HElib 1.0 Implementing Homomorphic Encryption

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replicate.h File Reference

Procedures for replicating a ciphertext slot across a full ciphertext. More...

`#include "FHE.h"`
`#include "EncryptedArray.h"`

Go to the source code of this file.

## Classes
class | ReplicateHandler
| A virtual class to handle call-backs to get the output of replicate. More...

## Functions
void | replicate (const EncryptedArray &ea, Ctxt &ctx, long pos)
| The value in slot #pos is replicated in all other slots. On an n-slot ciphertext, this algorithm performs O(log n) 1D rotations.
void | replicate0 (const EncryptedArray &ea, Ctxt &ctxt, long pos)
| A lower-level routine. Same as replicate, but assumes all slots are zero except slot #pos.
void | replicateAll (const EncryptedArray &ea, const Ctxt &ctxt, ReplicateHandler *handler, long recBound=64)
void | replicateAllOrig (const EncryptedArray &ea, const Ctxt &ctxt, ReplicateHandler *handler)

## Variables
bool | replicateVerboseFlag

## Detailed Description

Procedures for replicating a ciphertext slot across a full ciphertext.

This module implements a recursive, O(1)-amortized algorithm for replications. On an input ciphertext that encrypts (x_1, ..., x_n), we generate the n encrypted vectors (x_1, ..., x_1), ..., (x_n, ..., x_n), in that order.

To process the output vectors, a "call back" mechanism is used (so that we do'ne need to generate them all, and instead can return them one by one). For this purpose, the caller should pass a pointer to a class derived from the purely abstract class ReplicateHandler.

The replication procedures are meant to be used for linear algebra operation where a matrix-vector multiplication can be implemented for example by replicating each entry of the vector as a stand-alone ciphertext, then use the SIMD operations on these ciphertexts.

## Function Documentation

void replicateAll | ( | const EncryptedArray & | ea,
|  | const Ctxt & | ctxt,
|  | ReplicateHandler * | handler,
|  | long | recBound = `64`
| ) |  |

replicateAll uses a hybrid strategy, combining the O(log n) strategy of the replicate method, with an O(1) strategy, which is faster but introduces more noise. This tradeoff is controlled by the parameter recBound:

- recBound < 0: recursion to depth |recBound| (faster, noisier)
- recBound ==0: no recursion (slower, less noise)
- recBound > 0: the recursion depth is chosen heuristically, but is capped at recBound

The default value for recBound is 64, this ensures that the choice is based only on the heuristic, which will introduce noise corresponding to O(log log n) levels of recursion, but still gives an algorithm that theoretically runs in time O(n).

void replicateAllOrig | ( | const EncryptedArray & | ea,
|  | const Ctxt & | ctxt,
|  | ReplicateHandler * | handler
| ) |  |

This function is obsolete, and is kept for historical purposes only. It was a first attempt at implementing the O(1)-amortized algorithm, but is less efficient than the function above.