Why Ke(Kg(m))=m -Kg(Kg(m))? follows directly from modular arithmetic: (me mod n)d mod n med mod n =mde mod n =(md mod n)e mod n Security:8-26
Security: 8- 26 follows directly from modular arithmetic: (me mod n)d mod n = med mod n = mde mod n = (md mod n)e mod n Why K (K (m)) = m ? B B - + K (K (m)) B B + - =
Why is RSA secure? suppose you know Bob's public key(n,e).How hard is it to determine d? essentially need to find factors of n without knowing the two factors p and q fact:factoring a big number is hard Security:8-27
Why is RSA secure? Security: 8- 27 ▪ suppose you know Bob’s public key (n,e). How hard is it to determine d? ▪ essentially need to find factors of n without knowing the two factors p and q • fact: factoring a big number is hard
RSA in practice:session keys exponentiation in RSA is computationally intensive DES is at least 100 times faster than RSA use public key crypto to establish secure connection,then establish second key-symmetric session key-for encrypting data session key,Ks Bob and Alice use RSA to exchange a symmetric session key Ks once both have Ks,they use symmetric key cryptography Security:8-28
RSA in practice: session keys Security: 8- 28 ▪ exponentiation in RSA is computationally intensive ▪ DES is at least 100 times faster than RSA ▪ use public key crypto to establish secure connection, then establish second key – symmetric session key – for encrypting data session key, KS ▪ Bob and Alice use RSA to exchange a symmetric session key KS ▪ once both have KS , they use symmetric key cryptography
Chapter 8 outline What is network security? -Principles of cryptography -Authentication,message integrity ■Securing e-mail Securing TCP connections:TLS Network layer security:IPsec Security in wireless and mobile networks Operational security:firewalls and IDS Security:8-29
Chapter 8 outline ▪ What is network security? ▪ Principles of cryptography ▪Authentication, message integrity ▪ Securing e-mail ▪ Securing TCP connections: TLS ▪ Network layer security: IPsec ▪ Security in wireless and mobile networks ▪Operational security: firewalls and IDS Security: 8- 29
Authentication Goal:Bob wants Alice to "prove"her identity to him Protocol ap1.0:Alice says“I am Alice” “I am Alice” failure scenario?? Security:8-30
Authentication Security: 8- 30 Goal: Bob wants Alice to “prove” her identity to him Protocol ap1.0: Alice says “I am Alice” failure scenario?? “I am Alice