Alice & bob public key cryptography 101 - uncon dpc

Alice & Bob
Public key cryptography 101

DPC Uncon - May 2011
Amsterdam - Netherlands

‣ http://joind.in/3466

Friday, May 20, 2011

Who am I?

Joshua Thijssen (32)
Senior Software Engineer @ Enrise
Development in PHP, Python, Perl,
C, Java....

Blogs: http://www.adayinthelifeof.nl
http://www.enrise.com/blog

Email: joshua@enrise.com

Twitter: @jaytaph


What are we discussing?

‣ An introduction into public key encryption
‣ But ﬁrst of all...
‣ Who are Alice and Bob???


Terminology (1)


Terminology (1)

Meet Alice,
and Bob.


Terminology (2)

Fictional characters who are representing
either side of the (communication) line.
Person A(lice) is sending a message to
person B(ob).


Terminology (3)

http://labs.google.com/sets?hl=en&q1=plaintext&q2=ciphertext&q3=cipher&q4=deterministic&q5=rsa&btn=Large+Set
http://www.wordle.net/create

Encryption history

Before we look at
good encryptions,
let’s take a look at
some bad ones...

http://www.ﬂickr.com/photos/wwworks/4612188594/sizes/m/in/photostream/

Encryption history (1)

“algorithm”:
A = 1, B = 2, C = 3, ...., Z = 26

‣ SUBSTITUTION SCHEME



“algorithm”:
A = 1, B = 2, C = 3, ...., Z = 26

Encrypted message:
12,1,13,5




“algorithm”:
A = 1, B = 2, C = 3, ...., Z = 26

Encrypted message:
12,1,13,5
=
L,A,M,E




“algorithm”:
A = (A + key) mod 26,
B = (B + key) mod 26
....
Z = (Z + key) mod 26
or:
m = m + k mod 26

‣ CAESAREAN CIPHER



“algorithm”:
A = (A + key) mod 26,
....
or: Message: L A M E
m = m + k mod 26




“algorithm”:
A = (A + key) mod 26,
....
m = m + k mod 26
Ciphertext (key=1): M B N F




“algorithm”:
A = (A + key) mod 26,
....
m = m + k mod 26
Ciphertext (key=-1): K Z L D




“algorithm”:
A = (A + key) mod 26,
....
m = m + k mod 26
Ciphertext (key=26): L A M E




“algorithm”:
A = (A + key) mod 26,
....
m = m + k mod 26




“algorithm”:
A = (A + key) mod 26,
....
m = m + k mod 26
Ciphertext (key=13):Y N Z R (ROT13)




‣ FLAWS IN THESE CIPHERS



‣ Key is too easy to guess.




‣ Key has to be send to Bob.




‣ Deterministic.




‣ Deterministic.
‣ Prone to frequency analysis.



Frequency Analysis (1)



‣ The usage of every letter in the English (or
any other language) can be represented by
a percentage.



‣ The usage of every letter in the English (or
any other language) can be represented by
a percentage.
‣ ‘E’ is used 12.7% of the times in english
texts, the ‘Z’ only 0.074%.



Once upon a midnight dreary, while I pondered, weak and weary,
Over many a quaint and curious volume of forgotten lore—
While I nodded, nearly napping, suddenly there came a tapping,
As of some one gently rapping—rapping at my chamber door.
"'Tis some visitor," I muttered, "tapping at my chamber door—
Only this and nothing more."

Ah, distinctly I remember, it was in the bleak December,
And each separate dying ember wrought its ghost upon the floor.
Eagerly I wished the morrow;—vainly I had sought to borrow
From my books surcease of sorrow—sorrow for the lost Lenore—
For the rare and radiant maiden whom the angels name Lenore—
Nameless here for evermore.

And the silken sad uncertain rustling of each purple curtain
Thrilled me—filled me with fantastic terrors never felt before;
So that now, to still the beating of my heart, I stood repeating
"'Tis some visitor entreating entrance at my chamber door—
Some late visitor entreating entrance at my chamber door;—
This it is and nothing more."

‣ EDGAR ALLAN POE: THE RAVEN

http://www.gutenberg.org/cache/epub/14082/pg14082.txt


A small bit of text can result in differences, but still there
are some letters we can deduce..

‣ “THE RAVEN”, FIRST PARAGRAPH



We can deduce almost all letters just without even
CARING about the crypto algorithm used.

‣ “THE RAVEN”, ALL PARAGRAPHS


Encryption algorithms (1)

‣ SYMMETRICAL ALGORITHMS



‣ Previous examples were symmetrical encryptions.




‣ Same key is used for both encryption and decryption.




‣ Same key is used for both encryption and decryption.
‣ Good symmetrical encryptions: AES, Blowﬁsh, (3)DES




‣ THE PROBLEM WITH SYMMETRICAL ALGORITHMS



‣ How do we send over the key securely?




‣ How do we send over the key securely?
‣ O hai egg, meet chicken.



Public key encryption

Another encryption method:
asymmetrical encryption or public key encryption.

‣ FINALLY, WE HAVE ARRIVED...


Public key encryption (1)

Two keys instead of one:
public key - available for everybody.
Can be published on your blog.
private key - For your eyes only!



‣ USES 2 KEYS INSTEAD OF ONE: A KEYPAIR

http://upload.wikimedia.org/wikipedia/commons/f/f9/Public_key_encryption.svg


It is NOT possible to decrypt the message
with same key that is used to encrypt.

but

We can encrypt with either key.



‣ MULTIPLE APPLICATIONS FOR PUBLIC KEY ENCRYPTION



‣ Can be used for encrypting data.




‣ Can be used for encrypting data.
‣ Can be used for data validation and
authentication (signing).



Symmetrical vs Asymmetrical (1)

Symmetrical Asymmetrical
✓ quick. ✓ no need to send over the
✓ not resource intensive. (whole) key.
✓useful for small and large ✓ can be used for encryption
messages. and validation (signing).
✗ need to send over the key
✗ very resource intensive.
to the other side.
✗ only useful for small messages.



Use symmetrical encryption for the (large) message
and encrypt the key used with an asymmetrical
encryption method.



Hybrid
✓ quick
✓ not resource intensive
✓ useful for small and large messages
✓ safely exchange key data



Hybrid
✓ quick

+



Hybrid
✓ quick

+ =

http://www.zastavki.com/pictures/1152x864/2008/Animals_Cats_Small_cat_005241_.jpg


How does it work?

We will focus on the popular RSA,
but there are other algorithms as well:
DH, DSS(DSA) etc...


How does it work? (1)

Public key encryption works on the
premise that it is practically impossible
to refactor a large number back into 2
separate prime numbers.



Public key encryption works on the
premise that it is practically impossible
to refactor a large number back into 2
separate prime numbers.

Prime number is only divisible by 1 and
itself: 2, 3, 5, 7, 11, 13, 17, 19 etc...



‣ There is no proof that it’s impossible to refactor
quickly (all tough it doesn’t look plausible)



‣ Brute-force decrypting is always lurking around
(quicker machines, better algorithms).



‣ Brute-force decrypting is always lurking around
(quicker machines, better algorithms).
‣ Good enough today != good enough tomorrow.



(it’s 13 and 17 btw)



“large” number: 221




“large” number: 221

but we cannot calculate its
prime factors without brute force.
There is no “formula” (like e=mc 2)



Math example

‣ LET’S DO SOME MATH


Math example

This is mathness!


Math example

No, this is RSAAAAAAAA


Math example


Math example

‣ p = (large) prime number
‣ q = (large) prime number (but not too close to p)
‣ n = p . q (= bit length of the rsa-key)
‣ φ = (p-1) . (q-1) (the φ thingie is called phi)
‣ e = gcd(e, φ) = 1
‣ d = e^-1 mod φ
‣ public key = tuple (n, e)
‣ private key = tuple (n, d)


Math example

Step 1: select primes P and Q

‣ P = ? | Q = ? | N = ? | Phi = ? | e = ? | d = ?


Math example


‣ P = 11

‣ P = ? | Q = ? | N = ? | Phi = ? | e = ? | d = ?


Math example


‣ P = 11
‣ Q=3

‣ P = ? | Q = ? | N = ? | Phi = ? | e = ? | d = ?


Math example

Step 2: calculate N and Phi

‣ P = 11 | Q = 3 | N = ? | Phi = ? | e = ? | d = ?


Math example


‣ N = P . Q = 11 . 3 = 33

‣ P = 11 | Q = 3 | N = ? | Phi = ? | e = ? | d = ?


Math example


‣ N = P . Q = 11 . 3 = 33
‣ Phi = (11-1) . (3-1) = 10 . 2 = 20

‣ P = 11 | Q = 3 | N = ? | Phi = ? | e = ? | d = ?


Math example

Step 3: ﬁnd e

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = ? | d = ?


Math example

Step 3: ﬁnd e

‣ e = 3 (Fermat prime: 3, 17, 65537)

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = ? | d = ?


Math example

Step 3: ﬁnd e

‣ e = 3 (Fermat prime: 3, 17, 65537)
‣ gcd(e, phi) = 1 ==> gcd(3, 20) = 1

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = ? | d = ?


Math example

Step 4: ﬁnd d

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = ?


Math example

Step 4: ﬁnd d
‣ Extended Euclidean Algorithm gives 7

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = ?


Math example

Step 4: ﬁnd d
‣ brute force: (e.d mod n = 1)

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = ?


Math example

Step 4: ﬁnd d
‣ brute force: (e.d mod n = 1)
3 . 1 = 3 mod 20 = 3 3 . 6 = 18 mod 20 = 18
3 . 2 = 6 mod 20 = 6 3 . 7 = 21 mod 20 = 1
3 . 3 = 9 mod 20 = 9 3 . 8 = 24 mod 20 = 4
3 . 4 = 12 mod 20 = 12 3 . 9 = 27 mod 20 = 7
3 . 5 = 15 mod 20 = 15

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = ?


Math example

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = 7


Math example

That’s it:

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = 7


Math example

That’s it:
‣ public key = (n, e) = (33, 3)

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = 7


Math example

That’s it:
‣ public key = (n, e) = (33, 3)
‣ private key = (n, d) = (33, 7)

‣ P = 11 | Q = 3 | N = 33 | Phi = 20 | e = 3 | d = 7


Math example

The actual math is much more complex since
we use very large numbers, but it all comes
down to these (relatively simple) calculations..


Encrypting & decrypting

Encrypting a message:
c = me mod n

Decrypting a message:
m = cd mod n


Encrypting & decrypting (1)

Encrypting a message: private key = (n,d) = (33, 7):

m = 13, 20, 15, 5

13^7 mod 33 = 7
20^7 mod 33 = 26
15^7 mod 33 = 27
5^7 mod 33 = 14

c = 7, 26, 27,14



Decrypting a message: public key = (n,e) = (33, 3):

c = 7, 26, 27, 14

7^3 mod 33 = 13
26^3 mod 33 = 20
27^3 mod 33 = 15
14^3 mod 33 =5

m = 13, 20, 15, 5



‣ A message is an “integer”, not a block of data.



‣ A message must be between 2 and n-1.



‣ A message must be between 2 and n-1.
‣ Deterministic, so we must use a padding
scheme to make it non-deterministic.



‣ Public Key Cryptography Standard #1
‣ Pads data with (random) bytes up to n bits
in length (v1.5 or OAEP/v2.x).
‣ Got it ﬂaws and weaknesses too. Always
use the latest available version (v2.1)

‣ http://www.rsa.com/rsalabs/node.asp?id=2125



Data = 4E636AF98E40F3ADCFCCB698F4E80B9F

The encoded message block, EMB, after encoding but before encryption, with random
padding bytes shown in green:
0002257F48FD1F1793B7E5E02306F2D3228F5C95ADF5F31566729F132AA12009
E3FC9B2B475CD6944EF191E3F59545E671E474B555799FE3756099F044964038
B16B2148E9A2F9C6F44BB5C52E3C6C8061CF694145FAFDB24402AD1819EACEDF
4A36C6E4D2CD8FC1D62E5A1268F496004E636AF98E40F3ADCFCCB698F4E80B9F

After RSA encryption, the output is:
3D2AB25B1EB667A40F504CC4D778EC399A899C8790EDECEF062CD739492C9CE5
8B92B9ECF32AF4AAC7A61EAEC346449891F49A722378E008EFF0B0A8DBC6E621
EDC90CEC64CF34C640F5B36C48EE9322808AF8F4A0212B28715C76F3CB99AC7E
609787ADCE055839829E0142C44B676D218111FFE69F9D41424E177CBA3A435B

‣ PKCS#1 (v1.5) IN ACTION

http://www.di-mgt.com.au/rsa_alg.html#pkcs1schemes

Implementations of public keys in real life

http://farm4.static.ﬂickr.com/3538/3420164047_09ccc14e29.jpg

Web communication

public key encryption in

Web communications
(aka: I never use my credit card for internet purchases. It’s not safe.
Instead, I gave it to the waiter who walked away with it into the kitchen for 5 minutes..)


Web communication (1)

Welcome to 1991: HTTP is plaintext.
Everybody can be trusted. This page is under
construction, here’s a photo of my cat and a
link to geocities.

‣ BACK IN TIME



‣ BUT NOW...



‣ Free WiFi everywhere

‣ BUT NOW...



‣ Trafﬁc snooping

‣ BUT NOW...



‣ Trafﬁc snooping
‣ Authorization: Basic? (yes,VERY basic)

‣ BUT NOW...



‣ USING HTTPS



‣ HTTP encapsulated by TLS (previously SSL).

‣ USING HTTPS



‣ More or less: an encryption layer on top of http.

‣ USING HTTPS



‣ More or less: an encryption layer on top of http.
‣ Hybrid encryption.

‣ USING HTTPS



‣ Actual encryption methodology is decided
by the browser and the server (highest
possible encryption used).



‣ Symmetric encryption (AES-256, others)



‣ Symmetric encryption (AES-256, others)
‣ But both sides needs the same key, so we
have the same problem as before: how do we
send over the key?



‣ Key is exchanged in a public/private encrypted
communication.



communication.
‣ Which public key?



communication.
‣ Which public key?
‣ It is stored inside the server’s SSL certiﬁcate



‣ “GLOBAL” HTTPS HANDSHAKE



‣ Browser sends over its encryption methods.




‣ Server decides which one to use.




‣ Server send certiﬁcate(s).




‣ Client sends “session key” encrypted by the
public key found in the server certiﬁcate.




‣ Client sends “session key” encrypted by the
public key found in the server certiﬁcate.
‣ Server and client uses the “session key” for
symmetrical encryption.




‣ Thus: Public/private encryption is only used in
establishing a secondary (better!?) encryption.



‣ SSL/TLS is a separate talk (it’s way more complex
as this)



‣ SSL/TLS is a separate talk (it’s way more complex
as this)
‣ http://www.moserware.com/2009/06/ﬁrst-few-
milliseconds-of-https.html


Email communication

public key encryption in

Email communication
(aka: the worst communication method invented when it comes to privacy or secrecy, except for yelling)


Email communication (2)

http://change-your-ip.com/wp-content/uploads/image/nigerian_419_scam.jpg
http://torontoemerg.ﬁles.wordpress.com/2010/09/spam.gif


‣ DID YOU EVER SEND/RECEIVE EMAILS LIKE THIS?



‣ Did Bill really send this email?



‣ Do we know for sure that nobody has read
this email (before it came to us?)



‣ Do we know for sure that the contents of
the message isn’t tampered with?



‣ Do we know for sure that the contents of
the message isn’t tampered with?
‣ We use signing!


Signing (1)


Signing (1)

‣ Signing a message means adding a signature
that authenticates the validity of a message.


Signing (1)

‣ Like md5 or sha1, so when the message
changes, so will the signature.


Signing (1)

‣ Like md5 or sha1, so when the message
changes, so will the signature.
‣ This works on the premise that Alice and
only Alice has the private key that can
create the signature.


Signing (2)

http://en.wikipedia.org/wiki/File:Digital_Signature_diagram.svg


Signing (3)


Signing (3)

‣ GPG / PGP: Application for signing and/or
encrypting data (or emails).


Signing (3)

‣ Try it yourself with Thunderbird’s Enigmail
extension.


Signing (3)

‣ Try it yourself with Thunderbird’s Enigmail
extension.
‣ Public keys can be send / found on PGP-
servers so you don’t need to send your
keys to everybody all the time.


Signing (4)


Signing (5)



‣ ADVANTAGES OF SIGNING YOUR MAIL



‣ Everybody can send emails that ONLY YOU can read.




‣ Everybody can verify that YOU have send the email
and that it is authentic.




‣ Why is this not the standard?




‣ Why is this not the standard?
‣ No really, why isn’t it the standard?




Stupidity trumps
everything:
Don’t loose your
private key(s)
(as I did on multiple occasions)

http://farm4.static.ﬂickr.com/3231/2783827537_b4d2a5cc9a.jpg

Other applications

PGP / GPG
(encrypt / decrypt sensitive data)

OpenSSH
(Secure connection to other systems)

IPSEC
(VPN tunnels)

Software signing

‣ PUBLIC KEY ENCRYPTION IN OTHER FIELDS


Any questions?

‣ FOOTER TEXT

http://farm1.static.ﬂickr.com/73/163450213_18478d3aa6_d.jpg


Please rate my talk on joind.in: http://joind.in/3466

‣ THANK YOU FOR YOUR ATTENTION


Alice & bob public key cryptography 101 - uncon dpc

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