Encryption and Data Security

(1)

Encryption and Data Security

Research & Innovation Conference

April 28, 2008

Kurt Langfeld, David McMullan

School of Mathematics and Statistics University of Plymouth

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Plymouth Particle Physics Group:

Members:

Chris Harvey, Wolfgang Lutz (PhD) Anton Ilderton (PostDoc)

Tom Heinzl, Kurt Langfeld, Martin Lavelle, David McMullan 1−2 fm

(3)

Plymouth Particle Physics Group:

Members:

What are we doing?

(4)

Plymouth Particle Physics Group:

Members:

What are we doing?

Use Mathematics + High Performance Computing:

to understand the properties of matter

[e.g. when the universe was 10 µs old]

to explore quantum limits and applications

(5)

Example:

The (empty) vacuum

(6)

Example:

The (true) vacuum

Quantum Theory

... too naive

(7)

Example:

The (true) vacuum

Quantum Theory ... too naive Code breaking Encryption ? ? ?

The (empty) vacuum

(8)

Outline of the workshop:

(9)

Outline of the workshop:

Encryption

[history, basic techniques]

Hands on: encryption / decryption

(10)

Encryption

Code breaking

(11)

Encryption

Code breaking

Hands on: break the Caesar cipher

(12)

Encryption

Code breaking

Hands on: break the Caesar cipher

Encryption nowadays

[public-key cryptography]

[the political dimension of cryptography] [(some) modern tools]

(13)

Encryption: history and importance

Atbash Bible Code (2000 bc):

[reverted Hebrew alphabet]

(14)

Atbash Bible Code (2000 bc):

[reverted Hebrew alphabet]

Ceasar cipher (0000 ad):

[simple substitution]

a b c d e f g h i j k l m n o p q r s t u v w x y z

v w x y z a b c d e f g h i j k l m n o p q r s t u

plain text

(15)

(1775) Madame d’Urfé and

Giacomo Girolamo Casanova

[encrypted recipe for making gold]

[example of code breaking]

[University Archives, USA]

(16)

(1775) Madame d’Urfé and

Giacomo Girolamo Casanova

[encrypted recipe for making gold]

[example of code breaking]

[University Archives, USA]

London 1850: ciphered press advertisements

[message exchange between lovers]

[Babbage, Wheatstone:

(17)

(1918, 1st World War) Ludendorff Cipher (Westfront)

[bipart substitution] luden... FFGXFXXAFA... A D F G V X A c o 8 x f 4 m k 3 a z 9 n w l 0 j d 5 s i y h u p l v b 6 r e q 7 t 2 g D F G V X

(18)

(1918, 1st World War) Ludendorff Cipher (Westfront)

[bipart substitution] luden... FFGXFXXAFA... A D F G V X A c o 8 x f 4 m k 3 a z 9 n w l 0 j d 5 s i y h u p l v b 6 r e q 7 t 2 g D F G V X

(2nd World war) Enigma

[messaging between HQ and submarines] [multipart substitution]

(19)

Who is involved nowadays?

M.I.6 G.C.H.Q Governm. Communic._Headquarters

Defense Intelligence Ag.

CIA DIA

BND _{Fernmeldestatistik}

der Informationstechnik

U.S.I.B.

Central Intelligence Ag. historical: G.C.&C.S, war station, Station X,

since 1990: Amt fur Militarkunde Bundesamt fur ..

.. .. .. Room 47 foreign office

Bundesamt fur Sicherheit in

kanzleramt Bundes−

(20)

Encryption: history and importance

Who is involved nowadays?

M.I.6 G.C.H.Q Governm. Communic._Headquarters

Defense Intelligence Ag.

CIA DIA

BND _{Fernmeldestatistik}

der Informationstechnik

U.S.I.B.

Central Intelligence Ag. historical: G.C.&C.S, war station, Station X,

since 1990: Amt fur Militarkunde Bundesamt fur ..

.. .. .. Room 47 foreign office

Bundesamt fur Sicherheit in

kanzleramt Bundes− online banking e−health internet shopping mobile phones all of us ! ....

(21)

Hands on: The Ceasar cipher

Ceasar cipher:

25

different possibilities

(22)

Hands on: The Ceasar cipher

Ceasar cipher:

25

simple substitution:

replace each letter with another one

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Ceasar cipher:

25

simple substitution:

replace each letter with another one

25

×

24

×

. . .

×

3

×

2

≈

1

.

6

×

10

25

possible ciphers

difficult to remember

use a

password

⇒

construct the cipher

advantage:

cipher is easy to exchange

(24)

(25)

agree on a password; here:

tuesday

create your substitution table:

step 1

a b c d e f g h i j k l m n o p q r s t u v w x y z

t u e s d a y

(26)

agree on a password; here:

tuesday

step 1

a b c d e f g h i j k l m n o p q r s t u v w x y z t u e s d a y

step 2

a b c d e f g h i j k l m n o p q r s t u v w x y z e u t s d a y z b c f g h i j k l m n o p q r v w x

(27)

final step

e u t s d a y z b c f g h i j k l m n o p q r v w x a b c d e f g h i j k l m n o p q r s t u v w x y z encryption decryption

(28)

final step

e u t s d a y z b c f g h i j k l m n o p q r v w x a b c d e f g h i j k l m n o p q r s t u v w x y z encryption decryption

example:

c e a s a r c e a s a r e d t n t m e d t n t m

(29)

hands on !

(30)

Code breaking

Generically difficult ⇒ need knowledge on the cipher

(31)

Code breaking

[The Ceasar cipher was unbroken for hundred of years]

many codes get broken because of

the sloppy use of ciphers

The Register 2008:

Mafia boss undone by clumsy crypto

Clues left in the clumsily encrypted notes of a Mafia don have helped Italian investigators to track his associates and ultimately contributed to his capture after years on the run.

....instructions incorporating basic encryption on small scraps of paper, known locally as pizzini.

(32)

Code breaking

[The Ceasar cipher was unbroken for hundred of years]

many codes get broken because of

the sloppy use of ciphers

The Register 2008:

Mafia boss undone by clumsy crypto

Clues left in the clumsily encrypted notes of a Mafia don have helped Italian investigators to track his associates and ultimately contributed to his capture after years on the run.

....instructions incorporating basic encryption on small scraps of paper, known locally as pizzini.

What went wrong?

(33)

Code breaking

How can we break a

substitution cipher

?

(34)

Code breaking

How can we break a

substitution cipher

?

Frequency analysis:

in a simple substitution cipher,

each letter is replaced with another

certain letters and combinations of letters occur with varying frequencies

(35)

Frequency analysis:

abundance of letters in an English text:

(36)

Frequency analysis:

abundance of letters in an English text:

(37)

hands on !

(38)

Public Key Cryptography:

modern applications:

internet banking

sign electronic documents encrypt an email

(39)

internet banking

exchange of a

key

is very inconvenient

(40)

internet banking

exchange of a

key

can two parties exchange secure messages

without having met before?

(41)

modern applications:

internet banking

exchange of a

key

can two parties exchange secure messages

without having met before?

yes !

public key cryptography

(42)

How does it work?

door with a strange lock ⇒ two different keys

one key locks the door

(43)

Public Key Cryptography:

How does it work?

door with a strange lock ⇒ two different keys

one key locks the door

only the other key unlocks the door

Bob prepares himself

to receive encrypted messages ⇒ leaves his door open

⇒ puts ONE key beside the door

[public key]

(44)

Public Key Cryptography:

(45)

Alice wants to send Bob a message which only Bob can read

Bob finds his door locked [only he can open it]

private key

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Alice wants to send Bob a message which only Bob can read

Bob finds his door locked [only he can open it]

private key

(47)

Public Key Cryptography:

realisation

[administration]

⇒ everyone got an open door and a public/private key pair

⇒ Alice wants to make sure that she puts

the money transfer into the “open door” of the bank ⇒ certification authorities (CA) act as trusted third party

[VeriSign (57.6%), Comodo (8.3%), GoDaddy (6.4%)]

(48)

realisation

[administration]

⇒ everyone got an open door and a public/private key pair

⇒ Alice wants to make sure that she puts

the money transfer into the “open door” of the bank ⇒ certification authorities (CA) act as trusted third party

[VeriSign (57.6%), Comodo (8.3%), GoDaddy (6.4%)]

realisation

[where the maths is]

GCHQ (early 70s): Ellis, Cocks, Williamson [disclosed until 1997]

(49)

RSA encryption:

... it is all about

primes

(50)

RSA encryption:

... it is all about

primes

What are primes?

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RSA encryption:

... it is all about

primes

What are primes?

the high-profile cast of RSA:

public secret message n (huge) integer e public key d private key

m integer representing text

if you know the primes can be easily calculated

behind n

(52)

RSA in action::

Alice ciphers :

c

=

m

e

mod

n

(53)

RSA in action::

Alice ciphers :

c

=

m

e

mod

n

[security:

c

−→

m

not feasible]

theorem:

(

m

e

)

d

mod

n

=

m

[chinese remainder theorem, China 300 ad]

[Fermat’s little theorem, Pierre de Fermat, October 18, 1640]

(54)

RSA in action::

Alice ciphers :

c

=

m

e

mod

n

[security:

c

−→

m

not feasible]

theorem:

(

m

e

)

d

mod

n

=

m

[chinese remainder theorem, China 300 ad]

[Fermat’s little theorem, Pierre de Fermat, October 18, 1640]

(55)

RSA security aspects

how secure is the RSA standard ?

We don’t know !

(56)

We don’t know !

we do know:

if you know how to factorise an integer into primes, you can break the RSA code !

(57)

We don’t know !

we do know:

...but that is easy:

21 = 7

×

3

(58)

We don’t know !

we do know:

...but that is easy:

21 = 7

×

3

(59)

The RSA challange:

what about this number?

200 digits, 2 prime factors:

2799783391122132787082946763872260162107044678695 5428537560009929326128400107609345671052955360856 0618223519109513657886371059544820065767750985805 57613579098734950144178863178946295187237869221823983

(60)

The RSA challange:

what about this number?

2799783391122132787082946763872260162107044678695 5428537560009929326128400107609345671052955360856 0618223519109513657886371059544820065767750985805 57613579098734950144178863178946295187237869221823983

Using a HPC cluster, the problem was only solved in 2005

(61)

The RSA challange:

what about this number?

2799783391122132787082946763872260162107044678695 5428537560009929326128400107609345671052955360856 0618223519109513657886371059544820065767750985805 57613579098734950144178863178946295187237869221823983

Using a HPC cluster, the problem was only solved in 2005

[equivalent of 55 years on a single 2.2 GHz Opteron CPU]

and the winners are:

35324619344027701212726049781984643686711974001976250 23649303468776121253679423200058547956528088349

and

79258699544783330333470858414800596877379758573642 19960734330341455767872818152135381409304740185467

(62)

The RSA challange:

The RSA Security division of EMC has offered prizes

to factor huge numbers

[numbers used in devising secure RSA cryptosystems]

(63)

The RSA challange:

The RSA Security division of EMC has offered prizes

(⇒ political dimension !)

RSA-140: solved on February 2, 1999 RSA-200: solved on May 2005

RSA-640: solved on November 2, 2005

RSA-2048: Bank of England (effective 1 June 2006), not solved

(64)

The RSA challange:

The RSA Security division of EMC has offered prizes

(⇒ political dimension !)

RSA-140: solved on February 2, 1999 RSA-200: solved on May 2005

RSA-640: solved on November 2, 2005

RSA-2048: Bank of England (effective 1 June 2006), not solved

RSA challenges stopped in 2007

[why?]

RSA-640 took approximately 30 2.2GHz-Opteron-CPU years over five months of calendar time

(65)

Political dimension

conflict of interests:

necessity of encryption ↔ governmental control

(66)

Political dimension

US: International Traffic in Arms Regulations (ITAR)

1996-1997, classified strong cryptography as arms and prohibited their export

(67)

Political dimension

led to absurd legislation:

no restrictions on books, but

no export of encryption electronically

[MIT has printed a book with PGP in a machine readable OCR font.]

What next? Forbid the use of primes !

(68)

Political dimension

led to absurd legislation:

no restrictions on books, but

no export of encryption electronically

[MIT has printed a book with PGP in a machine readable OCR font.]

What next? Forbid the use of primes !

Where are we today?

[personal opinion]

governmental control not feasible

(69)

Quantum impact on crpytography:

Quantum computing

[bad news]

(70)

Quantum impact on crpytography:

Quantum computing

[bad news]

(71)

Quantum computing:

binary number: 0101(= 5) stored 1 bit per register

(72)

Quantum computing:

binary number: 0101(= 5) stored 1 bit per register Qubits advantages:

standard problems of

miniaturisation do not apply quantum registers store

(73)

Quantum computing:

Where is the bad news ?

(74)

Quantum computing:

(75)

Quantum computing:

quantum computer factorise huge integers

Is this the fall of RSA ?

Yes !

(76)

Quantum computing:

quantum computer factorise huge integers

Yes !

where are we today ?

(77)

Quantum computing:

quantum computer factorise huge integers

Yes !

where are we today ?

we don’t know (top secret).

2001: IBM Almaden Research Center, 7 Qubits, 15 = 5 × 3

(78)

Quantum cryptography:

[good news] basic idea:

create a one-time key between two parties and

(79)

Quantum cryptography:

[good news] basic idea:

create a one-time key between two parties and

be absolutely (!) sure that nobody has eavesdropped on the key

use quantum mechanics for “absolutely”

detecting a photon necessarily

changes its state

properties of light:

comes in packets (photons) photon has two states

(80)

why is it “absolutely” sure?

man in the middle

tries to

measure Alice photons

(81)

man in the middle

tries to

measurement

necessarily

changes their states

[quantum theory]

⇒

no-cloning theorem

Alice and Bob realise when a third party interferes

(82)

man in the middle

tries to

measurement

necessarily

changes their states

[quantum theory]

⇒

no-cloning theorem

Alice and Bob realise when a third party interferes

Alice and Bob agree on a

key

, and they know

that nobody else knows it !

(83)

Cryptographic tools:

You want to do:

[encrypt your data and communication] [sign your data and communication] [effectively manage your keys]

[access public key directories]

(84)

You want to do:

standard tool:

GNU Privacy Guard (GPG, PGP)

available for:

Linux, FreeBSD, OpenBSD

Windows 95/98/NT/2000/ME/XP MacOS X

(85)

You want to do:

standard tool:

GNU Privacy Guard (GPG, PGP)

available for:

Linux, FreeBSD, OpenBSD

Windows 95/98/NT/2000/ME/XP MacOS X

windows oriented version of GnuPG:

Windows Privacy Tools (WinPT)

(86)

You want to do:

[create a new encrypted container → drive ]

[create an encrypted CD] [mountvan encrypted CD]

(87)

You want to do:

[remove encryption from a container / CD]

linux: (all open source)

loop-AES, Cryptoloop, PPDD (Practical Privacy Disc Driver)

(88)

You want to do:

linux: (all open source)

windows: (open source)

(89)

You want to do:

TrueCrypt, FreeOTFE (high Linux compat.)

windows: (commercial)

BestCrypt (high Linux compat.), PGPdisk (supports MAC)

(90)

You want to do:

TrueCrypt, FreeOTFE (high Linux compat.)

windows: (commercial)

BestCrypt (high Linux compat.), PGPdisk (supports MAC)

... more “hands-on” CPD to come!

(91)

References:

Simon Singh,

The Code Book: The Secret History of Codes and Code-breaking

Fourth Estate; New Ed edition (8 Jun 2000)

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References:

Simon Singh,

The Code Book: The Secret History of Codes and Code-breaking

Fourth Estate; New Ed edition (8 Jun 2000)