The City University of New York

Delaram Kahrobaei

Vladimir Shpilrain

Ha Lam

Bren Cavallo

A system for producing a public ring that is fully homomorphically encrypted. The system comprises a processor which generates a first presentation G of a ring, wherein G=x, y|x=0, y=0, xy+(p+1)yx=1, where x and y are generators and p is a first private prime number. The system further generates a second presentation H of the ring. H is defined as follows: H=x, y, t|x=0, y=0, t=myx, xy+myx+t=1. In addition, mand mare positive integers and p+1=m+m, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring &#x124; that is fully homomorphically encrypted, where: N=pq and further, q is a second private prime number, and the public ring &#x124; is further, publically available. A corresponding method is also disclosed.

System and method for private-key fully homomorphic encryption and private search between rings

A system for producing a public ring that is fully homomorphically encrypted. The system comprises a processor which generates a first presentation G of a ring, where G=x,y|x=0,y=0,xy+(p+1)yx=1, where x and y are generators and p is a first private prime number. The system further generates a second presentation H of the ring. H is defined as follows: H=x,y,t|x=0,y=0,t=myx,xy+myx+t=1. In addition, mand mare positive integers and p+1=m+m, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring &#x124; that is fully homomorphically encrypted, where: N=pq and further, q is a second private prime number, and the public ring &#x124; is further, publically available. A corresponding method is also disclosed.

A method for delegating a computational burden from a computationally limited party to a computationally superior party is disclosed. Computations that can be delegated include inversion and exponentiation modulo any number m. This can be then used for sending encrypted messages by a computationally limited party in a standard cryptographic framework, such as RSA. Security of delegating computation is not based on any computational hardness assumptions, but instead on the presence of numerous decoys of the actual secrets.

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Delaram Kahrobaei