to define a digital signature to define security services and result of forgery to discuss digital signature scheme( RSA and DSS)

1. Digital Signatures
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digital signature

2. Outline
 What is digital signature?
 security services and attacks on digital
signature
 Digital signatures scheme
 RSA digital signature
 Digital Signature Standard (DSS)
 Elliptic curve digital signature
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G.N. Joel
digital signature

3. 1. What is digital signature?
 Signature is a proof that a document
come from the correct source.
 When A sends message to B, B
needs to check the authenticity of
sender.
 Digital signature is a process of
signing a message with sender’s
private key.
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G.N. Joel
digital signature

4. Lowry Memorial
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5. Comparison
Between conventional and Digital signature
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6.  Conventional signature is included in the
document.
 Conventional is part of document.
 Digital signature is separate from
documents.
 In digital signature:
The receiver receives Message and signature
and verify the sender’s signature.
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digital signature

7. 2. Relationship
 In conventional signature: is one to many
relation between signature and documents.
 A person uses same signature to signs many
documents.
 Digital signature, one to one relationship
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G.N. Joel
digital signature

8. 3. Verification method
 In conventional signature, a receiver
compare a signature with the one in
the files.
 Digital signature, a copy of signature
is not stored any where.
 The receiver apply verification
techniques to the message
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G.N. Joel
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9. 2.Process of digital signature
 The sender uses signing algorithm to
sign the message.
 The message and signature are sent
to the receiver.
 The receiver receives message and
signature.
 Receiver applies verifying algorithm if
result is true, the message is
accepted, else it is rejected.
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10. Digital Signature Process
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11. Cont’s
 Add Keys to Signature:
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12.  The sender uses his private key,
applied to a signing algorithm to
sign a document.
 The receiver uses the public key
of the sender, applied to verifying
algorithm to verify a document
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13. Symmetric-key
ciphers:
Block ciphers
Stream ciphers
Public-key
ciphers
Digital Signatures services
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Services
Confidentiality Data integrity Authentication Non-repudiation
Message authentication
Entity authenticationArbitrary length
hash functions
Message
Authentication
codes (MACs)
Digital signatures
Authentication
primitives
Digital signatures
MACs
Digital
signatures

14. Forgery Types
 If the attack is successful, then the
result is forgery.
 There Two types:
 Existential
 Selective
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15. 1. Existential forgery
• The eve(attacker) may be able to
create a valid message-signature pair.
• On other hand she can not use.
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16. Cont.'s
2. Selective forgery
The eve may be able to forge sender’s
signature on a message with the
content selectively chosen by eve
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17. Digital Signature Scheme
1. RSA digital signature
2. ElGamal digital signature
3. Schnorr Digital signature
4. Digital Signature Standard(DSS)
5. Elliptic Curve Digital Signature
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18. RSA signature algorithm
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19. RSA
 Developed in 1978 by Rivest, Shamir and
Adleman (RSA)
 Most popular public key cryptosystem
 Based on the hard problem of “integer
factorization”
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20. RSA Digital Signature scheme
 Following are the steps:
I. the private key and public key
belongs to the sender.
II. The sender uses his private key to
sign a document.
III.The receiver uses sender’s public to
verify a document.
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21. Key-Generation for RSA(1)
1. Generate two large random distinct primes
p and q, each roughly the same size
2. Compute n = pq and
3. Select random integer e:
1<e< ⌀ (n), such that gcd(e, ⌀)=1
2. Compute unique integer d:
1<d<⌀ (n), such that ed=1 mod ⌀ (n)
2. Public key is (n, e); Private key is d
( ) ( 1)( 1)n p q   
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22. RSA signature generation and verification
 Signing a message :
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Alice creates a signature out of the message using her
private exponent S=M
d
modn and sends the message
and the signature to Bob
 Verifying:
Bob receives M and S, bob applies alice’s public
exponent to the signature to create a copy of the
message M=S
e
mod n

23. Lowry Memorial
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24. RSA signature example
Alice
 p=5 q=7 n = 35 φ(n) = 4·6=24
 e = 5; d: ed = 5d=1 mod 24 => d = 5
Public key: (n=35, e=5) Private key: d=5
 M = [0, n-1]
 For all m Є M R(m)=m
 m = 26; R(m) = 26 s = 265 mod 35 = 31
Bob:
 R(m) = 315 mod 35 = 26 Є [0, n-1]
 m = R-1(m) = 26
m~
m~
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25. Possible Attacks on RSA signature
 Integer factorization
 If an adversary is able to factor n, then
 Multiplicative property of RSA
 If , then s is valid signature for m:
 Hence, to avoid this attack R must not be
multiplicative, i.e.
))n((ed:d)q)(p()n(,pqn  modfindand 111 
)n(ss)m~m~(m~sm~m~m~
)n(modm~s
)n(modm~s dd
d
d
modthenif 212121
22
11



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RMm~  )m(Rm~ 
)b(R)a(R)ba(RMb,a 

26. 26
Digital Signature Standard(DSS)

27. The DSS is a collection of procedures
and standards for generating a digital
signature used for authenticating
electronic documents.
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28.  The Digital Signature Standard is
intended to be used:
 In electronic funds transfer.
 In software distribution, electronic mail,
data storage and applications which require
high data integrity assurance.
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29. The Elliptic Curve Digital Signature
Algorithm (ECDSA)
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