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Digital Signatures
-Kannan Ravindran

Who am I ?

I am Kannan Ravindran, A Student of
Velammal Engineering College, Ambattur
undertaking Bachelor of Engineering
concentration on Computer Science and
Engineering. I am a member of NullCon -
International security conference(Chennai
Chapter). I am serving H4CK3R.in as a
Moderator.

Contents

Introduction

Symmetric Key Encryption

Message Digest

Birthday Attack

MD5, SHA and Other Techniques

Conclusion

Introduction – What is it?
Cryptography is primarily used as a tool to
protect national secrets and strategies. It is
extensively used by the military, the diplomatic
services and the banking sector.

One of the landmark developments in the history
of cryptography was the introduction of the
revolutionary concept of public-key.

A cryptographic algorithm or cipher, is a
mathematical function used in the encryption
and decryption process. This mathematical
function works in combination with a key to
encrypt the plaintext (the original message)

Introduction – How it works?
A cryptographic algorithm, plus all possible keys and the
protocols that make it work comprise a Cryptosystem.

Introduction - Objective
 Confidentiality is used to keep the content of
information secret from unauthorized Persons
This is achieved through symmetric and
asymmetric encryption.
 Data integrity addresses the unauthorized
alteration of data. This is addressed by hash
functions.
 Authentication is related to identification. This
applies to both entity and information itself. This
is achieved through digital signature certificates
and digital signatures.

Symmetric Cryptography

In conventional Cryptography, also called secret-key or
symmetric-key encryption , the same key is used for
both encryption and decryption.
Caesar's Cipher:
Julius Caesar didn‟t
trust his messengers.
So when he sent a
message to his
generals, he replaced
every „A‟ with
„D‟, every „B‟ with „E‟
and so on. Only the
Caesar generals knew the “shift by 3” rule. So if we want to
and the
encrypt the word “NULLCON” then the cipher will be “QXOOFRQ”.
While decrypting it we follow the same “shift by 3” rule, but we shift
in the opposite side.

Message Digest
The original text: 7391743
Operation Result
Multiply 7 by 3 21
Discard first digit 1
Multiply 1 by 9 9
Multiply 9 by 1 9
Multiply 9 by 7 63
Multiply 3 by 4 12
Multiply 2 by 3 6

The Message Digest is 6

Message Digest
Requirements:
The given message
should be very easy to
find its corresponding
message digest. Also the
message digest should
always be same every
time.

Message Digest
Requirements:
The message digest
should be in such a way
that, it must be very
difficult to find the original
message by just the
reverse algorithm

Birthday Attack
 How many people do you need so that the probability of
having two of them share the same birthday is > 50% ?
 Random sample of n birthdays (input) taken from k (365,
output)
 kn total number of possibilities
 (k)n=k(k-1)…(k-n+1) possibilities without duplicate
birthday
 Probability of no repetition:
 p = (k)n/kn  1 - n(n-1)/2k
 For k=366, minimum n = 23
 n(n-1)/2 pairs, each pair has a probability 1/k of having
the same output
 n(n-1)/2k > 50%  n>k1/2

Birthday Attack

Thus the birthday attack creates a problem
in which more than one message can yield
the same message digest. And this
probability of this type of collision is more
than 50% to prevent these birthday attacks
algorithms like MD5 and SHA are used.

How many bits for hash?

 m bits, takes 2m/2 to find two with the same
hash
 64 bits, takes 232 messages to search
(doable)
 Need at least 128 bits

Hash for authentication

 Alice to Bob: challenge rA
 Bob to Alice: MD(KAB|rA)
 Bob to Alice: rB
 Alice to Bob: MD(KAB|rB)
 Only need to compare MD results

MD5
input Message

Output 128 bits Digest

• Until recently the most widely used hash algorithm
– in recent times have both brute-force & cryptanalytic
concerns
• Specified as Internet standard RFC1321

MD5
1. Pad message so its length is 448 mod 512
2. Append a 64-bit original length value to
message
3. Initialise 4-word (128-bit) MD buffer (A,B,C,D)
Process message in 16-word (512-bit) blocks:
 Using 4 rounds of 16 bit operations on
message block & buffer
 Add output to buffer input to form new buffer
value
4. Output hash value is the final buffer value

SHA

 Developed by NIST, specified in the
Secure Hash Standard (SHS, FIPS Pub
180), 1993
 SHA is specified as the hash algorithm in
the Digital Signature Standard (DSS),
NIST

SHA
 Input message must be < 264 bits
 not really a problem
 Message is processed in 512-bit blocks
sequentially
 Message digest is 160 bits
 SHA design is similar to MD5, but a lot
stronger

MD5 Vs SHA
 Brute force attack is harder (160 vs 128
bits for MD5)
 Not vulnerable to any known cryptanalytic
attacks (compared to MD4/5)
 A little slower than MD5 (80 vs 64 steps)
 Both work well on a 32-bit architecture
 Both designed as simple and compact for
implementation

Revised Secure Hash Standards
 NIST have issued a revision FIPS 180-2
 adds 3 additional hash algorithms
 SHA-256, SHA-384, SHA-512
 designed for compatibility with increased
security provided by the AES cipher
 structure & detail is similar to SHA-1
 hence analysis should be similar

Conclusion

Thus different concepts of Digital
signatures are discussed and a
overview of the various algorithms
used are discussed

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