make sure the security guarantees are what you need

  15. Security through obscurity? • Always assume that the full details of crypto protocols and algorithms are public • Known as Kerckhoffs’ principle • The only secret information is a key • “Security through obscurity” is a bad idea… • True in general; even more true in the case of cryptography • Home-brewed solutions are BAD! • Standardized, widely-accepted solutions are GOOD!

  16. Security through obscurity? • Why not? • Easier to maintain secrecy of a key than an algorithm • Reverse engineering • Social engineering • Insider attacks • Easier to change the key than the algorithm • In general setting, much easier to share an algorithm than for everyone to use their own

  17. Private-key encryption

  18. Functional definition • Encryption algorithm: • Takes a key and a message (plaintext), and outputs a ciphertext • c  EK(m) possibly randomized! • Decryption algorithm: • Takes a key and a ciphertext, and outputs a message (or perhaps an error) • m = DK(c) • Correctness: for all K, we have DK(EK(m)) = m • We have not yet said anything about security…

  19. Bob Bob Alice Alice K K K shared info K c cEK(m) m=DK(c)

  20. A classic example: shift cipher • Assume the English uppercase alphabet (no lowercase, punctuation, etc.) • View letters as numbers in {0, …, 25} • The key is a random letter of the alphabet • Encryption done by addition modulo 26 • Is this secure? • Exhaustive key search • Automated determination of the key

  21. Another example: substitution cipher • The key is a random permutation of the alphabet • Note: key space is huge! • Encryption done in the natural way • Is this secure? • Frequency analysis • A large key space is necessary, but not sufficient, for security

  22. Another example: Vigenere cipher • More complicated version of shift cipher • Believed to be secure for over 100 years • Is it secure?

  23. Attacking the Vigenere cipher • Let pi (for i=0, …, 25) denote the frequency of letter i in English-language text • Known that Σ pi2 ≈ 0.065 • For each candidate period t, compute frequencies {qi} of letters in the sequence c0, ct, c2t, … • For the correct value of t, we expect Σ qi2 ≈ 0.065 • For incorrect values of t, we expect Σ qi2 ≈ 1/26 • Once we have the period, can use frequency analysis as in the case of the shift cipher

  24. Moral of the story? • Don’t use “simple” schemes • Don’t use schemes that you design yourself • Use schemes that other people have already designed and analyzed…

  25. A fundamental problem • A fundamental problem with “classical” cryptography is that no definition of security was ever specified • It was not even clear what it meant for a scheme to be “secure” • As a consequence, proving security was not even an option • So how can you know when something is secure? • (Or is at least based on well-studied, widely-believed assumptions)

  26. Defining security? • What is a good definition? • Why is a good definition important?

  27. Security goals? • Adversary unable to recover the key • Necessary, but meaningless on its own… • Adversary unable to recover entire plaintext • Good, but is it enough? • Adversary unable to determine any information at all about the plaintext • Formalize? • Sounds great! • Can we achieve it?

  28. Note • Even given our definition, we need to consider the threat model • Multiple messages or a single message? • Passive/active adversary? • Chosen-plaintext attacks? • The threat model matters! • The classical ciphers we have seen are immediately broken by a known-plaintext attack

  29. Defining secrecy (take 1) • Even an adversary running for an unbounded amount of time learns nothing about the message from the ciphertext • Perfect secrecy • Formally, for all distributions over the message space, all m, and all c: Pr[M=m | C=c] = Pr[M=m]

  30. Next time: the one-time pad; its limitations; overcoming these limitations

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