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Network Working Group                                         P. Hoffman
Internet-Draft                                                     ICANN
Intended status: Informational                           August 14, 2017
Expires: February 15, 2018


       The Transition from Classical to Post-Quantum Cryptography
                         draft-hoffman-c2pq-02

Abstract

   Quantum computing is the study of computers that use quantum features
   in calculations.  For over 20 years, it has been known that if very
   large, specialized quantum computers could be built, they could have
   a devastating effect on asymmetric classical cryptographic algorithms
   such as RSA and elliptic curve signatures and key exchange, as well
   as (but in smaller scale) on symmetric cryptographic algorithms such
   as block ciphers, MACs, and hash functions.  There has already been a
   great deal of study on how to create algorithms that will resist
   large, specialized quantum computers, but so far, the properties of
   those algorithms make them onerous to adopt before they are needed.

   Small quantum computers are being built today, but it is still far
   from clear when large, specialized quantum computers will be built
   that can recover private or secret keys in classical algorithms at
   the key sizes commonly used today.  It is important to be able to
   predict when large, specialized quantum computers usable for
   cryptanalysis will be possible so that organization can change to
   post-quantum cryptographic algorithms well before they are needed.

   This document describes quantum computing, how it might be used to
   attack classical cryptographic algorithms, and possibly how to
   predict when large, specialized quantum computers will become
   feasible.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any




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   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on February 15, 2018.

Copyright Notice

   Copyright (c) 2017 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
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   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Disclaimer  . . . . . . . . . . . . . . . . . . . . . . .   3
     1.2.  Executive Summary . . . . . . . . . . . . . . . . . . . .   3
     1.3.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   4
     1.4.  Not Covered: Post-Quantum Cryptographic Algorithms  . . .   5
     1.5.  Not Covered: Quantum Cryptography . . . . . . . . . . . .   5
     1.6.  Where to Read More  . . . . . . . . . . . . . . . . . . .   5
   2.  Brief Introduction to Quantum Computers . . . . . . . . . . .   6
     2.1.  Quantum Computers that Recover Cryptographic Keys . . . .   7
   3.  Physical Designs for Quantum Computers  . . . . . . . . . . .   7
     3.1.  Qubits, Error Detection, and Error Correction . . . . . .   8
     3.2.  Promising Physical Designs for Quantum Computers  . . . .   8
     3.3.  Challenges for Physical Designs . . . . . . . . . . . . .   8
   4.  Quantum Computers and Public Key Cryptography . . . . . . . .   9
     4.1.  Explanation of Shor's Algorithm . . . . . . . . . . . . .  10
     4.2.  Properties of Large, Specialized Quantum Computers Needed
           for Recovering RSA Public Keys  . . . . . . . . . . . . .  10
   5.  Quantum Computers and Symmetric Key Cryptography  . . . . . .  10
     5.1.  Explanation of Grover's Algorithm . . . . . . . . . . . .  11
     5.2.  Properties of Large, Specialized Quantum Computers Needed
           for Recovering Symmetric Keys . . . . . . . . . . . . . .  11
     5.3.  Properties of Large, Specialized Quantum Computers for
           Computing Hash Collisions . . . . . . . . . . . . . . . .  12
   6.  Predicting When Useful Cryptographic Attacks Will Be Feasible  12
     6.1.  Proposal: Public Measurements of Various Quantum
           Technologies  . . . . . . . . . . . . . . . . . . . . . .  13



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   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  14
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  14
   9.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  14
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  14
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  14
     10.2.  Informative References . . . . . . . . . . . . . . . . .  15
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  16

1.  Introduction

   Early drafts of this document use "@@@@@" to indicate where the
   editor particularly want input from reviewers.  The editor welcomes
   all types of review, but the areas marked with "@@@@@" are in the
   most noticeable need of new material.  (The editor particularly
   appreciates new material that comes with references that can be
   included in this document as well.)

1.1.  Disclaimer

   **** This is an early version of this draft. **** As such, it has had
   little in-depth review in the cryptography community.  Statements in
   this document might be wrong; given that the entire document is about
   cryptography, those wrong statements might have significant security
   problems associated with them.

   Readers of this document should not rely on any statements in this
   version of this draft.  As the draft gets more input from the
   cryptography community over time, this disclaimer will be softened
   and eventually eliminated.

1.2.  Executive Summary

   The development of quantum computers that can recover private or
   secret keys in classical algorithms at the key sizes commonly used
   today is at a very early stage.  None of the published examples of
   such quantum computers is useful in recovering keys that are in use
   today.  There is a great amount of interest in this development, and
   researchers expect large strides in this development in the coming
   decade.

   There is active research in standardizing signing and key exchange
   algorithms that will withstand attacks from large, specialized
   quantum computers.  However, all those algorithms to date have very
   large keys, very large signatures, or both.  Thus, there is a large
   sustained cost in using those algorithms.  Similarly, there is a
   large cost in being surprised about when quantum computers can cause
   damage to current cryptographic keys and signatures.




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   Because the world does not know when large, specialized quantum
   computers that can recover cryptographic keys will be available,
   organizations should be watching this area so that they have plenty
   of time to either change to larger key sizes for classical
   cryptography or to change to post-quantum algorithms.  See Section 6
   for a fuller discussion of determining how to predict when quantum
   computers that can harm current cryptography might become feasible.

1.3.  Terminology

   The term "classical cryptography" is used to indicate the
   cryptographic algorithms that are in common use today.  In
   particular, signature and key exchange algorithms that are based on
   the difficulty of factoring numbers into two large prime numbers, or
   are based on the difficulty of determining the discrete log of a
   large composite number, are considered classical cryptography.

   The term "post-quantum cryptography" refers to the invention and
   study of cryptographic mechanisms in which the security does not rely
   on computationally hard problems that can be efficiently solved on
   quantum computers.  This excludes systems whose security relies on
   factoring numbers, or the difficulty of determining the discrete log
   of one group element with respect to another.

   Note that these definitions apply to only one aspect of quantum
   computing as it relates to cryptography.  It is expected that quantum
   computing will also be able to be used against symmetric key
   cryptography to make it possible to search for a secret symmetric key
   using far fewer operations than are needed using classical computers
   (see Section 5 for more detail).  However, using longer keys to
   thwart that possibility is not normally called "post-quantum
   cryptography".

   There are many terms that are only used in the field of quantum
   computing, such as "qubit", "quantum algorithm", and so on.  Chapter
   1 of [NielsenChuang] has good definitions of such terms.

   Some papers discussing quantum computers and cryptanalysis say that
   large, specialized quantum computers "break" algorithms in classical
   cryptography.  This paper does not use that terminology because the
   algorithms' strength will be reduced when large, specialized quantum
   computers exist, but not to the point where there is an immediate
   need to change algorithms.

   The "^" symbol is used to indicate "the power of".  The term "log"
   always means "logarithm base 2".





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1.4.  Not Covered: Post-Quantum Cryptographic Algorithms

   This document discusses when an organization would want to consider
   using post-quantum cryptographic algorithms, but definitely does not
   delve into which of those algorithms would be best to use.  Post-
   quantum cryptography is an active field of research; in fact, it is
   much more active than the study of when we might want to transition
   from classical to post-quantum cryptography.

   Readers interested in post-quantum cryptographic algorithms will have
   no problem finding many articles proposing such algorithms, comparing
   the many current proposals, and so on.  An excellent starting point
   is the web site <http://pqcrypto.org/>.  The Open Quantum Safe (OQS)
   project <https://openquantumsafe.org/> is developing and prototyping
   quantum-resistant cryptography.  Another is the article on post-
   quantum cryptography at Wikipedia: <https://en.wikipedia.org/wiki/
   Post-quantum_cryptography>.

   Various organizations are working on standardizing the algorithms for
   post-quantum cryptography.  For example, the US National Institute of
   Standards and Technology (commonly just called "NIST") is holding a
   competition to evaluate post-quantum cryptographic algorithms.
   NIST's description of that effort is currently at
   <http://csrc.nist.gov/groups/ST/post-quantum-crypto/>.  Until
   recently, ETSI (the European Telecommunications Standards Institute)
   had a Quantum-Safe Cryptography (QSC) Industry Specification Group
   (ISG) that worked on specifying post-quantum algorithms; see
   <http://www.etsi.org/technologies-clusters/technologies/quantum-safe-
   cryptography> for results from this work.

1.5.  Not Covered: Quantum Cryptography

   Other than in this section, this document does not cover "quantum
   cryptography".  The field of quantum cryptography uses quantum
   effects in order to secure communication between users.  Quantum
   cryptography is not related to cryptanalysis.  The best known and
   extensively studied example of quantum cryptography is a quantum key
   exchange, where users can share a secret key while preventing an
   eavesdropper from obtaining the key.

1.6.  Where to Read More

   There are many reasonably accessible articles on Wikipedia, notably
   the overview article at <https://en.wikipedia.org/wiki/
   Quantum_computing> and the timeline of quantum computing developments
   at <https://en.wikipedia.org/wiki/Timeline_of_quantum_computing>.





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   [NielsenChuang] is a well-regarded college textbook on quantum
   computers.  Prerequisites for understanding the book include linear
   algebra and some quantum physics; however, even without those, a
   reader can probably get value from the introductory material in the
   book.

   [Turing50Youtube] is a good overview of the near-term and longer-term
   prospects for designing and building quantum computers; it is a video
   of a panel discussion by quantum hardware and software experts given
   at the ACM's Turing 50 lecture.

   @@@@@ Maybe add more references that might be useful to non-experts.

2.  Brief Introduction to Quantum Computers

   A quantum computer is a computer that uses quantum bits (qubits) in
   quantum circuits to perform calculations.  Quantum computers also use
   classical bits and regular circuits: most calculations in a quantum
   computer are a mix of classical and quantum bits and circuits.  For
   example, classical bits could be used for error correction or
   controlling the behavior of physical components of the quantum
   computer.

   A basic principle that makes it possible to speed up calculations on
   qubits in quantum computers is quantum superposition.  Informally,
   similarly to waves in classical physics, arbitrary number of quantum
   states can be added together and result will be another valid quantum
   state.  That means that, for example, two qubits could be in any
   quantum superposition of four states, three qubits in quantum
   superposition of eight states, and so on.  Generally n qubits can be
   in quantum superposition of 2^n states.

   The main challenge for quantum computing is to create and maintain a
   significantly large number of superposed qubits while performing
   quantum computations.  Physical components of quantum computers that
   are non-ideal results in the destruction of qubit state over time;
   this is the source of errors in quantum computation.  See Section 3.1
   for a description of how to overcome this problem.

   A good description of different aspects of calculations on quantum
   computer could be found in [EstimatingPreimage].

   A separate question is a measurement of a quantum state.  Due to
   uncertainty of the state, the measurement process is stochastic.
   That means that in order to get the correct measurement one should
   run several consequent calculations and corresponding measurement in
   order to the expected value which is considered as a result of
   measurement.



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   @@@@@ Discuss measurements and how they have to be done with
   correlated qubits.

2.1.  Quantum Computers that Recover Cryptographic Keys

   Quantum computers are expected to be useful in the future for some
   problems that take up too many resources on a large classical
   computer.  However, this document only discusses how they might
   recover cryptographic keys faster than classical computers.  In order
   to recover cryptographic keys, a quantum computer needs to have a
   quantum circuit specifically designed for the type of key it is
   attempting to recover.

   A quantum computer will need to have a circuit with thousands of
   qubits to be useful to recover the type and size keys that are in
   common use today.  Smaller quantum computers (those with fewer qubits
   in superposition) are not useful for using Shor's algorithm (as
   discussed in Section 4.1) at all.  That is, no one has devised a way
   to combine a bunch of smaller quantum computers to perform the same
   attacks on cryptographic keys via Shor's algorithm as a properly-
   sized quantum computer.

   This is why this document uses the term "large, specialized quantum
   computer" when describing ones that can recover keys: there will
   certainly be small quantum computers built first, but those computers
   cannot recover the type and size keys that are in common use today.
   Further, there are already quantum computers that have many qubits
   but without the circuits needed to make those qubits useful for
   recovering cryptographic keys.

   A straight-forward application of Shor's algorithm may not be the
   only way for large, specialized quantum computers to attack RSA keys.
   [LowResource] describes how to combine quantum computers with
   classical methods for recovering RSA keys at speeds faster than just
   using the classical methods.

3.  Physical Designs for Quantum Computers

   Quantum computers can be built using many different physical
   technologies.  Deciding which physical technologies are best to
   pursue is an extremely active research topic.  A few physical
   technologies (particularly trapped ions, super-conduction using
   Josephson junctions, and nuclear magnetic resonance) are currently
   getting the most press, but other technologies are also showing
   promise.

   One factor that is important to quantum computers that can be used
   for cryptanalysis is the speed of the operations (transformations) on



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   qubits.  Most of the estimates of speeds of these quantum computers
   assume that qubit operations will take about the same amount of time
   as operations in circuits that consist of classical gates and
   classical memory.  Current quantum circuits are slower than classical
   circuits, but will certainly become faster as quantum computers are
   developed in the future.

   Note that some current quantum computer research uses bits that are
   not fully entangled, and this will greatly affect their ability to
   make useful quantum calculations.

3.1.  Qubits, Error Detection, and Error Correction

   Researchers building small quantum computers have discovered that
   calculating the superposition of qubits often has a large rate of
   error, and that error rate increases rapidly over time.  Performing
   quantum calculations such as those needed to recover cryptographic
   keys is not feasible with the current state of quantum computers.

   In the future, actual quantum calculations will be performed on
   "logical qubits", that is, after the application of error correction
   codes on physical qubits.  Thus, the number of physical qubits will
   be higher than the number of logical qubits, depending on the
   parameters of the error correction code, which in turn depends on the
   parameters of a technology used for a physical implementation of
   qubits.  Currently, it is estimated that it takes hundreds or
   thousands of physical qubits to make a logical qubit. @@@@@ Need
   reference for this statement.

   @@@@@ Lots more material should go here.  We will need recent
   references for how many physical qubits are needed for each corrected
   qubit.  It's OK if this section has lots of references, but hopefully
   they don't contradict each other.

3.2.  Promising Physical Designs for Quantum Computers

   @@@@@ It would be useful to have maybe two paragraphs about each
   physical design that is being actively pursued.

3.3.  Challenges for Physical Designs

   Different designs have different challenges to overcome before the
   physical technology can be scaled enough to build a useful large,
   specialized quantum computer.  Some of those challenges include the
   following.  (Note that some items on this list apply only to some of
   the physical technologies.)





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   Temperature:  Getting stable operation without extreme cooling is
      difficult for many of the proposed technologies.  The definition
      of "extreme" is different for different low-temperature
      technologies.

   Stabilization:  The length of time every qubit in a circuit holds is
      value

   Quantum control:  Coherence and reproducibility of qubits

   Error detection and correction:  Getting accurate results through
      simultaneous detection of bit-flip and phase-flip.  See
      Section 3.1 for a longer description of this.

   Substrate:  The material on which the qubit circuits are built.  This
      has a large effect on the stability of the qubits.

   Particles:  The atoms or sub-atomic particles used to make the qubits

   Scalability:  The ability to handle the number of physical qubits
      needed for the desired the circuit

   Architecture:  Ability to change quantum gates in a circuit

4.  Quantum Computers and Public Key Cryptography

   The area of quantum computing that has generated the most interest in
   the cryptographic community is the ability of quantum computers to
   find the private keys in encryption and signature algorithms based on
   discrete logarithms using exponentially fewer operations than
   classical computers would need to use.

   As described in [RFC3766], it is widely believed that factoring large
   numbers and finding discrete logs using classical computers increases
   with the exponential size of the key.  [RFC3766] describes in detail
   how classical computers can be used to determine keys; even though
   that RFC is over a decade old, no significant changes have been made
   to the process of classical attacks on RSA and Diffie-Hellman. @@@@@
   CFRG: is that true?  Does RFC 3766 need to be updated?

   Shor's algorithm shows that these problems can be solved on quantum
   computers in polynomial time, meaning that the speed of finding the
   keys is a polynomial function (with reasonable-sized coefficients)
   based on the size of the keys, which would require significantly
   fewer steps than a classical computer.  The definitive paper on
   Shor's algorithm is [Shor97].





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4.1.  Explanation of Shor's Algorithm

   @@@@@ Pointers to understandable articles would be good here.

   @@@@@ Describe period-finding and why it applies to finding prime
   factors and discrete logs.

   @@@@@ Give the steps for applying Shor's algorithm to 2048-bit RSA.
   Describe how many rounds of the quantum subroutine would likely be
   needed.  Describe how many rounds of the classical loop would likely
   be needed.

   [ResourceElliptic] gives concrete estimates of the resources needed
   to build a quantum computer to compute elliptic curve discrete
   logarithms.  It shows that for the common P-256 elliptic curve, 2330
   logical qubits and over 10^11 Toffoli gates.

4.2.  Properties of Large, Specialized Quantum Computers Needed for
      Recovering RSA Public Keys

   Researchers have built small quantum computers that implement Shor's
   algorithm, factoring numbers with four or five bits.  These are used
   to show that Shor's algorithm is possible to realize in actual
   hardware.  (Note, however, that [PretendingFactor] indicates that
   these experiments may have taken shortcuts that prevent them from
   indicating real Shor designs.)

   @@@@@ References are needed here.  Did they implement all of Shor's
   algorithm, including the looping logic in the classical part and the
   looping logic in the quantum part?

   @@@@@ Numbers and explanation is needed below:

   A quantum computer that can determine the private keys for 2048-bit
   RSA would require SOME NUMBER GOES HERE correlated qubits and SOME
   NUMBER GOES HERE circuit elements.  A quantum computer that can
   determine the private keys for 256-bt elliptic curves would require
   SOME NUMBER GOES HERE correlated qubits and SOME NUMBER GOES HERE
   circuit elements.

5.  Quantum Computers and Symmetric Key Cryptography

   Section 4 is about Shor's algorithm and compromises to public key
   cryptography.  There is a second quantum computing algorithm,
   Grover's algorithm, that is often mentioned at the same time as
   Shor's algorithm.  With respect to cryptanalysis, however, Grover's
   algorithm applies to tasks of finding a preimage, including tasks of
   finding a secret key of a symmetric algorithm such as AES if there is



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   knowledge of plaintext-ciphertext pairs.  The definitive paper on
   Grover's algorithm is by Grover: [Grover96].  Grover later wrote a
   more accessible paper about the algorithm in [QuantumSearch].

   Grover's algorithm gives a way to search for keys to symmetric
   algorithms in the square root of the time that a normal exhaustive
   search would take.  Thus, a large, specialized quantum computer that
   implements Grover's algorithm could find a secret AES-128 key in
   about 2^64 steps instead of the 2^128 steps that would be required
   for a classical computer.

   When it appears that it is feasible to build a large, specialized
   quantum computer that can defeat a particular symmetric algorithm at
   a particular key size, the proper response would be to use keys with
   twice as many bits.  That is, if one is using the AES-128 algorithm
   and there is a concern that an adversary might be able to build a
   large, specialized quantum computer that is designed to attack
   AES-128 keys, move to an algorithm that has keys twice as long as
   AES-128, namely AES-256 (the block size used is not significant
   here).

   It is currently expected that large, specialized quantum computers
   that implement Grover's algorithm are expected to be built long
   before ones that implement Shor's algorithm are.  There are two
   primary reasons for this:

   o  Grover's algorithm is likely to be useful in areas other than
      cryptography.  For example, a large, specialized quantum computer
      that implements Grover's algorithm might help create medicines by
      speeding up complex problems that involve how proteins fold. @@@@@
      Add more likely examples and references here.

   o  A large, specialized quantum computer that can recover AES-128
      keys will likely be much smaller (and thus easier to build) than
      one that implements Shor's algorithm for 256-bit elliptic curves
      or 2048-bit RSA/DSA keys.

5.1.  Explanation of Grover's Algorithm

   @@@@@ Give the steps for applying Grover's algorithm to AES-128.

5.2.  Properties of Large, Specialized Quantum Computers Needed for
      Recovering Symmetric Keys

   [ApplyingGrover] estimates that a quantum computer that can determine
   the secret keys for AES-128 would require 2953 correlated qubits and
   2.74 * 2^86 gates.




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5.3.  Properties of Large, Specialized Quantum Computers for Computing
      Hash Collisions

   @@@@@ More goes here.  Also, discuss how Grover's algorithm does not
   appear to be useful for computing preimages (or say how it might be
   used.

6.  Predicting When Useful Cryptographic Attacks Will Be Feasible

   If quantum computers that perform useful cryptographic attacks can be
   built in the future, many organizations will want to start using
   post-quantum algorithms well before those computers can be built.
   However, given how few implementations of such quantum computers
   exist (even for tiny keys), it is impossible to predict with any
   accuracy when quantum computers that perform useful cryptographic
   attacks will be feasible.

   The term "useful" above is relative to the value of the material
   being protected by the cryptographic algorithm to the attacker.  For
   example, if the quantum computer attacking a particular key costs
   US$100 billion to build, costs US$1 billion a year to run, and can
   extract only one key a year, it is possibly useful to some
   governments, but probably not useful for attacking the TLS key used
   to protect a small mail server.  On the other hand, if later a
   similar computer costs US$1 billion to build, costs US$10 million a
   year to run, and can extract ten keys a year, many more keys become
   vulnerable.

   [BeReady] gives a simple way to approach the calculation of when one
   needs to deploy post-quantum algorithms.  In short, if the sum of how
   long you need your keys to be secure plus how long it takes to deploy
   new algorithms is longer than the length of time it will take for an
   attacker to create a large, specialized quantum computer and use it
   against your keys, then you waited too long.

   To date, few people have done systematic research that would give
   estimates for when useful quantum-based cryptographic attacks might
   be feasible, and at what cost.  Without such research, it is easy to
   make wild guesses but those are not of much value to people having to
   decide when to start using post-quantum cryptography.

   For example, in [NIST8105], NIST says "researchers working on
   building a quantum computer have estimated that it is likely that a
   quantum computer capable of recovering 2000-bit RSA in a matter of
   hours could be built by 2030 for a budget of about a billion
   dollars".  However, the referenced link is to a YouTube video
   [MariantoniYoutube] where the researcher, Matteo Mariantoni, says
   "maybe you should not quote me on that".  [NIST8105] gives no other



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   references for predictions on cost and availability of useful
   cryptographic attacks with quantum computers.

6.1.  Proposal: Public Measurements of Various Quantum Technologies

   In order to get a rough idea of when useful cryptographic attacks
   with quantum computers may be feasible, researchers creating such
   computers can demonstrate them when they can recover keys an eighth
   the size of those in common use.  That is, given that 2048-bit RSA,
   256-bit elliptic curve, and AES-128 are common today, when a research
   team has a computer than can recover 256-bit RSA, 32-bit elliptic
   curve, or AES-128 where only 16 bits are unknown, they should
   demonstrate it.

   Such a demonstration could easily be made fair with trusted
   representatives from the cryptographic community using verifiable
   means to pick the keys to recover, and verifying the time that it
   takes to recover each key.  It might be interesting to run the same
   tests in classical computers at the same time to give perspective.

   These demonstrations will have many benefits to those who have to
   decide when post-quantum algorithms should be deployed in various
   environments.

   o  Demonstrations will likely use designs that are considered most
      efficient.  This in turn will cause greater focus research on
      choosing good design candidates.

   o  The results of the demonstrations will help focus on issues
      important to cryptanalysis, namely the cost of building the
      systems and the speed of breaking a single key.

   o  Competing demonstrations will reveal where different research
      teams have made different optimizations from well-known designs.

   o  Public demonstrations could expose designs that work only in
      limited cases that are uncommon in normal cryptographic practice.
      (For example, [PretendingFactor] claims that all current
      factorization experiments have taken advantage of using a
      classical computer that already knows the answer to design the
      quantum circuits.)

   Note that this proposal would only give an idea of how public
   progress is being made on quantum computers.  Well-funded military
   agencies (and possibly even criminal enterprises) could be way ahead
   of the publicly-visible computers.  No one should rely on just the
   public measurements when deciding how safe their keys are against
   quantum computers.



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7.  IANA Considerations

   None, and thus this section can be removed at final publication.

8.  Security Considerations

   This entire document is about cryptography, and thus about security.

   See Section 1.1 for an important disclaimer about this document and
   security.

   This document is meant to help the reader predict when to transition
   from using classical cryptographic algorithms to post-quantum
   algorithms.  That decision is ultimately up to the reader, and must
   be made not only based on predictions of how quantum computing is
   progressing but also the value of every key that the user handles.
   For example, a financial institution using TLS to protect its
   customers' transactions will probably consider its keys more valuable
   than a small online store, and will thus be likely to begin the
   transition earlier.

9.  Acknowledgements

   The list here is meant to acknowledge input to this document.  The
   people listed here do not necessarily agree with ideas presented.

   Many sections of text were contributed by Grigory Marshalko and
   Stanislav Smyshlyaev.

   Some of the ideas in this document come from Denis Butin, Philip
   Lafrance, Hilarie Orman, and Tomofumi Okubo.

10.  References

10.1.  Normative References

   [Grover96]
              Grover, L., "A fast quantum mechanical algorithm for
              database search", 1996, <https://arxiv.org/abs/quant-
              ph/9605043>.

   [Shor97]   Shor, P., "Polynomial-Time Algorithms for Prime
              Factorization and Discrete Logarithms on a Quantum
              Computer", 1997,
              <http://epubs.siam.org/doi/pdf/10.1137/S0097539795293172>.






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10.2.  Informative References

   [ApplyingGrover]
              Grassl, M., Langenberg, B., Roetteler, M., and R.
              Steinwandt, "Applying Grover's algorithm to AES: quantum
              resource estimates", 2015, <https://arxiv.org/
              abs/1512.04965>.

   [BeReady]  Mosca, M., "Cybersecurity in an era with quantum
              computers: will we be ready?", 2015,
              <http://eprint.iacr.org/2015/1075>.

   [EstimatingPreimage]
              Amy, M., Di Matteo, O., Gheorghiu, V., Mosca, M., Parent,
              A., and J. Schanck, "Estimating the cost of generic
              quantum pre-image attacks on SHA-2 and SHA-3", 2016,
              <https://eprint.iacr.org/2016/992>.

   [LowResource]
              Bernstein, D., Fiassse, J., and M. Mosca, "A low-resource
              quantum factoring algorithm", 2017,
              <https://eprint.iacr.org/2017/352.pdf>.

   [MariantoniYoutube]
              Mariantoni, M., "Building a Superconducting Quantum
              Computer", 2014, <https://www.youtube.com/watch?v=wWHAs--
              HA1c>.

   [NielsenChuang]
              Nielsen, M. and I. Chuang, "Quantum Computation and
              Quantum Information, 10th Anniversary Edition", ISBN
              97801-107-00217-3 , 2010.

   [NIST8105]
              Chen, L. and et. al, "Report on Post-Quantum
              Cryptography", 2016,
              <http://nvlpubs.nist.gov/nistpubs/ir/2016/
              NIST.IR.8105.pdf>.

   [PretendingFactor]
              Smolin, J., Vargo, A., and J. Smolin, "Pretending to
              factor large numbers on a quantum computer", 2013,
              <https://arxiv.org/abs/1301.7007>.

   [QuantumSearch]
              Grover, L., "From Schrodinger's Equation to the Quantum
              Search Algorithm", 2001, <https://arxiv.org/abs/quant-
              ph/0109116>.



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   [ResourceElliptic]
              Roetteler, M., Naehrig, M., Svore, K., and K. Lauter,
              "Quantum Resource Estimates for Computing Elliptic Curve
              Discrete Logarithms", 2017,
              <https://eprint.iacr.org/2017/598>.

   [RFC3766]  Orman, H. and P. Hoffman, "Determining Strengths For
              Public Keys Used For Exchanging Symmetric Keys", BCP 86,
              RFC 3766, DOI 10.17487/RFC3766, April 2004,
              <http://www.rfc-editor.org/info/rfc3766>.

   [Turing50Youtube]
              Vazirani, U., Aharonov, D., Gambetta, J., Martinis, J.,
              and A. Yao, "Quantum Computing: Far Away? Around the
              Corner?", 2017, <https://www.youtube.com/
              watch?v=SzfJRR5JrgQ>.

Author's Address

   Paul Hoffman
   ICANN

   Email: paul.hoffman@icann.org




























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