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Cryptography and Network Security Chapter 9 Fifth Edition  Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared by both sender and receiver if this key is disclosed communications are compromised also is symmetric, parties are equal hence does not...

Cryptography and Network Security Chapter 9 Fifth Edition  Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared by both sender and receiver if this key is disclosed communications are compromised also is symmetric, parties are equal hence does not protect sender from receiver forging a message & claiming is sent by sender  Public-Key Cryptography probably most significant advance in the 3000 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 crypto  Why Public-Key Cryptography? developed to address two key issues: key distribution – how to have secure communications in general without having to trust a KDC with your key digital signatures – how to verify a message comes intact from the claimed sender public invention due to Whitfield Diffie & Martin Hellman at Stanford Uni in 1976 known earlier in classified community  Public-Key Cryptography public-key/two-key/asymmetric cryptography involves the use of two keys: a public-key, which may be known by anybody, and can be used to encrypt messages, and verify signatures a related private-key, known only to the recipient, used to decrypt messages, and sign (create) signatures infeasible to determine private key from public is asymmetric because those who encrypt messages or verify signatures cannot decrypt messages or create signatures Public-Key Cryptography Symmetric vs Public-Key Public-Key Cryptosystems  Public-Key Applications can classify uses into 3 categories: encryption/decryption (provide secrecy) digital signatures (provide authentication) key exchange (of session keys) some algorithms are suitable for all uses, others are specific to one  Public-Key Requirements Public-Key algorithms rely on two keys where: it is computationally infeasible to find decryption key knowing only algorithm & encryption key it is computationally easy to en/decrypt messages when the relevant (en/decrypt) key is known either of the two related keys can be used for encryption, with the other used for decryption (for some algorithms) these are formidable requirements which only a few algorithms have satisfied  Public-Key Requirements need a trapdoor one-way function one-way function has Y = f(X) easy X = f–1(Y) infeasible a trap-door one-way function has Y = fk(X) easy, if k and X are known X = fk–1(Y) easy, if k and Y are known X = fk–1(Y) infeasible, if Y known but k not known a practical public-key scheme depends on a suitable trap-door one-way function Security of Public Key Schemes like private key schemes brute force exhaustive search attack is always theoretically possible but keys used are too large (>512bits) security relies on a large enough difference in difficulty between easy (en/decrypt) and hard (cryptanalyse) problems more generally the hard problem is known, but is made hard enough to be impractical to break requires the use of very large numbers hence is slow compared to private key schemes  RSA by Rivest, Shamir & Adleman of MIT in 1977 best known & widely used public-key scheme based on exponentiation in a finite (Galois) field over integers modulo a prime nb. exponentiation takes O((log n)3) operations (easy) uses large integers (eg. 1024 bits) security due to cost of factoring large numbers nb. factorization takes O(e log n log log n) operations (hard)  RSA En/decryption to encrypt a message M the sender: obtains public key of recipient PU={e,n} computes: C = Me mod n, where 0≤M