02-02-2012, 03:19 PM
Network Security
RSA Continues
Choose an integer e such that 1 < e < φ(pq), and e and φ(pq) share no divisors other than 1 (i.e. e and φ(pq) are coprime).
e is released as the public key exponent.
RSA Continues
Determine d which satisfies the congruence relation .
Stated differently, ed − 1 can be evenly divided by the totient (p − 1)(q − 1).
d is kept as the private key exponent.
RSA Example
Choose two prime numbers
p = 61 and q = 53
Compute n = pq
Compute the totients of product. For primes the totient is maximal and equals x − 1. Therefore
RSA Example Continues
Choose any number e > 1 that is coprime to 3120. Choosing a prime number for e leaves you with a single check: that e is not a divisor of 3120.
e = 17
RSA Example Continues
Compute d such that
d . e = 1 mod Ǿ(pq)
d = 2753
since 17 · 2753 = 46801 and 46801 mod 3120 = 1, this is the correct answer.
RSA Example Continues
The public key is (n = 3233, e = 17).
The private key is (n = 3233, d = 2753).
RSA Example Continues
For instance, in order to encrypt m = 123, we calculate
To decrypt c = 855, we tap
Authentication
KERBEROS
In Greek mythology, a many headed dog, the guardian of the entrance of Hades
KERBEROS
Provides a centralized authentication server to authenticate users to servers and servers to users.
Relies on conventional encryption, making no use of public-key encryption
Two versions: version 4 and 5
Version 4 makes use of DES
Kerberos Version 4
Terms:
C = Client
AS = authentication server
V = server
IDc = identifier of user on C
IDv = identifier of V
Pc = password of user on C
ADc = network address of C
Kv = secret encryption key shared by AS an V
TS = timestamp
| = concatenation
RSA Continues
Choose an integer e such that 1 < e < φ(pq), and e and φ(pq) share no divisors other than 1 (i.e. e and φ(pq) are coprime).
e is released as the public key exponent.
RSA Continues
Determine d which satisfies the congruence relation .
Stated differently, ed − 1 can be evenly divided by the totient (p − 1)(q − 1).
d is kept as the private key exponent.
RSA Example
Choose two prime numbers
p = 61 and q = 53
Compute n = pq
Compute the totients of product. For primes the totient is maximal and equals x − 1. Therefore
RSA Example Continues
Choose any number e > 1 that is coprime to 3120. Choosing a prime number for e leaves you with a single check: that e is not a divisor of 3120.
e = 17
RSA Example Continues
Compute d such that
d . e = 1 mod Ǿ(pq)
d = 2753
since 17 · 2753 = 46801 and 46801 mod 3120 = 1, this is the correct answer.
RSA Example Continues
The public key is (n = 3233, e = 17).
The private key is (n = 3233, d = 2753).
RSA Example Continues
For instance, in order to encrypt m = 123, we calculate
To decrypt c = 855, we tap
Authentication
KERBEROS
In Greek mythology, a many headed dog, the guardian of the entrance of Hades
KERBEROS
Provides a centralized authentication server to authenticate users to servers and servers to users.
Relies on conventional encryption, making no use of public-key encryption
Two versions: version 4 and 5
Version 4 makes use of DES
Kerberos Version 4
Terms:
C = Client
AS = authentication server
V = server
IDc = identifier of user on C
IDv = identifier of V
Pc = password of user on C
ADc = network address of C
Kv = secret encryption key shared by AS an V
TS = timestamp
| = concatenation