A method for a Diffie Hellman key exchange, the method including selecting a field size p in the form p=hq+1, where q is a prime number that is one plus a factorial number b, such that q=(b!+1), and h is a cofactor, such that p=hq+1 is prime; selecting a generator integer g whose order modulo p is the prime q or is divisible by q; choosing a private key x; computing a public key gx mod p by raising said generator g to the power of said private key x, using arithmetic modulo said prime field size p; sending said public key gx mod p to a correspondent; receiving, from the correspondent, a second public key B comprising g raised to a second private key y selected by the correspondent, in the form gy; and creating a key Bx from the received second public key B, by raising said second public key B to the power of said private key x, using arithmetic modulo said prime field size p.