Abstract: Improvements are obtained in key generation and cryptographic applications in public key cryptography, by reducing the bit-length of public keys, thereby reducing the bandwidth requirements of telecommunications devices, such as wireless telephone sets.

Abstract: A method, system, and computer program product initializes a cryptosystem that implements XTR by reformulating an irreducibility test of a polynomial of the form F(c,X)=X3−cX2+cpX−1&egr;GF(p2)[X], for random c&egr;GF(p2), as an irreducibility problem for a third-degree polynomial of the form P(c,X)=X3+(cp+c)X2+(cp+1+cp+c−3)X+c2p+c2+2−2cp−2c, and testing the third-degree polynomial for irreducibility over GF(p). Testing the third-degree polynomial comprises eliminating the coefficient of X2 from P(c,X) to generate the polynomial P(c,X−(cp+c)/3)=X3+ƒ1X+ƒ0, and computing a discriminant &Dgr;=ƒ02+4ƒ13/27&egr;GF(p) by considering a polynomial of the form X2+ƒ0X−(ƒ1/3)3.