R/homomorphicOps.R

In iamtrask/R-Homomorphic-Encryption-Package: Fully Homomorphic Encryption

#' Homomorphic operations on ciphertexts
#' 
#' These special operations overload the standard behaviour of the
#' arithmetic operations to work instead homomorphically on ciphertexts.
#' 
#' Note that not all homomorphic encryption schemes will support all operations.
#' Also, it is important to note that typically homomorphic operations cause
#' an increase in the noise within a ciphertext.  Once a certain number of 
#' operations have taken place the cipertext may no longer correctly decrypt.
#' If a scheme is *fully* homomorphic, then it may be possible to apply a
#' bootstrapping procedure which reduces the noise.
#' 
#' @name Arithmetic
#' @aliases + - *
#' 
#' @usage
#' ct1 + ct2
#' ct1 - ct2
#' ct1 * ct2
#' 
#' @param ct1,ct2 ciphertexts resulting from a call to \code{\link{enc}}
#' 
#' @return
#' A new ciphertext with the encrypted result of applying the operation to the
#' messages held by the two original cipertexts.
#' 
#' @examples
#' p <- pars("FandV")
#' keys <- keygen(p)
#' ct1 <- enc(keys$pk, 2)
#' ct2 <- enc(keys$pk, 3)
#' ctAdd <- ct1 + ct2
#' ctSub <- ct1 - ct2
#' ctMul <- ct1 * ct2
#' 
#' # Decrypt to 5, -1 and 6: the result of applying +, - and * to plain messages
#' dec(keys$sk, ctAdd)
#' dec(keys$sk, ctSub)
#' dec(keys$sk, ctMul)
NULL

#' Vectors of cipher texts
#' 
#' Vectors of cipher texts can be seemlessly created and manipulated in the same
#' way one normally works with vectors in R.
#' 
#' Vectors of cipher texts can be seemlessly created either at encryption time
#' by passing a vector message argument to \code{\link{enc}}, or after encryption
#' using the standard concatenation operator \code{\link[base]{c}}.
#' 
#' Standard operations which can be used on regular vectors can also be used
#' on vectors of cipher texts, where the scheme supports it.
#' 
#' As with regular scalar operations, note that not all homomorphic encryption 
#' schemes will support all vector operations.
#' Also, it is important to note that typically homomorphic operations cause
#' an increase in the noise within a ciphertext.  Once a certain number of 
#' operations have taken place the cipertext may no longer correctly decrypt.
#' If a scheme is *fully* homomorphic, then it may be possible to apply a
#' bootstrapping procedure which reduces the noise.
#' 
#' @name Vectors
#' @aliases c sum prod
#' 
#' @usage
#' enc(keys$pk1, c(m1, m2, ...))
#' c(ct1, ct2)
#' 
#' ct1 + ct2
#' ct1 - ct2
#' ct1 * ct2
#' ct1 \%*\% ct2
#' sum(ct1)
#' prod(ct1)
#' 
#' @examples
#' p <- pars("FandV")
#' keys <- keygen(p)
#' ct1 <- enc(keys$pk, c(2,3))
#' ct2 <- enc(keys$pk, c(4,5))
#' ctConcat <- c(ct1, ct2)
#' ctAdd <- ct1 + ct2
#' ctSub <- ct1 - ct2
#' ctMul <- ct1 * ct2
#' ctIP <- ct1 %*% ct2
#' 
#' # Decrypt to the equivalent of the above operations applied to the vectors
#' # c(2,3) and c(4,5)
#' dec(keys$sk, ctConcat)
#' dec(keys$sk, ctAdd)
#' dec(keys$sk, ctSub)
#' dec(keys$sk, ctMul)
#' dec(keys$sk, ctIP)
NULL