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CMSC 414 Computer and Network Security Lecture 2 Jonathan Katz

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JCE tutorial In class next Tuesday

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A high-level survey of cryptography

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Caveat Everything I present will be (relatively) informal –I may simplify, but I will try not to say anything that is an outright lie… Cryptography is about precise definitions, formal models, and rigorous proofs of security (which we will not cover here) –For more details, take CMSC 456 with me (or read my book)!

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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 –…–…

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Private- vs. public-key settings For the basic goals of confidentiality and integrity, 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

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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

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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

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Private-key cryptography For confidentiality: –Private-key (symmetric-key) encryption For data integrity: –Message authentication codes –(archaic: cryptographic checksums)

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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

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Alice Bob shared info K K Alice K Bob K

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K K

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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

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Security through obscurity? Always assume that the full details of crypto protocols and algorithms are public –Known as Kerckhoffs’ principle –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!

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Private-key encryption

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Functional definition Encryption algorithm: –Takes a key and a message (plaintext), and outputs a ciphertext –c E K (m) Decryption algorithm: –Takes a key and a ciphertext, and outputs a message (or perhaps an error) –m = D K (c) Correctness: for all K, we have D K (E K (m)) = m We have not yet said anything about security…

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Alice Bob shared info K K Alice K Bob K c c E K (m) m=D K (c)

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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

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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

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Another example: Vigenere cipher More complicated version of shift cipher Believed to be secure for over 100 years Is it secure? –Index of coincidence method

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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…

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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 would mean for an encryption scheme to be “secure” As a consequence, proving security was not even an option –So how can you know when something is secure?

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Defining security? What is a good definition?

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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?

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Note Even given our definition, we need to consider the threat model –Multiple messages or a single message? –Passive/active adversary? –Chosen-plaintext attacks?

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

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