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Seminar Report On SIGNCRYPTION
Post: #1

Seminar Report
COCHIN - 682022
2005Page 2

Department of Computer Science CUSAT
COCHIN “ 682022
This is to certify that the Seminar report entitled
submitted by Anil C.B., Semester I, in the partial fulfillment of the
requirement for the award of M.Tech. Degree in Software Engineering is
a bonafide record of the Seminar presented by him in the academic year
Dr. Sumam Mary Idicula
Dr. K Paulose Jacob
Seminar Guide
Head of the DepartmentPage 3

Department of Computer Science CUSAT
I express our profound gratitude to the Head of Department Dr. K
Paulose Jacob for allowing me to proceed with the seminars and also for
giving me full freedom to access the lab facilities.
My heartfelt thanks to my guide Dr. Sumam Mary Idicula for
taking time and helping me through my seminars. She has been a constant
source of encouragement without which the seminars might not have been
completed on time. I am very grateful for her guidance.
I am also thankful to Mr. G Santhosh Kumar, Lecturer,
Department of Computer Science, for helping me with my seminars. His
ideas and thoughts have been of great importance
.Page 4

Department of Computer Science CUSAT
Signcryption is a new cryptographic primitive, which simultaneously
provides both confidentiality and authenticity. Previously, these two goals had been
considered separately, with encryption scheme provide confidentiality and digital
signature provides authenticity. In cases where both required, the encryption
operations and digital signature operations were simply sequentially composed. In
1998, Zheng demonstrated that by combining both goals into a single primitive it is
possible to achieve significant savings both in computational and communication
overhead. Since a wide variety of signcryption schemes have been proposed. In this
seminars we discuss one algorithm for signcryption and advantages and
disadvantages of signcryption. Compares signcryption with signature then
encryption and application of signcryption.Page 5

Department of Computer Science CUSAT
1. 1)
Why Signcryption¦¦¦¦¦¦¦¦¦¦¦¦.¦¦¦.4
SIGNCRYPTION- how its works¦¦¦¦¦¦¦¦¦¦¦¦¦..4
2. 1)
Steps involved in signcrypting a message¦¦¦¦¦¦.5
2. 2)
Steps involved in unsigncrypting a message¦¦¦¦¦.8
Handshake protocol¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦..16
ATM networks¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦..17
6. CONCLUSION¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦¦.18
Appendix (A)- Cryptography basics¦¦¦¦¦¦¦¦¦¦¦¦¦..20
Appendix (B)- Encryption and digital signatures¦¦¦¦¦¦¦¦..23Page 6

Department of Computer Science CUSAT
1. Introduction
In order to send a confidential letter in a way that it cannot be forged, it has been a
common practice for the sender of the letter to sign it, put it in an envelope and then
seal it before handing it over to be delivered.
Discovering Public key cryptography has made communication between people who
have never met before over an open and insecure network, in a secure and
authenticated way possible. Before sending a message, the sender has to do the
Sign it using a Digital Signature (DS) scheme
Encrypt the message and the signature using a private key encryption
algorithm under randomly chosen message encryption key
Encrypt the random message encryption key using the receiverâ„¢s public
Send the message following steps 1 to 3.
This approach is knows as signature-then-encryption. The main disadvantage of this
approach is that, digitally signing a message and then encrypting it, consumes more
machine cycles and bloats the message by introducing extended bits to it. Hence,
decrypting and verifying the message at the receiverâ„¢s end, a lot of computational
power is used up. Thus you can say that the cost of delivering a message using
signing-then-encryption is in effect the sum of the costs of both digital signatures
and public key encryption.
Is it possible to send a message of arbitrary length with cost less than that required
by signature-then-encryption?
Signcryption is a new paradigm in public key cryptography that simultaneously
fulfils both the functions of digital signature and public key encryption in a logically
single step, and with a cost significantly lower than that required by the traditional
signature followed by encryption.Page 7

Department of Computer Science CUSAT
Why Signcryption?
Based on discrete algorithm problem, Signcryption costs 58% less in average
computation time and 70% less in message expansion than does signature-then-
Using RSA cryptosystem, it costs on average 50% less in computation time
and 91% less in message expansion than signature-then-encryption does.
Signcryption “ How it works
Signcryption can be defined as a combination of two schemes; one of digital
signatures and the other of public key encryption.
One can implement Signcryption by using ElGamalâ„¢s shortened digital signature
scheme, Schnorrâ„¢s signature scheme or any other digital signature schemes in
conjunction with a public key encryption scheme like DES, 3DES or SPEED. This
choice would be made based on the level of security desired by the users.
Here we present the implementation of Signcryption using ElGamalâ„¢s shortened
signature scheme and a public key encryption algorithm denoted by E and D
(Encryption and Decryption algorithms).
Compared with DSS, SDSS1 and SDSS2 have the following advantages:
1. Their signatures are shorter
2. No modular inversion or division is required in signature verification.
3. They both admit provable security, albeit in the random oracle modelPage 8

Department of Computer Science CUSAT
These are the parameters involved in the Signcryption algorithm: -
Parameters public to all
p “ a large prime number
q “ a large prime factor of p-1
g “ an integer with order q modulo p chosen randomly
from [1,¦,p-1]
Hash “ a one-way hash function whose output has, say,
at least 128 bits
KH “ a keyed one-way hash function
(E, D) “ the encryption and decryption algorithms of a
private key cipher
Aliceâ„¢s keys
“ Alice™s private key, chosen uniformly at random
from [1,¦,q-1]
“ Alice™s public key (y
= g
mod p)
Bobâ„¢s keys
“ Bob™s private key, chosen uniformly at random
from [1,¦,q-1]
“ Bob™s public key (y
= g
mod p)
2.1 Steps involved in Signcrypting a message
We are taking an example in which Alice is sender and bob is receiver. So Alice is
having a message m, which wants to send to bob in an unsecured channel, hence
he uses signcryption mechanism to send the message to bob so tat message would
remain safe. So below steps are discussed which are involved in Signcrypting the
message.Page 9

Department of Computer Science CUSAT
Alice chooses a value x from the large range 1,¦,q-1
2. She then uses Bobâ„¢s public key and the value x and computes the hash of it.
This will give her a 128-bit string. K = hash (y
x mod p)
3. She then splits this 128-bit value K into two 64-bit halves. We can name them as
and k
and refer to them as the key pair.
Figure 2.1 Signcryption - generating k
and k
4. Next, Alice encrypts the message m using a public key encryption scheme E with
the key k
. This will give her the cipher text c. c = E k
5. Then, she uses the key k
in the one-way keyed hash function KH to get a hash of
the message m. This will give her a 128-bit hash, which we will call r. This process
uses the SDSS Algorithm. r = KH k
Just like in SDSS, Alice then computes the value of s. She does this using the value
of x, her private key x
, the large prime number q and the value of r. s = x / (r + x
mod qPage 10

Department of Computer Science CUSAT
Figure 2.2 Signcryption - generating components c and r
Figure 2.3 Signcryption - generating component s
7. Alice now has three different values, c, r and s. She then has to get these three
values to Bob in order to complete the transaction. She can do this in a couple of
ways. She can send them all at one time. She can also send them at separately
using secure transmission channels, which would increase security. Thus on her
part, Signcryption of the message is done.Page 11

Department of Computer Science CUSAT
Steps involved in Unsigncrypting a message
Bob receives the 3 values that Alice has sent him, c, r and s. He uses the
values of r and s, his private key x
, Aliceâ„¢s public key y
and p and g to compute a
hash which would give him 128-bit result.
K = hash ((y
* g
X x
mod p)
Figure 2.4 Unsigncryption - generating component k
This 128-bit hash result is then split into two 64-bit halves which would give him a key
pair (k
). This key pair would be identical to the key pair that was generated while
Signcrypting the message.
Bob then uses the key, k
, to decrypt the cipher text c, which will give
him the message m.
m = Dk
©Page 12

Department of Computer Science CUSAT
Figure 2.5 Unsigncryption “ obtaining the message m
Now Bob does a one-way keyed hash function on m using the key k
compares the result with the value r he received from Alice. If they match, it
means that the message m was indeed signed and sent by Alice, if not Bob will
know that the message was either not signed by Alice or was intercepted and
modified by an intruder. Thus Bob accepts the message only if KHk
(m) = r.
Figure 3.3.2 © Unsigncryption “ verification of the message mPage 13

Department of Computer Science CUSAT
Features and Security Aspects of Signcryption
3.1 Features
Digital Signcryption strives to do digital signature and public key encryption in
one logical step, with a cost less than that required by each of those steps done
separately. Let us assume that S is the Signcryption algorithm and U is the
Unsigncryption algorithm. The following three aspects define the features of
Signcryption: -
3.1.1 Unique unsigncryptability: - A message m of arbitrary length is
Signcrypted using the algorithm S. This will give a Signcrypted output c. The
receiver can apply Unsigncryption U on c to verify the message m. This
Unsigncryption is unique to the message m and the sender.
3.1.2 Security: - Since Signcryption is a combination of two security
schemes, digital signatures as well as public key encryption, it is likely to be more
secure and would ensure that the message sent couldnâ„¢t be forged, the contents of
which are confidential and ensures non-repudiation.
3.1.3 Efficiency: - The cost of computation involved when applying the
Signcryption and Unsigncryption algorithms as well as the communication
overhead is much smaller than with signature-then-encryption schemes.Page 14

Department of Computer Science CUSAT
3.2.1 Unforgeability: - Bob is in the best position to be able to forge any
Signcrypted message from Alice as only he is in possession of his private key, x
which is required to directly verify Aliceâ„¢s message. Given the Signcrypted text of
c, r and s, Bob can only obtain the message m by decrypting it using his private
key x
. Any changes he then makes to the message m will reflect in the next step
of Signcryption, which will ensure that the one-way keyed hash function on the
message m, will not match the value r. Thus Bob, the prime candidate for this kind
of attack, is prevented from forging Aliceâ„¢s Signcrypted message.
3.2.2 Confidentiality: - Given that an attacker has obtained all three
components of the Signcrypted message, c, r and s, he still would not be able to get
any partial information of the message m because he would have to also know
Bobâ„¢s private key as well as the two large prime number p and its factorial q,
known only to Alice and Bob. This is not feasible, as we know that deriving a
factorial from a large prime number is not practical.
Comparisons: -
The advantage of signcryption over signature-then-encryption lies in the dramatic
reduction of computational cost and communication overhead, which can be
symbolized by the following inequality:
Cost (Signcryption)< Cost (signature)+Cost (encryption)Page 15

Department of Computer Science CUSAT
Advantages and Disadvantages of Digital Signcryption
4.1 Advantages
4.1.1 Low computational cost
Signcryption is an efficient scheme as it does two steps at once during
Signcryption and Unsigncryption. When you think of this in terms of one person
sending a Signcrypted message to another person using a mobile device,
computation cost does not really matter much. Computational power of processors
has developed vastly these days, so if you were to consider Signcrypting network
traffic between two stations or all of the traffic on a certain network, then
computational power as well as savings in bandwidth are major factors.
4.1.2higher security
One can argue the fact that whether the bringing together of two security schemes
would increase or decrease security. In our groupâ„¢s view, it would only increase
security. We base this on the fact that when you combine two security schemes,
which by themselves are complex enough to withstand attacks, it can only lead to
added security.
Consider the following: -
X “Any Digital Signature Algorithm
Y “ Any Encryption Algorithm
X™ “ Total Number of Signature Algorithms known
Y™ “ Total Number of Encryption Algorithms known
Therefore the combination of the schemes X and Y would give you the
Signcryption scheme S. S = X U YPage 16

Department of Computer Science CUSAT
Figure 4.1 Security of Combination of Algorithms
If you consider the fact that both X and Y involve complex mathematical
functions, it is only logical to assume that S, which is a combination of both X and
Y will involve the combination of the complexities of both X and Y and thus be
more complex. More the complexity, more the harder it is for cryptanalysis.
Another point to be noted here is that X, the digital signature algorithm, can be
chosen from a large range of existing digital signature algorithms, Xâ„¢. Similarly
the encryption algorithm for Y can be chosen from any encryption algorithm like
3DES, DES, etc from the range Yâ„¢. Thus the Signcryption algorithm can be
implemented using any of the values in Xâ„¢ and Yâ„¢. This would make it very
difficult for a cryptanalyst to figure out which implementation was used in the
Signcrypting algorithm. Basically he would have Xâ„¢ x Yâ„¢ >= Xâ„¢ V Yâ„¢ i.e. the
cryptanalyst would have to decide between the number of total digital signature
algorithms times the number of encryption algorithms, which is greater or equal to
either the number of Xâ„¢ or Yâ„¢.Page 17

Department of Computer Science CUSAT
4.1.3 Message Recovery
Consider the following scenario: Alice signs and encrypts a message and sends it
to Bob. A while later, she wants to use the contents of the message again. To
satisfy Alice's requirement, her electronic mail system has to store some data
related to the message sent. And depending on cryptographic algorithms used,
Alice's electronic mail system may either
keep a copy of the signed and encrypted message as evidence of
transmission, or
in addition to the above copy, keep a copy of the original message,
either in clear or encrypted form.
A cryptographic algorithm or protocol is said to provide a past recovery ability if
Alice can recover the message from the signed and encrypted message using only
her private key. While both Signcryption and signature-then-encryption-with-a-
static-key" provide past recovery, signature-then-encryption" does not. One may
view signature-then-encryption" as an information black hole" with respect to
Alice the sender: whatsoever Alice drops in the black hole" will never be
retrievable to her, unless a separate copy is kept properly.Page 18

Department of Computer Science CUSAT
Figure 4. 2 Disadvantage of Signcryption
The way Signcryption algorithm works currently, Alice has to use Bobâ„¢s public
key to signcrypt a message. This has a disadvantage when you consider the need to
broadcast a Signcrypted text. Imagine a bank needs to send a Signcrypted message
to a number of share traders. With the current algorithm, it needs to signcrypt the
message with each of itâ„¢s intended recipientâ„¢s public keys and send them
separately to each one of them. This approach is redundant in terms of bandwidth
consumption and computational resource usage.
There is a research going on to solve this by introducing a group key between the
bank and the clients that it intends to send Signcrypted text and use that to
broadcast Signcrypted messages.Page 19

Department of Computer Science CUSAT
5. Possible Applications of Digital Signcryption
5.1 LM Signcryption and its application in WTLS handshake protocol
The mobile telecommunications business is booming. Tiny digital telephones and
sleek pocketsize PDAs (personal digital assistants) are now more than just fashion
accessories. The ability to connect to the Internet is a major feature that attracts
people to them. It means that mobile communication devices and client mobile
devices are now ready to access the Web. This scenario has given rise to a big
question in the minds of users, is it secure? Accordingly, operators and
manufactures have responded by establishing the WAP (Wireless Application
Protocol) forum.
The WAP forum has already developed WTLS (Wireless Transport Layer
Security) layer for secured communication in the WAP environment. The primary
goal of WTLS is to provide privacy, data integrity and AKA (Authentication and
Key Agreement) between communication entities.
Authenticity and confidentiality must be provided by a suitable encryption scheme
in case of mobile communication. One way to implement this is to first digitally
sign the message and encrypt it. This is commonly known as Signature-then-
encryption. The other is vice-versa, called encryption-then-signature.
Currently, the WTLS handshake protocol is used for secure communication
through mobile devices. This handshake uses AKA protocol with an end-to-end
connection. In handshake message flow, user certificate is sent to the recipient
without encryption or another cryptographic scheme. In this scenario an attacker
can get the certificate by eavesdropping on the transmission interface and can
figure out user information from the certificate. This can provide the attacker with
the user's location and activity.
If Signcryption is used to send messages with mobile devices it will rectify this
gap by providing stronger security. By the use of Signcryption, bandwidth use can
be reduced and computational load can be decreased without compromising on the
security of the message.Page 20

Department of Computer Science CUSAT
5.2 Using Signcryption in unforgeable key establishment over ATM Networks
The asynchronous transfer mode (ATM) is a high speed networking technique
for public networks capable of supporting many classes of traffic.
It is essentially a packet-switching technique that uses short fixed length packets
called cells. Fixed length cells simplify the design of an ATM switch at the high
switching speeds involved. The selection of a short fixed length cell reduces the
delay. ATM is capable of supporting a wide range of traffic types such as voice,
video, image and various data traffic.
In ATM networks data packets are typically 53 bytes. Only 48 bytes out of 53
bytes in an ATM cell can be used for transmitting data, as the remaining 5 bytes
are reserved for storing control information. Thus transmitting encryption key
materials of more than 384 bits (48 bytes) over an ATM network would require
two or more ATM cells. In a fast network such as ATM, if data packets are divided
then there could be considerable delay due to packetization, buffering and re-
assembling data units.
So, the need of the hour is to design an authenticated key establishment protocol
does not rely on a key distribution system,
has low resource requirements,
message is as short as possible and
offers unforgeability and non-repudiation.
In such a scenario, Signcryption or a modified usage of Signcryption can solve the
problem by minimizing message size as well as ensuring unforgeability and non-
Extensive research is going on in use of Signcryption in key establishment over
ATM networks. It is expected that within a few years it will actually be
implemented.Page 21

Department of Computer Science CUSAT
6. Conclusion
Signcryption is a very novel idea that, if implemented in the right way, can be
very useful.
Figure 6 Future Scenario of Signcryption
In life, it is human nature to try and do two things at once, or to Ëœkill two birds in
one stoneâ„¢. Humans do this to make shortcuts, save on time and resources. Is this
best approach to do things? In terms of computer security, like we explained
before, we believe that by combining two complex mathematical functions, you
will increase the complexity and in turn increase security. Signcryption still has a
long way to go before it can be implemented effectively and research is still going
on in various parts of the world to try to come up with a much more effective way
of implementing this.Page 22

Department of Computer Science CUSAT
. Bibliography and Internet Resources
Computer networks By TanenbaumPage 23

Department of Computer Science CUSAT
Appendix A
Cryptography basics
Suppose that someone wants to send a message to a receiver, and wants to be sure
tat no-one else can read the message. However, there is the possibility that someone
else opens the letter or hears the electronic communication.
In cryptographic terminology, the message is called a Plaintext or clear text.
Encoding the contents of the message in such a way that hides its content from
outsiders is called encryption. The encrypted message is called ciphertext. The
process of retrieving the plaintext from the ciphertext is called decryption.
Encryption and decryption usually makes use of a key, and the coding method is
such that only knowing the proper key can perform decryption.
Cryptography is the art or science of mathematical techniques related to such aspects
of data security as
¢ Confidentiality, or keeping secret the content of information from
unauthorized parties.
¢ Data integrity, or detecting the unauthorized alteration of data.
¢ Authentication, or identifying either entities or data origins.
¢ Non-repudiation, or preventing an entity from denying previous
commitments or actions.
¢ Cryptanalysis is the study of mathematical methods, which are used in
attempting to defeat cryptographic techniques. Cryptology means the study
of cryptography and crypt analysis.
The method of encryption and decryption is called a cipher. Some cryptographic
methods rely on the secrecy of the encryption algorithms; such algorithms are only
of historical interest and are not adequate for real world needs. Instead of the secrecy
of the methods itself, all modern algorithms base their security on the usage of aPage 24

Department of Computer Science CUSAT
key; a message can be decrypted only if the key used for decryption matches the key
used for encryption.
There are two classes of key-based algorithms, symmetric (or secret-key) and
asymmetric (or public-key) algorithms. The difference is that symmetric algorithms
use the same key for encryption and decryption, where as asymmetric algorithms use
a different key for encryption and decryption, and the decryption key cannot be
derived from the encryption key.
Symmetric algorithms can e derived into stream ciphers and block ciphers. Sream
ciphers encrypt a single bit of plaintext at a time , whereas block ciphers take a
number of bits, and encrypt them as a single unit. Many symmetric ciphers are
described on algorithms page.
Asymmetric ciphers (also called public key algorithms) permit the encryption key to
be public ( if it can be published to a website), allowing anyone to encrypt with the
key, whereas only the proper recipient ( who knows the decryption key) can decrypt
the message. The encryption key is also called the public key and the decryption key
the private key. The security provided by the ciphers is based on keeping the private
key secret.
Modern cryptographic algorithms are no longer pencil-and-paper ciphers. Strong
cryptographic algorithms are designed to be executed by the computers or
specialized hardware devices. In most applications, cryptography is done in
computer software.
Generally, symmetric algorithms are much faster to execute on a computer than
symmetric ones. In practice they are often used together, so that the public key
algorithm is used to encrypt a randomly generated encryption key, and random key
is used to encrypt the actual message using a symmetric algorithm. This is
sometimes called hybrid encryption.
Description of many good cryptographic algorithms are widely and publicly
available from any major bookstore, scientific library or on the internet. The most
studied and probably the most widely spread symmetric cipher is DES (DataPage 25

Department of Computer Science CUSAT
encryption standard). Because of the increase in the computing power of computers,
the basic version of DES cannot be considered sufficiently safe any more. Therefore
a new, more powerful cipher called AES (Advanced encryption standards) was
standardized in 2000. It will likely replace DES as the most widely used symmetric
encryption algorithm. RSA is probably the best known asymmetric encryption key
algorithm.Page 26

Department of Computer Science CUSAT
Appendix B
RSA Algorithm used for encryption and digital signatures
RSA is a cipher algorithm. It is an asymmetric algorithm and plays a key role in
public key cryptography. It is widely used in electronic commerce protocols. The
algorithm was described in 1977 by Ron Rivest, Adi Shamir and Len Adleman who
were all at MIT at the time; the letters RSA are the initials of their surnames.
Clifford Cocks, a British mathematician working for GCHQ, described an equivalent
system in an internal document in 1973. His discovery, however, was not revealed
until 1997 due to its top-secret classification.
The security of the RSA system relies on the difficulty of factoring very large
numbers; were such factorization to be quick, cryptanalysis of RSA messages would
be quick as well. New fast algorithms in this field could render the RSA algorithm
insecure, but this is generally considered unlikely. At the moment, just as for all
ciphers, inadequately long RSA keys are vulnerable to a brute force search approach.
The likely effect of an improvement in factoring technique will be to increase the
size of adequately long RSA keys. As of 2004, there is no known method of attack
which is feasible against the basic algorithm, and sufficiently long RSA keys make
brute force attacks infeasible -- that is, effectively impossible.
Here's the relatively easy to understand math behind RSA public key
1. Find P and Q, two large (e.g., 1024-bit) prime numbers.
2. Choose E such that E is greater than 1, E is less than PQ, and E and (P-
1)(Q-1) are relatively prime, which means they have no prime factors in
common. E does not have to be prime, but it must be odd. (P-1)(Q-1)
can't be prime because it's an even number.
3. Compute D such that (DE - 1) is evenly divisible by (P-1)(Q-1).
Mathematicians write this as DE = 1 (mod (P-1)(Q-1)), and they call D
the multiplicative inverse of E. This is easy to do -- simply find anPage 27

Department of Computer Science CUSAT
integer X which causes D = (X(P-1)(Q-1) + 1)/E to be an integer, then
use that value of D.
4. The encryption function is C = (T^E) mod PQ, where C is the ciphertext
(a positive integer), T is the plaintext (a positive integer), and ^ indicates
exponentiation. The message being encrypted, T, must be less than the
modulus, PQ.
5. The decryption function is T = (C^D) mod PQ, where C is the ciphertext
(a positive integer), T is the plaintext (a positive integer), and ^ indicates
Your public key is the pair (PQ, E). Your private key is the number D (reveal it
to no one). The product PQ is the modulus (often called N in the literature). E
is the public exponent. D is the secret exponent.
You can publish your public key freely, because there are no known easy
methods of calculating D, P, or Q given only (PQ, E) (your public key). If P
and Q are each 1024 bits long, the sun will burn out before the most powerful
computers presently in existence can factor your modulus into P and Q.
Shortened Digital Signature Scheme (SDSS proposed by ElGamal)
the signature algorithm used is the SDSS scheme proposed by ElGamal. This
scheme enables one person to send a digitally signed message to another person and
the receiver can verify the authenticity of this message. This scheme uses the private
key of the sender to sign the message and the receiver uses the senderâ„¢s public key
to verify the signature.
The parameters involved are: -
m “ the message
p “ a large prime number
q “ a large prime factor of p.
g “ an integer with order q modulo p chosen randomly from the range 1,..,p-1Page 28

Department of Computer Science CUSAT
x “ a number chosen uniformly at random from the range 1,¦,q-1
“ Alice™s private key chosen randomly from the range 1,..,p-1
“ Alice™s public key y
= g
mod p
The first step is to compute the component, r, which is essentially a hash of the
message m with additional parameters involved.
Figure B.1 Computing r in SDSS
Next we compute the component, s, using Aliceâ„¢s private key. We do this as
follows: -
Figure B.2 Computing s in SDSS
Next these two components, (r and s) are sent to Bob, along with the message m. On
receiving this, Bob uses r, s and Aliceâ„¢s public key to obtain the value k. Then he
does a hash of the message using k and verifies that it is equal to r.Page 29

Department of Computer Science CUSAT
Figure 3.1 © SDSS Verification
Bob accepts the message only if the hash of m and k gives him the same message, m that
he received from Alice. This will ensure that Alice indeed did digitally sign the message
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