Private-Key Cryptography = = Public-Key Cryptography =a = = = i also is symmetric, parties are equal i hence does not protect sender from traditional private/secret/single key | cryptography uses one key shared by both sender and receiver if this key is disclosed communications are compromised receiver forging a message & claiming is sent by sender probably most significant advance in the 3 year history of cryptography \ uses two keys — a public & a private key asymmetric since parties are not equal \ uses clever application of number theoretic | \ concepts to function \ complements rather than replaces private key) cryptosytemWhy Public-Key Cryptography? i developed to address two key issues: i key distribution - how to have secure communications in general without havin trust a KDC with your key \ 8 digital signatures — how to verify a messag comes intact from the claimed sender i public invention due to Whitfield Diffie a Martin Hellman at Stanford University i in, 1976/1977 i known earlier in classified community Public-Key Cryptography i public-key/two-key/asymmetric cryptog rai involves the use of two keys: a public-key, which may be known by anybody, end used to encrypt messages, and verify signatures | i a private-key, known only to the recipient, used to 4 messages, and sign (create) signatures is asymmetric because i those who encrypt messages or verify signatures cann decrypt messages or create signatures |Public-Key Cryptography (@) Encryption Public-Key Characteristics Public-Key algorithms rely on two keys wt il it is computationally infeasible to find decrypti key knowing only algorithm & encryption key | lit is computationally easy to en/decrypt messages when the relevant (en/decrypt) key is known \ either of the two related keys canbe used for | encryption, with the other used for decryption some algorithms)Public-Key Cryptosystems Source A Destination B Public-Key Applications | can classify uses into 3 categories’ | encryption/decryption (provide secrec’ i digital signatures (provide authenticatio | key exchange (of session keys) i some algorithms are suitable for all u others are specific to one1 can classify uses into 3 categories! i encryption/decryption (provide secrec’ i digital signatures (provide authenticatio | key exchange (of session keys) i some algorithms are suitable for all us others are specific to one \ Security of Public Key Schemes i like private key schemes brute force exhi search attack is always theoretically poss but keys used are too large (>512bits) security relies on a large enough difference difficulty between easy (en/decrypt) and ha (cryptanalyse) problems more generally the hard problem is known, bf made hard enough to be impractical to break l requires the use of very large numbers a hence is slow compared to private key schegfDiffie-Hellman Key Exchange/Ag Algorithm \ i Diffie Hellman (DH) key exchange algorith method for securely exchanging cryptograp! keys over a public communications channel] i Keys are not actually exchanged — they are! jointly derived. It is named after their invent Whitfield Diffie and Martin Hellman (1976 & The beauty of this algorithm is that two pa who wants to communicate securely ca on a symmetric key. Algorithm Steps Firstly, Ram and Shyam agree on two large prime nt These two integer need not to be kept secret. Ram, can use an insecure channel to agree onthem. | i Ram chooses another large random number x, and C! such that A=g*x mod n. Ram sends the number to Shyam. Shyam independently chooses another large random and calculate B such that \ B = g*y mod n. Shyam sends the number B to Ram. A now compute the secret key K1: K1 = B*x modn B now Compute the secret key K2: 2 = A’y modnExample & Letn=11 and g=7 i Compute A = g*x mod N Assume x=3. Then, A = 743 mod 11 = 343 mod 11 =2 i Ram Sends 2 to Shyam. i Compute B = g*y mod n i Assume y=6. Then, B = 7*6 mod 11 = 117649 mod 11 = 4 i Compute Key K1= B’x mod n K1 = 443 mod 11 = 64 mod 11 =9 i Compute Key k2 = A‘y mod n K2 = 246 mod 11 = 64mod 11 =9Advantages i The sender and receiver don't need, any prior knowledge of each other. \ i Once the keys are exchanged, the communication of data can be done, through an insecure channel. | The sharing of the secret key is safe Disadvantages 1 The algorithm can not be used for al asymmetric key exchange. 1 Similarly, can not be used for signing digital signatures. \ 1 Since it doesn't authenticate any party the transmission, the Diffie-Hellman ké exchange is susceptible to a man-in- | middle attack.The RSA Algorithm i RSA Algorithm Based on the ide factorization of integers into the prime factors Is is hard. * rompute D distinct prime n nun | & RSA AGeTiAI Proposed by Ron | Rivest, Adi Shamir, and Leonard | \ Adleman \ in 1978 a RSA algorithm is an asymmetri cryptography algorithm which m there should be two keys involve while communicating, i.e., public and private key. i Public Key same for all users in th Network. \ i Private key is the separate key or \ 4 secret key for decryption.RSA Algorithm « Chooses two primes p,q and compute n=p.q & Compute $(n)= (p-1)(q-1) i Chooses e with 1 1024 bits. i even 2048 bits long key are used. w ws On the processing speed front, Elgamal is q RSA and ElGamal Schemes - A Comparison RSA ElGamal Itis more efficient for encryption. Itis more efficient for decryptiol It is less efficient for decryption. Itis more efficient for decryption For a particular security level, lengthy For the same level of security, v keys are required in RSA. short keys are required. Itis widely accepted and used. Itis new and not very popular ir