Efficient Encryption and Storage of Close Distance Messages with Applications to Cloud Storage

We present a result related to encryption, shared storage and similarity. The new protocol for secure storage of information solves a recent problem of how multiple independent and non-communicating individuals/processes can store and retrieve the same file in a shared storage facility without the use of a key escrow facility. That is, we present a method in which each individual

i

stores the ciphertext

C

M

,

i

for the same message

M

in shared storage at different time with a protocol requiring

O

(1) ciphertext memory size (i.e., a ciphertext whose size is independent of the number of individuals). Though the individuals can “store” / create the ciphertext for

M

at different times without communicating with one another or having pre-shared secret data, they must also be able to decrypt the same ciphertext at different times without communicating directly or indirectly with one another. As will be noted in the Introduction, this problem is motivated by approaches used by cloud storage providers. We further extend the result by enhancing the technique to allow an individual

i

to store

$C_{M_i,i}$

where each

M

i

is similar, but possibly different, yet use less memory than storing multiple ciphertext of each messages.

The result has practical implications in privacy and shared storage as has recently been demonstrated by a regulatory complaint to a cloud storage provider. The result uses multiple techniques from both cryptography and coding theory.