Public key algorithm

Dec 25, 2018Download as pptx, pdf1 like29 views

This document discusses public key algorithms such as RSA. It begins by explaining that public key algorithms use different keys for encryption and decryption, addressing limitations of symmetric key algorithms. The document then provides details on how public key algorithms work, including that users have a public key for encryption and private key for decryption. It describes the RSA algorithm specifically, outlining the key generation process involving large prime numbers. Finally, it gives an example of encrypting and decrypting a message using RSA and discusses other public key algorithms like Knapsack.

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.

This document describes the RSA algorithm for public key cryptography. RSA is based on the idea that factoring large integers into their prime factors is difficult. It involves choosing two prime numbers p and q, computing n=pq, and selecting a public key e such that gcd(e,(p-1)(q-1))=1. The private key d is computed such that ed=1 (mod φ(n)). To encrypt a message M, the sender computes C=Me (mod n) using the recipient's public key. The recipient decrypts by computing M=Cd (mod n) using their private key. The security of RSA relies on the difficulty of factoring the modulus n.

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Public key algorithm

1. PUBLIC KEY ALGORITHMS by, PRIYANKA G. MCA

2. 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).

3. 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.

4. 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.

5. 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

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

7. 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 .

8. 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.

9. 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

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

11. 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

12.  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

13. 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.

14. THANK YOU…..!

Public key algorithm

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Public key algorithm