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Fundamental Concepts in Security and its Application Cloud Computing

Fundamental Concepts in Security and its Application Cloud Computing. Basics of Cryptography. Relationship between the plaintext and the ciphertext. Secret-Key Cryptography. Monoalphabetic substitution each letter replaced by different letter Given the encryption key,

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Fundamental Concepts in Security and its Application Cloud Computing

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  1. Fundamental Concepts in Security and its Application Cloud Computing

  2. Basics of Cryptography Relationship between the plaintext and the ciphertext

  3. Secret-Key Cryptography • Monoalphabetic substitution • each letter replaced by different letter • Given the encryption key, • easy to find decryption key • Secret-key crypto called symmetric-key crypto • Issues: key distribution; only as safe as the key

  4. Public-Key Cryptography • Directly address the issues with symmetric keys • All users pick a public key/private key pair • publish the public key • private key not published • Public key is the encryption key • private key is the decryption key

  5. RSA (Rivest, Shamir, Adelman) Encryption To find a key pair e, d: 1. Choose two large prime numbers, P and Q (each greater than 10100), and form: N = P x Q Z = (P–1) x (Q–1) 2. For d choose any number that is relatively prime with Z (that is, such that d has no common factors with Z). We illustrate the computations involved using small integer values for P and Q: P = 13, Q = 17 –> N = 221, Z = 192 d = 5 3. To find e solve the equation: e x d = 1 mod Z That is, e x d is the smallest element divisible by d in the series Z+1, 2Z+1, 3Z+1, ... . e x d = 1 mod 192 = 1, 193, 385, ... 385 is divisible by d e = 385/5 = 77

  6. RSA Encryption (contd.) To encrypt text using the RSA method, the plaintext is divided into equal blocks of length k bits where 2k < N (that is, such that the numerical value of a block is always less than N; in practical applications, k is usually in the range 512 to 1024). k = 7, since 27 = 128 The function for encrypting a single block of plaintext M is: (N = P X Q = 13X17 = 221), e = 77, d = 5: E'(e,N,M) = Me mod N for a message M, the ciphertext is M77 mod 221 The function for decrypting a block of encrypted text c to produce the original plaintext block is: D'(d,N,c) = cd mod N The two parameters e,N can be regarded as a key for the encryption function, and similarly d,N represent a key for the decryption function. So we can write Ke= <e,N> and Kd = <d,N>, and we get the encryption function: E(Ke, M) ={M}K (the notation here indicating that the encrypted message can be decrypted only by the holder of the private key Kd) and D(Kd, ={M}K ) = M. <e,N> - public key, d – private key for a station

  7. Application of RSA • Lets say a person in Atlanta wants to send a message M to a person in Buffalo: • Atlanta encrypts message using Buffalo’s public key B  E(M,B) • Only Buffalo can read it using it private key b: E(b, E(M,B))  M • In other words for any public/private key pair determined as previously shown, the encrypting function holds two properties: • E(p, E(M,P))  M • E(P, E(M,p))  M

  8. How can you authenticate “sender”? • In real life you will use signatures: we will look at concept of digital signatures next. • Instead of sending just a simple message, Atlanta will send a signed message signed by Atlanta’s private key: • E(B,E(M,a)) • Buffalo will first decrypt using its private key and use Atlanta’s public key to decrypt the signed message: • E(b, E(B,E(M,a))  E(M,a) • E(A,E(M,a))  M

  9. SSH protocol • ssh (SSH client) is a program for logging into a remote machine and for executing commands on a remote machine. • Provides secure encrypted communications between two untrusted hosts over an insecure network. • X11 connections , arbitrary TCP/IP ports and SFTP can also be forwarded over the secure channel.

  10. SSH with RSA • ssh supports RSA based authentication (SHA-1, SHA-2). The scheme is based on public-key cryptography: there are cryptosystems where encryption and decryption are done using separate keys, and it is not possible to derive the decryption key from the encryption key. • RSA is one such system. The idea is that each user creates a public/private key pair for authentication purposes.

  11. SSH (contd.) • The server knows the public key, and only the user knows the private key. • The file $HOME/.ssh/authorized_keys lists the public keys that are permitted for logging in. • When the user logs in, the ssh program tells the server which keypair it would like to use for authentication. • The server checks if this key is permitted, and if so, sends the user (actually the ssh program running on behalf of the user) a challenge, a random number, encrypted by the user's public key. • The challenge can only be decrypted using the proper private key. • The user's client then decrypts the challenge using the private key, proving that he/she knows the private key but without disclosing it to the server.

  12. More uses of SSH • Password-less access: • The user creates his/her RSA key pair by running ssh-keygen. • This stores the private key in $HOME/.ssh/identity and the public key in $HOME/.ssh/identity.pub in the user's home directory. • The user should then copy the identity.pub to $HOME/.ssh/authorized_keys in his/her home directory on the remote machine (the authorized_keys file corresponds to the conventional $HOME/.rhosts file, and has one key per line, though the lines can be very long). • After this, the user can log in without giving the password.

  13. Why are we interested in PKI? • PKI : public key infrastructure • Of course, this is the way we can automate authentication (of programs running on users’ behalf) into remote system. • Lets look at amazon aws , ec2, and other systems as examples.

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