cloud computing and security 03

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Cloud Computing and Security Some Algorithms and insight into RSA!

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Page 1: Cloud computing and security 03

Cloud Computing and Security

Some Algorithms and insight into RSA!

Page 2: Cloud computing and security 03

Various Algorithms

RSA Cryptoystem - To secure internet, Banking and credit card transaction.

Paillier Algorithm – Used in E voting systems, Threshold Scheme.

Gorti’s Non-interactive Exponential Homomorphic Encryption Scheme [NEHE]

Enhanced Homomorphic Cryptosystem (EHC) - Efficient Secure Message Transmission in Mobile Ad Hoc

Networks.

Algebra Homomorphic Encryption Scheme Based On Updated ElGamal (AHEE) - In Hybrid systems.

BGV - For the security of integer polynomials.

Page 3: Cloud computing and security 03

RSA Cryptosystem

1. Key Generation Step 1: Each user generates a public/private

key pair by selecting two large primes at random – say p & q.

Step 2: Computing RSA-modulus N = p . q

& ø(N) = (p-1) (q-1). Step 3: Selecting at random the encryption key e where, 1 < e < ø(N) such that GCD (e , ø(N)) = 1. Step 4: Publish their public encryption key:

KU= { e , N } & keep the secret private decryption key: KR= {d , N}.

2. Encryption

Step 1: Obtains public key of recipient KU={e , N}

Step 2: Computes: C = M^e mod N,

where 0≤M<N. 3. Decryption

Step 1: Uses their private key KR={d , N}

Step 2: Computes: M=C.d mod N

Page 4: Cloud computing and security 03

An Example

1. Key Generation Step 1: p=11 & q = 13 Step 2: System modulus N = 11 . 13 = 143.

and ø(143) = (11-1) (13-1) = 120. Step 3: Random Encryption key e ,

where, 1 < e < 120 : GCD (e , 120) = 1 ; e = 23 Step 4: Public Encryption Key: KU = {23,143}

Secret Private Decryption Key: KR= { d ,N }. To Calculate : 23 . d ≡ 1 mod ø(143), Now, 23 . d + k . 120 = 1 = GCD(e,120) . Hence from the above equation, d = 47 & k = -9

Encrypt(message) ≡ Message^pub.key mod RSA-modulus

OR

Encrypt(message) ≡ Message^23 mod 143

Property is :

Encrypt(m) * Encrypt(n) = Encrpyt(m*n)

Page 5: Cloud computing and security 03

Contd... (Area of a Square)Width = 7 private key : (47,143)Height = 3 public key : (23,143)

E(w) = width^e mod N = 7^23 mod 143 = 2

E(h) = height^e mod N = 3^23 mod 143 = 126

E(Area) = 252

D(E(Area)) = cipher^d mod N = 252^47 mod 143

= 21.

VOILA! Area = 21!

Page 6: Cloud computing and security 03

Fin.

Thank you!