Question

Using a Trusted Central Authority, reduce the number of secure channels to share common secret keys for a symmetric cryptosystem where N=9 users with p=37 where: Trent chooses a=6, b=23, c=15, from ℤ!" # = {1,2,3, … ,36} and each user u1, u2, … , ua respectively chooses z1 = 5, z2 = 36, z3 = 5, z4 = 11, z5 = 7, z6 = 21, z7 = 30, z8 = 19, z9 = 2 Calculate: 1. What Trent sends to u5 and u8 via a secure channel? 2. What polynomials do u5 and u8 form, from Trent’s information? 3. If u5 and u8 wish to communicate, find the common key they form by finding what both u5 and u8 both calculate.

Answer 1

The following problem is based on Key Pre distribution. In Symmetric key crytography for N users we require Keys. For large N this becomes in efficient. For reducing no. of keys required we us epre key distribution scheme involving centralized trust authority.

For answers please find images attached