Abstract: 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.

Abstract: 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.

Abstract: 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|x2=0, y2=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|x2=0, y2=0, t=m1yx, xy+m2yx+t=1. In addition, m1 and m2 are positive integers and p+1=m1+m2, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring ? that is fully homomorphically encrypted, where: H ^ = ? x , y , t ? N · 1 = 1 , x 2 = 1 , y 2 = 0 , xyx = x , yxy = y , tx = 0 , yt = 0 , t 2 = t + m 2 2 - m 2 m 1 ? tyx ? , N=pq and further, q is a second private prime number, and the public ring ? is further, publically available. A corresponding method is also disclosed.

Abstract: 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|x2=0, y2=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|x2=0, y2=0, t=m1yx, xy+m2yx+t=1. In addition, m1 and m2 are positive integers and p+1=m1+m2, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring ? that is fully homomorphically encrypted, where: H ^ = ? x , y , t ? N · 1 = 1 , x 2 = 1 , y 2 = 0 , xyx = x , yxy = y , tx = 0 , yt = 0 , t 2 = t + m 2 2 - m 2 m 1 ? tyx ? , N=pq and further, q is a second private prime number, and the public ring ? is further, publically available. A corresponding method is also disclosed.

Abstract: 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|x2=0,y2=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|x2=0,y2=0,t=m1yx,xy+m2yx+t=1. In addition, m1 and m2 are positive integers and p+1=m1+m2, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring ? that is fully homomorphically encrypted, where: H ^ = ? x , y , t ? N · 1 = 1 , x 2 = 1 , y 2 = 0 , xyx = x , yxy = y , tx = 0 , yt = 0 , t 2 = t + m 2 2 - m 2 m 1 ? tyx ? , N=pq and further, q is a second private prime number, and the public ring ? is further, publically available. A corresponding method is also disclosed.

Abstract: 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.

Abstract: 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|x2=0, y2=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|x2=0, y2=0, t=m1yx, xy+m2yx+t=1. In addition, m1 and m2 are positive integers and p+1=m1+m2, wherein t is a generator and the first presentation G and the second presentation H are isomorphic. The system further produces a public ring ? that is fully homomorphically encrypted, where: H ^ = ? x , y , t ? N · 1 = 1 , x 2 = 1 , y 2 = 0 , xyx = x , yxy = y , tx = 0 , yt = 0 , t 2 = t + m 2 2 - m 2 m 1 ? tyx ? , N=pq and further, q is a second private prime number, and the public ring ? is further, publically available. A corresponding method is also disclosed.

Abstract: 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.