This paper investigates the randomness and cryptographic properties of the Narayana series modulo p, where p is a prime number. It is shown that the period of the Narayana series modulo p is either p*p+p+1 (or a divisor) or p*p-1 (or a divisor). It is shown that the sequence has very good autocorrelation and crosscorrelation properties which can be used in cryptographic and key generation applications.