Public key algorithm

PUBLIC KEY ALGORITHMS
by,
PRIYANKA G. MCA

PUBLIC KEY ALGORITHM
 Commonly we are using this algorithm to encrypt &
decrypt a message/images etc…
 Before this algorithm ,we were using the Symmetric
key algorithm.
 In that algorithm ,both encryption & decryption keys
are same.
 So, the message can easily robbed by a 3rd
party.(drawback of this algorithm).

INTRODUCTION
 In 1976,researchers at Stanford University, Diffie &
Hellman proposed a new kind of cryptosystem.
 Encryption & decryption key were different.
 Decryption key could not feasibly be derived from the
encryption key.
 This algorithm had to meet three requirement,
1. D(E(P))=P
2.It is exceedingly difficult to deduce D from E
3.E cannot be broken by a chosen plaintext attack.

PUBLIC KEY ALGORITHM
 In this algorithm everyone has 2 different keys.
 That is ,
1. public key – not only for personal.
2. private key – only for personal use.
(eg: fb id /email id and password)
 Here, we use
public key for – encryption.
private key for – decryption.
 Every public key must be unlocked by that’s private
key.

EXAMPLE
 ENCRYPTION:
Hi = (h) (i)
=(h+1) (i+1)
ciphertext = (i)(j)=ij
 DECRYPTION:
ciphertext= ij= (i)(j)
=(i-1)(j-1)
plain/orginal text =(h)(i)=Hi

APPLICATIONS
 BANKING - Transactions
 Online payment
 Social medias
 Email
 Etc…….

EXAMPLE:
 2 person named Alice & Bob both are sharing a
message to each other.
 Alice send a message is named P.
P- is a orginal text.
Alice Bob
EB(P) DB(EB(P))=P
o Bob replies to Alice named R
Bob Alice
EA(R) DA(EA(R))=R
No one else can read the encrypted text, because
this encryption system is soo strong .

RSA ALGORITHM
 Discovered by MIT group at 1978.
 The three discoverers Rivest, Shamir, Adlemen
(RSA).
 One of the very strong security based on it.
 This algorithm fully depends on Prime Numbers.

ALGORITHM:
 5 important steps:
1.Choose 2 different large random numbers.
(i,e) p & q
2.Calculate modulus n=p*q
3.Calculate totient function Q(x)=(p-1)(q-1).
4.Choose an random integer, “e” – shoud be
considered as a public key.
condition for choosing “e” is :-
1) 1<e<Q(x) / gcd(e,Q(x))=1
5. Calculate “d”=[1+k(Q(x))]/e ,0<=k<e

 ENCRYPTION:
C=Me mod n
here,
C-ciphertext,M- message
 DECRYPTION:
M=Cd mod n

EXAMPLE
 1.p=3,q=11
 2.n=p*q
 =3*11=33
 3.Q(x)=(p-1)(q-1)
 =(3-1)(11-1)=2*10=20
 4.e=3 1<e<Q(x),gcd(3,20)=1 1*3,1*20
 5.d=1+1(20)/3=21/3=7

 ENCRYPTION:
 S=19 orginal text (plain text value<n)
 C=Me mod n
 =193 mod 33=28
 C=28 cipher text
 DECRYPTION:
 C=28 cipher text
 M=Cd mod n
 =287 mod 33=19
 19=S orginal text

OTHER PUBLIC-KEY ALGORITHMS
 The 1st public-key algorithm was the Knapsack
algorithm.(Merkle & Hellman,1978).
 Here, someone owns a large number of objects, each
with a different weight.
 The owner encodes the message by secretly selecting
a subset of the objects and placing them in the
knapsack.
 The total weight of the objects in the knapsack is made
public ,as is the list of all possible objects.
 The list of objects in the knapsack is kept secret.
 With certain additional restrictions,the problem of
figuring out a possible list of objects with the given
weights was to be computationally infeasible &formed
the basics of the public key algorithm.

Public key algorithm

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