SecurityThe Security Environment ThreatsBasics of CryptographySecret-Key CryptographyPublic-Key CryptographyRSA EncryptionRSA Encryption (contd.)Application of RSAHow can you authenticate “sender”?Digital SignaturesDigest FunctionsAlice’s bank account certificateDigital signatures with public keysLow-cost signatures with a shared secret keyOne-Way FunctionsSlide 16Buffer OverflowCovert Channels (1)Covert Channels (2)Covert Channels (3)SecurityChapter 99.1 The security environment 9.2 Basics of cryptography 9.3 User authentication 9.4 Attacks from inside the system 9.5 Attacks from outside the system 9.6 Protection mechanisms 9.7 Trusted systemsThe Security EnvironmentThreatsSecurity goals and threatsBasics of CryptographyRelationship between the plaintext and the ciphertext•Monoalphabetic substitution–each letter replaced by different letter•Given the encryption key, –easy to find decryption key•Secret-key crypto called symmetric-key cryptoSecret-Key CryptographyPublic-Key Cryptography•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 keyRSA 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 = 53. To find e solve the equation:e x d = 1 mod ZThat 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 de = 385/5 = 77RSA 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 Nfor a message M, the ciphertext is M77 mod 221The function for decrypting a block of encrypted text c to produce the original plaintext block is:D'(d,N,c) = cd mod NThe 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 stationApplication 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)) MHow 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)) MDigital Signatures•Strong digital signatures are essential requirements of a secure system. These are needed to verify that a document is:•Authentic : source•Not forged : not fake•Non-repudiable : The signer cannot credibly deny that the document was signed by them.Digest Functions•Are functions generated to serve a signatures. Also called secure hash functions.•It is message dependent.•Only the Digest is encrypted using the private key.Alice’s bank account certificate1. Certificate type: Account number2. Name: Alice3. Account: 62626264. Certifying authority: Bob’s Bank5. Signature: {Digest(field 2 + field 3)}KBprivDigital signatures with public keys{h}KpriMSigningVerifyingE(Kpri, h)128 bitsH(M)hMhH(doc)D(Kpub,{h}) {h}Kprih'h = h'?Msigned docLow-cost signatures with a shared secret keyMSigningVerifyingH(M+K)hh'H(M+K)hh = h'?KMsigned docMKOne-Way Functions•Function such that given formula for f(x)–easy to evaluate y = f(x)•But given y–computationally infeasible to find xDigital Signatures•Computing a signature block•What the receiver gets(b)Buffer Overflow•(a) Situation when main program is running•(b) After program A called•(c) Buffer overflow shown in grayCovert Channels (1)Client, server and collaborator processesEncapsulated server can still leak to collaborator via covert channelsCovert Channels (2)A covert channel using file lockingCovert Channels (3)•Pictures appear the same•Picture on right has text of 5 Shakespeare plays–encrypted, inserted into low order bits of color valuesZebrasHamlet, Macbeth, Julius CaesarMerchant of Venice, King
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