A pair of Paillier ciphertexts representing the integer and
fractional parts of a real number, together with the denominator
used to scale the fractional part. Two PaillierEncryptedReal
values encrypted under the same key with the same denominator
combine via the standard arithmetic operators.
Usage
PaillierEncryptedReal(
int = PaillierCiphertext(),
frac = PaillierCiphertext(),
den = NULL
)Arguments
- int
the PaillierCiphertext holding the integer part.
- frac
the PaillierCiphertext holding the scaled fractional part.
- den
the denominator used to scale the fractional part (a gmp::bigq).
Value
an S7 object of class PaillierEncryptedReal with properties int,
frac and den: the PaillierCiphertext carrying the integer
part, the PaillierCiphertext carrying the fractional part scaled
by den, and the denominator itself. It adds and subtracts with +
and -; decrypt() recombines the two parts and re-centers the
result into (-n/2, n/2) so that signed values round-trip. Produced
by encrypt_real().
Signed-arithmetic convention
Paillier's plaintext space is Z_n (a residue class modulo n,
the modulus carried by the public key). Negative real numbers and
running totals that cross zero are stored in their mod-n
representation, which lives in the upper half of [0, n). The
decrypt() method for PaillierEncryptedReal re-centers the raw
decrypted residues into the interval (-n/2, n/2) so that signed
values round-trip correctly. This means a PaillierEncryptedReal
is correct for signed real arithmetic as long as the true
cleartext stays in (-n/2, n/2) — for default 1024-bit keys, that
is > 10^307, well beyond any plausible statistical workload.
This convention applies only to PaillierEncryptedReal. The
integer-only PaillierCiphertext decrypt method preserves raw
mod-n semantics and does not center.