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Revision #3 to TR12-129 | 14th January 2013 22:24

Limits on the Usefulness of Random Oracles

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Revision #3
Authors: Iftach Haitner, Eran Omri, Hila Zarosim
Accepted on: 14th January 2013 22:24
Downloads: 729
Keywords: 


Abstract:

In the random oracle model, parties are given oracle access to a random function (i.e., a
uniformly chosen function from the set of all functions), and are assumed to have unbounded
computational power (though they can only make a bounded number of oracle queries). This
model provides powerful properties that allow proving the security of many protocols, even such that cannot be proved secure in the standard model (under any hardness assumption). The random oracle model is also used for showing that a given cryptographic primitive cannot be used in a black-box way to construct another primitive; in their seminal work, Impagliazzo and
Rudich [STOC ’89] showed that no key-agreement protocol exists in the random oracle model,
yielding that key-agreement cannot be black-box reduced to one-way functions. Their work has
a long line of followup works (Simon [EC ’98], Gertner et al. [STOC ’00] and Gennaro et al.
[SICOMP ’05], to name a few), showing that given oracle access to a certain type of function
family (e.g., the family that “implements” public-key encryption) is not sufficient for building
a given cryptographic primitive (e.g., oblivious transfer). Yet, the following question remained
open:

What is the exact power of the random oracle model?

We make progress towards answering the above question, showing that, essentially, any no
private input, semi-honest two-party functionality that can be securely implemented in the
random oracle model, can be securely implemented information theoretically (where parties are
assumed to be all powerful, and no oracle is given). We further generalize the above result to
function families that provide some natural combinatorial property.

Our result immediately yields essentially that the only no-input functionalities that can be
securely realized in the random oracle model (in the sense of secure function evaluation), are the
trivial ones (ones that can be securely realized information theoretically). In addition, we use
the recent information theoretic impossibility result of McGregor et al. [FOCS ’10], to show the
existence of functionalities (e.g., inner product) that cannot be computed both accurately and in
a differentially private manner in the random oracle model; yielding that protocols for computing
these functionalities cannot be black-box reduced to the existence of one-way functions.


Revision #2 to TR12-129 | 14th January 2013 21:48

Limits on the Usefulness of Random Oracles





Revision #2
Authors: Iftach Haitner, Eran Omri, Hila Zarosim
Accepted on: 14th January 2013 21:48
Downloads: 756
Keywords: 


Abstract:

In the random oracle model, parties are given oracle access to a random function (i.e., a
uniformly chosen function from the set of all functions), and are assumed to have unbounded
computational power (though they can only make a bounded number of oracle queries). This
model provides powerful properties that allow proving the security of many protocols, even such
that cannot be proved secure in the standard model (under any hardness assumption). The
random oracle model is also used for showing that a given cryptographic primitive cannot be
used in a black-box way to construct another primitive; in their seminal work, Impagliazzo and
Rudich [STOC ’89] showed that no key-agreement protocol exists in the random oracle model,
yielding that key-agreement cannot be black-box reduced to one-way functions. Their work has
a long line of followup works (Simon [EC ’98], Gertner et al. [STOC ’00] and Gennaro et al.
[SICOMP ’05], to name a few), showing that given oracle access to a certain type of function
family (e.g., the family that “implements” public-key encryption) is not sufficient for building
a given cryptographic primitive (e.g., oblivious transfer). Yet, the following question remained
open:

What is the exact power of the random oracle model?

We make progress towards answering the above question, showing that, essentially, any no
private input, semi-honest two-party functionality that can be securely implemented in the
random oracle model, can be securely implemented information theoretically (where parties are
assumed to be all powerful, and no oracle is given). We further generalize the above result to
function families that provide some natural combinatorial property.
Our result immediately yields essentially that the only no-input functionalities that can be
securely realized in the random oracle model (in the sense of secure function evaluation), are the
trivial ones (ones that can be securely realized information theoretically). In addition, we use
the recent information theoretic impossibility result of McGregor et al. [FOCS ’10], to show the
existence of functionalities (e.g., inner product) that cannot be computed both accurately and in
a differentially private manner in the random oracle model; yielding that protocols for computing
these functionalities cannot be black-box reduced to the existence of one-way functions.



Changes to previous version:

The name of the paper was changed from ``On the Power of Random Oracles" to ``Limits on the Usefulness of Random Oracles"


Revision #1 to TR12-129 | 14th January 2013 21:44

Limits on the Usefulness of Random Oracles





Revision #1
Authors: Iftach Haitner, Eran Omri, Hila Zarosim
Accepted on: 14th January 2013 21:44
Downloads: 742
Keywords: 


Abstract:

In the random oracle model, the parties are given oracle access to a random member of
a (typically huge) function family, and are assumed to have unbounded computational power
(though they can only make a bounded number of oracle queries). This model provides powerful
properties that allow proving the security of many protocols, even such that cannot be proved
secure in the standard model (under any hardness assumption). The random oracle model is also
used to show that a given cryptographic primitive cannot be used in a black-box way to construct
another primitive; in their seminal work, Impagliazzo and Rudich [STOC ’89] showed that in the
random function model – when the function family is the set of all functions – it is impossible
to construct (secure) key-agreement protocols, yielding that key-agreement cannot be black-box
reduced to one-way functions. Their work has a long line of followup works (Simon [EC ’98],
Gertner et al. [STOC ’00] and Gennaro et al. [SICOMP ’05], to name a few), showing that given
oracle access to a certain type of function family (e.g., the family that “implements” public-key
encryption) is not sufficient for building a given cryptographic primitive (e.g., oblivious transfer).
Yet, in the more general sense, the following fundamental question remained open:

What is the exact power of the random oracle model, and more specifically, of the
random function model?

We make progress towards answering the above question, showing that any (no private input)
semi-honest two-party functionality that can be securely implemented in the random function
model, can be securely implemented information theoretically (where parties are assumed to be
all powerful, and no oracle is given). We further generalize the above result to function families
that provide some natural combinatorial property.

To exhibit the power of our result, we use the recent information theoretic impossibility result
of McGregor et al. [FOCS ’10], to show the existence of functionalities (e.g., inner product) that
cannot be computed both accurately and in a differentially private manner in the random
function model; yielding that protocols for computing these functionalities cannot be black-box
reduced to the existence of one-way functions.



Changes to previous version:

The name of the paper was changed from ``On the Power of Random Oracles" to ``Limits on the Usefulness of Random Oracles"


Paper:

TR12-129 | 9th October 2012 15:01

On the Power of Random Oracles





TR12-129
Authors: Iftach Haitner, Eran Omri, Hila Zarosim
Publication: 9th October 2012 15:26
Downloads: 1047
Keywords: 


Abstract:

In the random oracle model, the parties are given oracle access to a random member of
a (typically huge) function family, and are assumed to have unbounded computational power
(though they can only make a bounded number of oracle queries). This model provides powerful
properties that allow proving the security of many protocols, even such that cannot be proved
secure in the standard model (under any hardness assumption). The random oracle model is also
used to show that a given cryptographic primitive cannot be used in a black-box way to construct
another primitive; in their seminal work, Impagliazzo and Rudich [STOC ’89] showed that in the
random function model – when the function family is the set of all functions – it is impossible
to construct (secure) key-agreement protocols, yielding that key-agreement cannot be black-box
reduced to one-way functions. Their work has a long line of followup works (Simon [EC ’98],
Gertner et al. [STOC ’00] and Gennaro et al. [SICOMP ’05], to name a few), showing that given
oracle access to a certain type of function family (e.g., the family that “implements” public-key
encryption) is not sufficient for building a given cryptographic primitive (e.g., oblivious transfer).
Yet, in the more general sense, the following fundamental question remained open:

What is the exact power of the random oracle model, and more specifically, of the
random function model?

We make progress towards answering the above question, showing that any (no private input)
semi-honest two-party functionality that can be securely implemented in the random function
model, can be securely implemented information theoretically (where parties are assumed to be
all powerful, and no oracle is given). We further generalize the above result to function families
that provide some natural combinatorial property.

To exhibit the power of our result, we use the recent information theoretic impossibility result
of McGregor et al. [FOCS ’10], to show the existence of functionalities (e.g., inner product) that
cannot be computed both accurately and in a differentially private manner in the random
function model; yielding that protocols for computing these functionalities cannot be black-box
reduced to the existence of one-way functions.



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