ROHINI COLLEGE OF ENGINEERING & TECHNOLOGY
1.6 DIGITAL SIGNATURE AND AUTHENTICATION PROTOCOLS
The most important development from the work on public-key cryptography is
the digital signature. Message authentication protects two parties who exchange
messages from any third party. However, it does not protect the two parties
against each other. A digital signature is analogous to the handwritten signature.
It must have the following properties:
• It must verify the author and the date and time of the signature
• It must to authenticate the contents at the time of the signature
• It must be verifiable by third parties, to resolve disputes
Requirements for a digital signature:
The signature must be a bit pattern that depends on the message being
signed.
The signature must use some information unique to the sender, to prevent
both forgery and denial.
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It must be relatively easy to produce the digital signature.
It must be relatively easy to recognize and verify the digital signature.
It must be computationally infeasible to forge a digital signature.
It must be practical to retain a copy of the digital signature in storage.
Types: Direct and arbitrated
Direct Digital Signatures
involve only sender & receiver
assumed receiver has sender’s public-key
digital signature made by sender signing entire message or hash with
private-key
security depends on sender’s private-key
Drawback: Forgery
Arbitrated Digital Signatures
involve use of arbiter A
– validates any signed message
– then dated and sent to recipient
requires a great deal of trust in arbiter
can be implemented with either private or public-key algorithms
arbiter may or may not see message
Digital Signature Scheme
The National Institute of Standards and Technology (NIST) has published
Federal Information Processing Standard FIPS 186, known as the Digital
Signature Standard (DSS).
The DSS makes use of the Secure Hash Algorithm (SHA) and presents a
new digital signature technique, the Digital Signature Algorithm (DSA).
The DSS uses an algorithm that is designed to provide only the digital
signature function and cannot be used for encryption or key exchange,
unlike RSA.
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Two approaches of Digital signature
RSA approach
DSS approach
RSA APPROACH
In the RSA approach, the message to be signed is input to a hash function that
produces a secure hash code of fixed length. This hash code is then encrypted
using the sender’s private key to form the signature. Both the message and the
signature are then transmitted. The recipient takes the message and produces a
hash code. The recipient also decrypts the signature using the sender’s public key.
If the calculated hash code matches the decrypted signature, the signature is
accepted as valid. Because only the sender knows the private key, only the sender
could have produced a valid signature.
DSS APPROACH
DSS uses an algorithm that is designed to provide only digital signature
function. Unlike RSA, it cannot be used for encryption or key exchange.
The DSS approach makes use of a hash function.
The hash code is provided as input to a signature function along with a
random number k generated for this particular signature.
The signature function also depends on the sender’s private key (PRa) and
the global public key (PUG)
The result is a signature consisting of two components, labeled s and r.
At the receiving end, the hash code of the incoming message is generated.
This plus the signature is input to a verification function.
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The verification function also depends on the global public key as well as
the sender’s public key (PUa), which is paired with the sender’s private
key.
The output of the verification function is a value that is equal to the
signature component if the signature is valid.
The signature function is such that only the sender, with knowledge of the
private key, could have produced the valid signature.
THE DIGITAL SIGNATURE ALGORITHM
1. Global Public key Components
p- prime no. where 2L-1 < p< 2 L for 512 ≤L ≤1024
q – prime divisor of ( p-1 )
Choose g = h (p-1)/q mod p
where h is any integer with 1 < h < (p-1) such that h (p-1)/q mod p > 1
2. User’s Private key
x - random or pseudo random integer with 0 < x < q
3. User’s Public key
y = g x mod p
4. User’s Per Message Secret Number
k = random or pseudo random integer with 0 < k < q
5. DSA Signature Creation
To sign a message M the sender: the sender generates a random signature
key k, k<q
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Computes signature pair:
r =(gk mod p)mod q
s = [k-1(H(M)+ xr)] mod q
Signature = (r,s)
6. DSA Signature Verification
After received M & signature (r,s)
Verify a signature, recipient computes:
w = (s’)-1 mod q
u1= [H(M’)w ]mod q
u2= (r’w)mod q
v = [(gu1 yu2)mod p ]mod q
If v=r then signature is verified.
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