shared3p_oblivious_ram.sc

Module with functions for oblivious array lookup and write (ORAM)

Functions:

These functions are useful for obliviously reading or writing by several secret indices or when reading from or writing to several vectors by secret indices.

Note that both reading and writing consist of two functions: "prepare" (oramPrepareRead / oramPrepareWrite) and the actual action (oramPerformRead / oramPerformWrite). The prepare* functions are slower, but only require the secret indices vector, not the actual data vector to read from or write to. Therefore, a single prepare* function can be used to invoke several read/write functions (using the same seed). If you want to obliviously read/write only a few values, use *Lookup and *Update functions from the oblivious module instead.

oramPerformRead

Obliviously reads values from source vector indicated by the indices vector.

Detailed Description

D - shared3p protection domain

Supported types - uint8 / uint16 / uint32 / uint64 / int8 / int16 / int32 / int64

Parameters

src

- vector to read from

shuffleSeed

- random seed (32 bytes), has to be the same as used for oramPrepareRead

sortperm

- sorting permutation, output of oramPrepareRead

Returns a new vector result, where result[i] = src[indices[i]]

Given that size(src) = m and size(indices) = n then oramPrepareRead works in Ο((m+n)log(m+n)) and oramPerformRead in Ο(m+n) time.

None

Function Overloads

D uint8 oramPerformRead(D uint8[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D uint16 oramPerformRead(D uint16[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D uint32 oramPerformRead(D uint32[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D uint64 oramPerformRead(D uint64[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D int8 oramPerformRead(D int8[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D int16 oramPerformRead(D int16[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D int32 oramPerformRead(D int32[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

D int64 oramPerformRead(D int64[[1]] src, D uint8[[1]] shuffleSeed, uint[[1]] sortperm)

oramPerformWrite

Obliviously replaces (some) values in the original values vector with those contained in the replacement values vector.

Detailed Description

D - shared3p protection domain

Supported types - uint8 / uint16 / uint32 / uint64 / int8 / int16 / int32 / int64

Parameters

arr

- original values vector

vals

- replacement values vector

shuffleSeed1

- random seed (32 bytes), has to be the same as used for oramPrepareWrite

shuffleSeed2

- random seed (32 bytes), has to be the same as used for oramPrepareWrite

sigmatau

- sorting permutation, output of oramPrepareWrite

Returns a copy of arr , where arr[indices[i]] = vals[i]

Given that size(arr) = m and size(indices) = n then oramPrepareWrite works in Ο((m+n)log(m+n)) and oramPerformWrite in Ο(m+n) time.

None

Function Overloads

D uint8 oramPerformWrite(D uint8[[1]] arr, D uint8[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D uint16 oramPerformWrite(D uint16[[1]] arr, D uint16[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D uint32 oramPerformWrite(D uint32[[1]] arr, D uint32[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D uint64 oramPerformWrite(D uint64[[1]] arr, D uint64[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D int8 oramPerformWrite(D int8[[1]] arr, D int8[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D int16 oramPerformWrite(D int16[[1]] arr, D int16[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D int32 oramPerformWrite(D int32[[1]] arr, D int32[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

D int64 oramPerformWrite(D int64[[1]] arr, D int64[[1]] vals, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2, uint[[1]] sigmatau)

oramPrepareRead

Prepares a sort permutation for oblivious read function oramPerformRead.

Detailed Description

D - shared3p protection domain

See supported types for oramPerformRead

Parameters

srcLen

- length of the vector to read from

indices

- indices (in the src vector) to read from

shuffleSeed

- random seed (32 bytes)

sorting permutation, used as sortperm in oramPerformRead

Note that the output sorting permutation is a public value. Based on its input data, oramPrepareRead computes a secret permutation that is represented as combination of a public output permutation and a secret shuffleSeed. Therefore, the public permutation alone does not leak anything as it is masked by the secret permutation. This works similarly to one-time-pad. However, for the same reason the shuffleSeed value must not be reused for other prepare* (or shuffle) calls.

None

Function Overloads

uint oramPrepareRead(uint srcLen, D uint[[1]] indices, D uint8[[1]] shuffleSeed)

oramPrepareWrite

Prepares a sort permutation for oblivious write function oramPerformWrite.

Detailed Description

D - shared3p protection domain

See supported types for oramPerformWrite

Parameters

arrLen

- length of the original values vector (arr in oramPerformWrite)

indices

- vector specifying where to write the corresponding value from the replacement values vector (vals in oramPerformWrite)

shuffleSeed1

- random seed (32 bytes)

shuffleSeed2

- random seed (32 bytes)

sorting permutation, used as sigmatau in oramPerformWrite

Note that the output sorting permutation is a public value. Based on its input data, oramPrepareWrite computes a secret permutation that is represented as combination of a public output permutation and secret shuffleSeed1 and shuffleSeed2. Therefore, the public permutation alone does not leak anything as it is masked by the secret permutation. This works similarly to one-time-pad. However, for the same reason shuffleSeed1 shuffleSeed2 values must not be reused for other prepare* (or shuffle) calls.

None

Function Overloads

uint oramPrepareWrite(uint arrLen, D uint[[1]] indices, D uint8[[1]] shuffleSeed1, D uint8[[1]] shuffleSeed2)