Language Modeling andEncryption on

Packet Switched Networks

Kevin McCurley

A.A. Markovof 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 cryptosystem4. Prove that the 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 isat least as important as a proof.

Security models

The real

world

Complexity- theoreticsecurity

Information theoreticsecurity

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)

Informationsource

Transmitter

Noise

Receiver DestinationChannel

A discrete Markov process on a finite domain

Information theoreticperfect secrecy

• Messages are drawn from an underlying known probability distribution

• An encryption system has perfect secrecy if P(ciphertext | plaintext) is independent of plaintext.

The one time pad has perfect secrecy.

BUT: messages must all be the same length or else you lose perfect secrecy.

One time pad

What about infinite message spaces?

Theorem. (Chor-Kushilevitz, 1989) It is impossible to construct an information-theoretically secure cryptosystem on a countably infinite message space.

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?

Is leaking the message length unavoidable?

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

What can be learned from the length of a message?

In practical systems, bandwidth and storage are not free!

How can we deal with message lengths?

Pad the messages to be all the same length Keep talking at all times

i3or uqpcs hrt nbqpdn 0xcae opx

How does one approach the question?is it encrypted or just gibberish?what language is it?what is the character set?who said it?when did they say it?how was it encrypted?

What is this the encryption of?

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.

# ####### ### ## ##### #### ###### ### ######## ######## #### #### #### ##### #### ## # #######

###### ########

An cryptanalyst would have a tremendous advantage in guessing the message!

I usually get my stuff from people who promised somebody else that they would keep it a secret.

Walter Winchell

Suppose I told you where the spaces were

Word lengths in 3 translations of a Tolstoy novel

Word length transitions

1 2 3 4 5 6 7 8S1

S2

S3

S4

S5

S6

S7

S8

1 2 3 4 5 6 7 8S1

S2

S3

S4

S5

S6

S7

S8

French

1 2 3 4 5 6 7 8

S1

S2

S3

S4

S5

S6

S7

S8

English

German

Internet CommunicationsAre Packet Switched

Packets are formed and transmitted according to the “language of the application”

Complications arise from buffering, Nagle’s algorithm, etc.

SYNACK

SYN-ACK

Banner

Login:

mab

password:

w

h

. . .

The “language” of ssh (simplified)

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

• VoIP has high quality of service demands.

• VoIP packets are easy to recognize.

• VoIP 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.

If a known packet is repeatedly encrypted,

then the padding distribution may be

recognizable, and can be subtracted.

Note: simple padding is NOT enough

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

2

n

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

Informationsource

Transmitter

Noise

Receiver DestinationChannel

“Frequently the messages have meaning; that is they referto 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 1980s)

• 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

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