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7/31/2019 Expose Celine

1/10

The RSA Algorithm

Table of contents

Introduction

Operation of the

RSA algorithm

Key generation

Encryption

Decryption

Security

Conclusion

The RSA Algorithm
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2/10

The RSA Algorithm

Table of contents

Introduction

Operation of theRSA algorithm

Key generation

Encryption

Decryption

Security

Conclusion

Table of contents

Introduction

Operation of the RSA algorithm

Key generation

Encryption

Decryption

Security

Conclusion
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3/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Introduction

by Rivest, Shamir & Adleman (RSA) in

1977

best known & widely used

protection of many things (ex credit cards)

the most secure code
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4/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Introduction

In cryptography, RSA is an algorithm for publickey cryptography.

The RSA algorithm involves the use of two

keys :

a public key, which may be known by

anybody, and can be used to encrypt

messages a private key, known only by the recipient,

and used to decrypt messages
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5/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Operation of the RSA algorithmKey generation

1. Choose 2 distinct random prime numbers :p,q

2. Compute n= p.q

3. Compute (n) = (p1)(q1) (Eulerstotient function)

4. Choose an integer e, such that

1 < e< (n) and gcd(e,(n)) = 1

5. Compute d e1 mod [(n)]

6. Publish the public encryption key : (e,n)

7. Keep secret private decryption key : (d,n)
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6/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Operation of the RSA algorithmEncryption

To encrypt a message the sender has to :

obtain public key of recipient (e,n) represent the message as an integer m in

[0,n1]

compute : c = me mod n
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7/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Operation of the RSA algorithmDecryption

To decrypt the ciphertext c the recipient :

uses his private key (d,n)

computes : m= cd mod n
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8/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Security

When attempting to attack the RSA, theattacker :

has access to the public key (e,n)

wants the private key (d,n)

Three ways to attack RSA :

force the search of key ( impossible given

the size of the numbers) launch attacks during the decryption

mathematical attack
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9/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

SecurityMathematical attack

To get d :

factorize n p and q (n) d

For small numbers, it is very easy to hack a RSA

code.

Factorize the number n.

With Maple : write " ifactor(n) ".

possible only for numbers < 1035.

very easy to find large prime numbers.


10/10

The RSA Algorithm

Table of contents

Introduction


Key generation

Encryption

Decryption

Security

Conclusion

Conclusion

The RSA algorithm is based on the fact that

it is far more difficult to factorize a product

of two primes than it is to multiply the two

primes.

Factoring n is the best known attack against

RSA to date.

It cannot guarantee 100% security, onlyadded protection.

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