BCIS 4630 Fundamentals of IT Security
CRYPTOGRAPHY
Dr. Andy Wu
Overview
• Key crypto concepts
– Key terms
– XOR
• Symmetric encryption
• Asymmetric encryption
• Hashes
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Cryptography
• Cryptography primarily protects confidentiality,
integrity, authentication, and non-repudiation.
• All the current encryption schemes are based
upon an algorithm, a recursive computational
procedure for solving a problem in finite steps.
– Modern cryptography manipulates data in binary
form.
– ASCII provides a standard way to map characters
to numbers.
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Key Terms (No Pun Intended)
• Plaintext
– The data that you want to keep secret.
– It is a human-readable text file or a computer-recognizable binary
file.
• Ciphertext
– Once the plaintext is encrypted, it becomes ciphertext.
– No longer human-readable or computer-recognizable.
• Algorithm
– Predefined procedures regarding how the plaintext will be
scrambled.
• Key
– Needed to scramble the plaintext.
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Caesar’s Cipher
•
•
•
•
•
A is now D; B is E; C is F; etc.
Shift the alphabet by three positions (key)
Plaintext: BCIS
Ciphertext: EFLV
To decrypt, shift back three positions (key)
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Ensuring Security
• Putting the algorithm under public review actually
improves the strength of the algorithm.
• A common attack on cryptography is the bruteforce attack.
– It tries every possible key until the correct one is found.
– Advances in technology and computer performance
have made brute-force attacks increasingly practical.
• Any predictability in key space makes the attacker’s
job easier.
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The Key
• The strength of a cryptosystem lies in the secrecy and length
(size) of the keys that are used, rather than keeping the
algorithm itself a secret.
– Key size is usually expressed in bits.
• A longer key increases the number of possible keys.
• The keyspace comprises all possible key values.
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Exclusive OR (XOR)
• A useful bit manipulation technique in cryptography.
• The symbol for XOR is .
• The XOR product is
– 0, if the two bits are the same.
– 1, if the two bits are different.
• Encryption takes advantage of an important property of
XOR:
– If A  B = A’, then A’  B = A
XOR
0
1
0
0
1
1
1
0
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XOR Example
11011001
10110011
= 01101010
10110011
= 11011001
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Symmetric Encryption
• The same key is used to:
– Encrypt the plaintext into ciphertext.
– Decrypt the ciphertext into plaintext.
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Symmetric Encryption Is Like A …
… dead bolt lock. The
same key is used to lock
(encrypt) the door (data)
and to unlock (decrypt)
the door (data).
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DES
• DES cuts up the plaintext into 64-bit blocks. It
uses 56-bit keys.
• It then “scrambles” the plaintext (via
“substitution” and then “permutation”) with the
key repeatedly. Each repetition is called a
“round”.
• DES performs 16 rounds on the plaintext.
• This is carried on until the entire message has
been encrypted with DES.
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A DES Round
Source: William Stallings, Cryptography and Network Security.
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3DES
• 3DES is a lot more than
three times stronger than
DES.
• Some times Key A = Key
C.
• A brute force attack would
have to try 2112  5.19 
1033 possible key values.
– Suppose the processing
speed is 1012 keys/second,
– 5.19  1033 @ 1012
keys/sec. = 5.19  1021
sec. = 1.65  1014 year).
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Other Symmetric Algorithms
• AES (Rijndael)
– Pronounced as “Rain-Doll”, Flemish for “XYZ.”
– The candidate algorithm that NIST chose over the other four
finalist as the replacement for DES.
– Supports 128-, 192-, and 256-bit keys.
• RC series
– RC4 is a stream cipher algorithm for symmetric encryption that
normally uses a 128-bit key.
– RC4 is ten times faster than DES.
• IDEA
• CAST
• Blowfish
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Problems with Symmetric Crypto
• Requires the sender and the receiver to have the
same key (a.k.a. shared key encryption).
• Prior arrangement for key distribution (called “outof-band” communication) is a must.
• In practice, people also faced a lot of scenarios in
which they need the ability to tell who has
encrypted a piece of information.
• However, if a symmetric key is shared between two
or more people, any one can encrypt it. To be able
to decrypt it tells nothing about who has encrypted
it; only that you also have the key.
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Symmetric Encryption
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Asymmetric Encryption
• Also known as public key cryptography.
• Typically are based on difficult math problems, many of which
are simple to do in one direction but difficult to do in the
opposite direction.
• Much slower than symmetric algorithms
– Rely on exponentiation, which is processor-intensive;
– Keys generally are larger (1024- or 2048-bit)
– Software implementation of RSA can be hundreds times slower
than DES.
– Thus, asymmetric algorithms typically are used only for encryption
of small amounts of information, e.g., the shared key for
symmetric encryption.
• Slow ≠ Weak
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Keys in Asymmetric Cryptography
• Uses two keys instead of one.
– The two keys are mathematically related through one-way
functions.
– One is publicly available; this “public key” is not protected.
– The other key is the “private key” and should be kept by the
owner only.
– If the private key is comprised, this key pair is no longer
safe to use.
• Either key can be used to encrypt data. However,
once a key is used to generate a ciphertext, it
cannot be used to decrypt that same ciphertext.
The other key has to be used for decryption.
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Asymmetric Encryption
If this is used to
encrypt …
Public key,
This has to be used
to decrypt.
Therefore …
which is available
to anyone
If Alice wants to encrypt a
message to Bob, she will go
which supposedly is find Bob’s public key. Bob is
accessible only to
the only one having the
the owner
matching private key to decrypt
it. (used for confidentiality)
Private key,
Public key,
which supposedly
is accessible only
to the owner
Private key,
If Alice can use Bob’s public
key to decrypt an encrypted
which is available to file, Bob must be the one who
anyone
encrypted the file. (used for
authentication)
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Asymmetric Encryption - Confidentiality
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Asymmetric Encryption - Authentication
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Two Uses of Asymmetric Encryption
• For Confidentiality
– Alice wants to send a secret message to Bob
– Alice uses Bob’s public key to encrypt message
– Bob uses Bob’s private key to decrypt message
• For Authentication
– Alice needs to let Bob know she is the sender of a message
– Alice encrypts the message with Alice’s private key
– Bob decrypts the message with Alice’s public key
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Asymmetric Cryptography
• No key distribution headache
– If Alice wants to send an encrypted message to Bob,
she doesn’t have to share a key with him beforehand.
She just encrypts the data with his public key.
– The ciphertext can only be decrypted by Bob with his
private key.
• Better authentication than symmetric encryption.
– If a messaged can be decrypted by Alice’s public key,
then it must be from Alice as Alice supposedly is the
only one who has the matching private key.
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RSA
• Name after its creators, Rivest, Shamir, and Adleman.
• One of the most popular and secure asymmetric algorithms.
• It capitalizes on the fact that there is no efficient way to factor
very large (100-200 digits) prime numbers.
– A prime number is a real number that is only divisible by 1 and
itself, e.g., 1, 3, 5, 7, 11, …
– Factoring is the process of determining whether an integer x is a
prime number, and if not, which two numbers when multiplied will
render the product x.
– Multiplying two large integers to arrive at an even larger number is
easy to do. To do the reverse (factoring) is extremely, if possible
at all, difficult.
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Other Asymmetric Algorithms
• Diffie-Hellman
– Enables two people to share a secret key without prior contacts.
– It relies on the difficulty in modular logarithms.
• El Gamal
– An extension of the Diffie-Hellman key exchange algorithm.
– It is based on the difficulty of calculating discrete logarithms in a
finite field.
• Elliptic Curve Cryptography (ECC)
– Its mathematic basis is the study of elliptic curves.
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Symmetric vs. Asymmetric
Symmetric
Asymmetric
Algorithm
Manipulation of bits
Mathematics
Number of Keys
One
Two
Key distribution
The key has to be shared
“out-of-band” before
encryption.
No prior arrangement is
necessary. Just use the
recipient's public key
Authentication
Cannot pinpoint the
sender if key is shared by
more than two people.
Can trace the message to
the owner of the related
private key.
Use
Bulk encryption
Key distribution
Digital signature
Speed
Fast
Slow
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Hash Function
• A hash function is a special mathematical algorithm
that performs one-way manipulate on a file.
– Widely used functions include MD5 and SHA-1.
• The algorithm takes a message of any length and
produces a fixed-length output.
• The hash is often called message digest.
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Properties of Hash
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Property 1: Non-Reversibility
• Both symmetric and asymmetric algorithms
are reversible.
– They can be converted from plaintext to ciphertext
and back again, if the right key is used.
• Hash algorithms, however, are not reversible.
– Once the hash is created, there is no way to take
the hash and retrieve the file that was used to
generate it.
– That is, you cannot reconstruct the message from
the digest.
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Property 2: Uniqueness
• You can’t find two files that produce the same
hash.
• A hash value is always mathematically unique
because it is extremely dependent on the
contents of the file.
– If anyone changes the file by so much as one
binary digit, the resulting hash value will be
different.
• The hash value can be used as a smaller,
easier-to-handle identifier of the file.
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Collisions
• A collision occurs when two different inputs are
hashed to the same value.
• Collisions are possible.
– Both SHA-1 and MD5 have been cracked.
– Fortunately, it is also unlikely that two documents with
the same hash value both make sense.
– The other file is likely to be a series of random
characters that just happens to result in the same hash
value.
• Therefore, the hash of a file can be used as the
file’s unique identifier.
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Hash Length
• Usually, the longer the hash value produced by the
hashing algorithm, the less susceptible it is to collisions.
– SHA-1 and RIPEMD-160 hashes are 160-bit long.
– MD5 hashes are 128-bit long.
Algorithm
# of Messages Required to Find
Collision
MD5
264 ≈ 1.8 x 1019
SHA-1
280 ≈ 1.2 x 1024
RIPEMD-160 280 ≈ 1.2 x 1024
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Source: Carlton Davis, IPSec, Securing VPNs.
Secure Hash Algorithm (SHA)
• SHA was developed in 1993 by the NIST
for secure hashing in the U.S. Digital
Signature Standard (DSS).
• The revised version is SHA-1.
– It uses block mode, accepting an input of up to
264 bits and compressing it to 160 bits.
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MD5
• Message Digest 5 is similar to the MD4
algorithm, but it is slightly slower and more
secure.
• MD5 creates a 128-bit hash of a message
of any length.
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Common Uses of Hashes
• Hash can be used to guard integrity of files.
– The sender sends with a message the hash
value of the message. The recipient runs the
message through the same hash function and
obtains her own hash value.
– If HSender = HRecipient, then the file has not been
tampered with.
• This use is based on the “uniqueness”
property.
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Verifying File Integrity with Hashes
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Verifying File Integrity with Hashes
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