A company is considering different alternatives to implement a secure communication among its 1000 employees:

If a pair-wise secure communication using symmetric key cryptology is used, how many keys would need to be exchanged in total?

If a symmetrickey cryptographic system is used, in which cryptographic keys are randomly chosen from a set of all n-bit string, approximately what should n be in order to provide 512 bits of security against the Birthday Attack?

Considering the total number of keys found previously in a, the company has concerns in the distribution mechanism of the keys among the employees. Name and explain a cryptologic system alternative to enable a secure communication solution to avoid key distribution among the employees.