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I once heard about a type of crypto system that behaves in the following way: I have x secret keys that work together to decrypt messages encrypted with a public key d. If I get at least n of the x secret keys together, I can decrypt messages encrypted with d in their entirety. If I have anything less than n, I get no information about those messages.

When this system was being described to me, I was told that an example of this system in the real world is ICANN's system for recovering the DNS registry in the event of some catastrophic failure. In their case, x = 7.

I heard about this a little while ago, and I don't remember exactly what the system is called. I have tried to research it with the ICANN website, but I can't seem to find an actual name of the system that I can use to then do a deeper dive into this. Does anyone know the name of the system I just described? Also, since I am trying to dive rather deeply into this, I would also appreciate any resources (research papers, open-source implementations, additional real-world examples, etc.) that could be listed.

Thank you!

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I believe you are talking about Shamir's Secret Sharing.


Here is the original paper

Related papers

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IANA operation details on the root key ceremonies and procedures are at https://www.iana.org/dnssec

You may be interested by section §4.2.2 of https://www.iana.org/dnssec/dps/ksk-operator/ksk-dps.txt

   Access to and management of cryptographic hardware is based on the
   principle of successive barriers in three tiers, requiring at least
   seven trusted persons from four different roles.  These barriers are
   as follows:

   Tier 5:
         Physical access to safe room requires one person from the Key
         Ceremony Administrator role in combination with one person from
         the Internal Witness roles.

   Tier 6:
         Physical access to cryptographic hardware (HSM) and activation
         material requires one out of two of the Safe Security
         Controller #1s, and one out of the two Safe Security Controller
         #2s in addition to the Trusted Persons required at Tier 5 and
         7.

   Tier 7:
         Activation of a HSM requires three out of seven Crypto Officers
         to extract activation material from above safe deposit boxes
         using their physical key.  Safe deposit box operation that
         involves opening of any one of the deposit box requires three
         out of seven Crypto Officers to be present.

   Restoration of the contents of a HSM requires at least six trusted
   persons from two different roles, as follows:

   Secret share:
         Reconstruction of the secret key used for encryption of the
         application keys requires five out of seven Recovery Key Share
         Holders.

   Encrypted application keys:
         Physical access to the encrypted application keys requires one
         person from the Ceremony Administrators role, one person from

And section §5.2.2:

5.2.2.  Private key (m-of-n) multi-person control

   The RZ KSK Operator has implemented technical and procedural
   mechanisms that require the participation of multiple trusted
   individuals to perform sensitive cryptographic operations.  The RZ
   KSK Operator splits activation data needed to make use of the RZ KSK
   private key onto separate smartcards controlled by trusted
   individuals (Crypto Officers) selected from members of the Internet
   community not already part of root zone management operations.
   Specifically, organizationally separate parties, not affiliated with
   PTI, ICANN or Verisign.

   A threshold number of smartcards (m) out of the total number of
   smartcards created and distributed for a particular hardware security
   module (n) is required to activate a RZ KSK private key stored on the
   module.  The threshold number of cards needed to sign using the RZ
   KSK is three out of seven.  The smartcards are protected in
   accordance with Section 5.4.2.

Typically, when you create a key on an HSM, you can generate various Officers access to it, and decide how many of them will be required to unlock the private key. You can find example at Standards for secure key backup of master keys with secret sharing

Note that is it not about "for recovering the DNS registry in the event of some catastrophic failure. " DNSSEC adds cryptography in the DNS in the sense that each zones signs its records with some key and some (other) key are stored in the parent and so on until the root. IANA (ICANN) handles the root procedure-wise and for the ceremonies and such, while Verisign manages the day to day operations of it (technically of the A root nameserver, which is the one from which all other ones derive their configuration).

So the question is more around how the root key is protected, and what happens when it is lost. But even outside of those edge cases, the root key ceremonies also need multiple crypto officers to unlock the key when it is needed (twice per year). You will see in mainstream media sensationalist articles about the 7 people to have the keys to the Internet (example of such bad writing: https://www.theguardian.com/technology/2014/feb/28/seven-people-keys-worldwide-internet-security-web), while https://www.cloudflare.com/dns/dnssec/root-signing-ceremony/ will give you both a more accurate description with more real technical details.

You can see at https://www.iana.org/dnssec/tcrs the current list of crypto officers (needed for bi annual key rotation ceremonies) and the "recovery key share holders". The first one are needed to just unlock the private key, the second ones to reconstruct it if it gets lost/damaged/unrecoverable/etc., per §5.2.4:

5.2.4.  Private key backup

   Encrypted copies of the RZ KSK private key(s) are backed up onto
   portable media held by the RZ KSK Operator and sent by courier to the
   other facilities.  The key used to encrypt the private key(s) is
   backed up using a five out of seven threshold scheme with smartcards
   distributed to trusted individuals (Recovery Key Share Holders)
   selected from members of the Internet community not already part of
   root zone management operations (specifically, organizationally
   separate parties, not affiliated with PTI, ICANN or Verisign).  The
   Recovery Key Share Holders keep the cards in tamper-evident bags,
   stored in geographically dispersed locations under their control.
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  • Thank you! This is great detail, and I will continue to review this as I'm doing my work. Aug 9 '20 at 19:57

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