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Language Modeling and Encryption on Packet Switched Networks Kevin Mc. Curley

A. A. Markov of St. Petersburg 1856 -1922 Андрей Андреевич Марков

The science of cryptology 1. Devise a mathematical model of communication 2. Devise a mathematical model of an adversary 3. Construct a cryptosystem 4. Prove that theoretical adversary cannot break the cryptosystem (perhaps under assumptions)

The application of cryptology • Choose a construction for a cryptosystem • Adapt it to your model of communication • Watch it get broken by adversaries who don’t fit the model. The choice of a model is at least as important as a proof.

Security models Complexitytheoretic security Information theoretic security The real world

Attacks that have fallen outside the scope of security models • Electromagnetic radiation measurements • Timing analysis • Power analysis • Fault analysis • Acoustic attacks • Cache attacks …

Micali and Reyzin “Physical Observable Security” TCC 2004 • Extension of security models to include physical instantiation of computation. • Better description of adversary results in a more robust model.

Are these the only attacks? • Micali & Reyzin address the physical act of computation • What about the physical act of communication? How do we even define communication?

Claude E. Shannon “The mathematical theory of communication” (1948) “The communication theory of secrecy systems” (1949)

Shannon’s linear model of communication (1948) Information source Transmitter Channel Receiver Destination Noise A discrete Markov process on a finite domain

Information theoretic perfect secrecy • Messages are drawn from an underlying known probability distribution • An encryption system has perfect secrecy if P(ciphertext | plaintext) is independent of plaintext.

One time pad The one time pad has perfect secrecy. BUT: messages must all be the same length or else you lose perfect secrecy.

What about infinite message spaces? Theorem. (Chor-Kushilevitz, 1989) It is impossible to construct an informationtheoretically secure cryptosystem on a countably infinite message space.

Is leaking the message length unavoidable? Theorem (Goldreich) A semantically secure encryption scheme cannot hide the length of the plaintext against polynomial time adversaries. Are these just theoretical concerns? or do they show up in practice?

What can be learned from the length of a message? Example: communication to a stock broker with messages of “buy IBM” or “sell IBM” Example: in a file system, sizes of many files may provide evidence that encrypted files are copies of known files Example: in the military, voluminous communications may indicate a command or intelligence center with multimedia

How can we deal with message lengths? § Pad the messages to be all the same length § Keep talking at all times In practical systems, bandwidth and storage are not free!

What is the encryption of? i 3 or uqpcs hrt nbqpdn 0 xcae opx How does one approach the question? Ÿ it encrypted or just gibberish? is Ÿ what language is it? Ÿ what is the character set? Ÿ who said it? Ÿ when did they say it? Ÿ how was it encrypted?

A related problem: communication is segmented • Human spoken language is broken into syllables, words, sentences. • Human written communication is broken into paragraphs, chapters, articles, books. • Movies are broken into frames. • Internet communication is packet switched.

Suppose I told you where the spaces were # ####### ###### I usually get my stuff from people ######## #### who promised somebody else that ##### ## # ####### they would keep it a secret. ######## Walter Winchell An cryptanalyst would have a tremendous advantage in guessing the message!

Word lengths in 3 translations of a Tolstoy novel

Word length transitions French German English

Internet Communications Are Packet Switched § Packets are formed and transmitted according to the “language of the application” § Complications arise from buffering, Nagle’s algorithm, etc.

The “language” of ssh (simplified) SYN ACK SYN-ACK Banner Login: m a b password: w h . . .

Cryptanalytic attacks based on packet timings and size • Keystroke timings (Song, Wagner, Tiang) • Probable plaintext (Bellovin) • Several traffic classification studies: – Moore and Zuev (2005) 95% accuracy with supervised Bayesian analysis

Another looming attack: voice over IP • Vo. IP has high quality of service demands. • Vo. IP packets are easy to recognize. • Vo. IP supports “silence suppression” for bandwidth savings.

IPSEC traffic padding (TFC) • Omitted in early versions of IPSEC • Added in recent versions of tunnel mode to obfuscate traffic patterns. • No theoretical basis for security arguments. • No guidance on how to generate dummy traffic.

Note: simple padding is NOT enough If a known packet is repeatedly encrypted, then the padding distribution may be recognizable, and can be subtracted.

Do we have to packetize data? § Success of Internet depends on it § § § Fairness in a shared medium Quality of service Buffering Error correction retransmission

Can we afford to keep the Internet channels full? • Everyone depends on everyone else using only what they need. • Internet exists as a sparse graph: – O(n) total nodes to connect n endpoints – To support circuits, we would need a much denser graph • Alternatives in onion routing, mixes

Shannon’s epic 1949 paper “Communication Theory of Secrecy Systems” 1. Concealment systems, that obscure the existence of communication. 2. Privacy systems, requiring special communication hardware. 3. Secrecy systems, utilizing mathematical transformations. Shannon addressed only secrecy systems, calling concealment a “psychological problem”

What is an appropriate definition of communication?

Shannon’s communication model revisited Information source Transmitter Channel Receiver Destination Noise “Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. ”

Deficiencies in Shannon’s model • Communication should be bidirectional. • Communication is a physical process with side effects. • Communication is segmented. • Communication has context.

Temporal aspects of communication Do nothing secretly; for time sees and hears all things, and discloses all. - Sophocles, 496 -406 B. C.

Two versions of Shannon’s paper • Bell System Technical Journal (1948) – “A Mathematical Theory of Communication” • University of Illinois Press (1949) – “The Mathematical Theory of Communication” – With a section by Warren Weaver: “Recent Contributions to The Mathematical Theory of Communication”

Weaver’s three levels of communication Level A. How accurately can the symbols of communication be transmitted? (the technical problem) Level B. How precisely do the transmitted symbols convey the desired meaning? (the semantic problem) Level C. How effectively does the received meaning effect conduct in the desired way? (the effectiveness problem)

Definitions of communication • Shannon: – Reproducing the output from a stochastic process either approximately or exactly. • Lasswell’s definition: – Who says what to whom in what channel with what effect • The exchange of messages that change the a priori expectation of events. • Griffin: the management of messages for the purpose of creating meaning • Schramm: a purposeful effort to establish a commonness between a source and receiver

The DIKW Hierarchy (from the 1980 s) • Data (bits or raw symbols) – ’k’, 51771 • Information (symbols with relationships) – ‘e’ is more common than ‘z’ • Knowledge (useful information) – ‘e’ is energy; ‘e’ is a mathematical constant • Wisdom (understanding of knowledge) – Extrapolative, non-deterministic process.

DIKW Hierarchy (the origins) • Where is the wisdom we have lost in knowledge? • Where is the knowledge we have lost in information? T. S. Eliot, 1934 “The Rock”

Moving up the DIWK Hierarchy • Data Information – Understanding structure • Information Knowledge – Understanding patterns, context, relationships • Knowledge Wisdom – Understanding principles, applications, meaning, interpretation.

At what layer does a cryptanalyst work? • Data: what is the fifth symbol in this message? • Information: Are there more 1’s than 0’s in this message? Is there ever a sequence 00010000000? • Knowledge: what language is being spoken in this communication? • Wisdom: did the initiator just ask a question or give a command? Should I expect a response? Who is in command?

At what layer does the crypto designer work? • Data: make sure that this bit is unrecognizable from a random bit. • Information: make sure that they can’t estimate the distribution of bits accurately. • Knowledge: make sure that the adversary cannot recover the encoded knowledge. • Wisdom: make sure the cryptanalyst has no understanding of what they observe.

Closing thoughts • We need better models of communication in order to advance cryptology. • We need better definitions of knowledge and wisdom in order to advance cryptology. • Absolute security for internet communication is probably impossible.

Security is mostly a superstition. . Life is nothing if not a grand adventure. - Helen Keller http: //mccurley. org/papers/traffic/ for updates

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