The City University of New York

Vladimir Shpilrain

Delaram Kahrobaei

Ha Lam

Bren Cavallo

Dima Grigoriev

A method for redacting a private blockchain comprises applying a hash function to a prefix and new content to compute a hash for a block of the blockchain; performing a modulo operation to convert the hash to an integer modulo; determining an inverse of the integer modulo; computing a redactable suffix from the prefix and the inverse of the integer modulo; replacing current content of the blockchain with the new content; and applying the redactable suffix to the block having the new content.

Redactable blockchain

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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New York, NY, United States of America

Vladimir Shpilrain