Praise for Fundamentals of WiMAX

7.3 Security 247Sidebar 7.2 The Math Behind Asymmetric Key Encryption:RSA AlgorithmAsymmetric key encryption is based on the simple fact that it is quite easy tomultiply two large prime numbers but computationally very intensive to findthe two prime factors of a large number. In fact, even using a supercomputer,it may take millions of years to do prime factorization of large numbers, suchas a 1,024-bit number. It should be noted that although no computationallyefficient algorithms are known for prime factorization, it has not been provedthat such algorithms do not exist. If someone were to figure out an easy wayto do prime factorization, the entire PKI encryption system would collapse.Here are the steps the RSA (Rivest-Shamin-Adleman) algorithm uses forpublic/private key encryption [52].1. Find two large prime numbers p and q such that N = pq. N is oftenreferred to as the modulus.2. Choose E, the public exponent, such that 1 < E < N, and E and(p –1) (q – 1) are relatively prime. Two numbers are said to be relativelyprime if they do not share a common factor other than 1.N and E together constitute the public key.3. Compute D, the private key, or secret exponent, such that (DE –1) isevenly divisible by (p –1) (q – 1). That is, DE = 1{mod[(p –1) (q –1)]}.This can be easily done by finding an integer X that causesD =(X(p –1)(q – 1) + 1)/E to be an integer and then using that value of D.4. Encrypt given message M to form the ciphertext C, using the functionC = M E [mod(N)], where the message M being encrypted must be lessthan the modulus N.5. Decrypt the ciphertext by using the function M = C D [mod(N)]. To crackthe private key D, one needs to factorize N.7.3.3 Authentication and Access ControlAccess control is the security mechanism to ensure that only valid users are allowed access to thenetwork. In the most general terms, an access control system has three elements: (1) an entity thatdesires to get access: the supplicant, (2) an entity that controls the access gate: the authenticator,and (3) an entity that decides whether the supplicant should be admitted: the authentication server.Figure 7.11 shows a typical access control architecture used by service providers. Accesscontrol systems were first developed for use with dial-up modems and were then adapted forbroadband services. The basic protocols developed for dial-up services were PPP (point-to-pointprotocol) [60] and remote dial-in user service (RADIUS) [50]. PPP is used between the