Patent ID: 7315945

Claim:
A method of operating an identity based directoryless key-code cryptographic communication system comprising two users A and B and a universal authority U, involving the generation of a public modulus M, being the product of two primes P and Q which are both congruent to 3 mod 4, and the operation of a publicly available secure one-way hash function #, comprising the following steps: i) having U determine the public modulus M; ii) having U apply the #A's identity to produce a value a modulo M such that the Jacobi symbol ( a M ) is+1 and then to calculate the square root modulo M of a or −a and supply a resulting root, r, to A; iii) having B compute a and transmit a bit of cryptovariable b to A encrypted as s=(t+a/t)mod M, where t is a random number modulo M such that the Jacobi symbol ( t M ) = b and b is coded as either +1 or −1; iv) having B retransmit the bit of cryptovariable b to A encrypted as s ′ = ( t ′ - a t ′ ) ⁢ ⁢ mod ⁢ ⁢ M , where t′ is a different random number modulo M to t such than ( t ′ M ) = ( t M ) = b ; v) having user A recover cryptovariable bit b by computing b = ( s + 2 ⁢ r M ) ⁢ ⁢ or ⁢ ⁢ b = ( s ′ + 2 ⁢ r M ) .