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@ -517,27 +517,27 @@ The process between Alice and Bob verifying each other would be:
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method supported by Alice's device.
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method supported by Alice's device.
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7. Bob's device ensures it has a copy of Alice's device key.
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7. Bob's device ensures it has a copy of Alice's device key.
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8. Bob's device creates an ephemeral Curve25519 key pair
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8. Bob's device creates an ephemeral Curve25519 key pair
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(*K*<sub>*B*</sub><sup>*p**r**i**v**a**t**e*</sup>, *K*<sub>*B*</sub><sup>*p**u**b**l**i**c*</sup>),
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(*K<sub>B</sub><sup>private</sup>*, *K<sub>B</sub><sup>public</sup>*),
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and calculates the hash (using the chosen algorithm) of the public
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and calculates the hash (using the chosen algorithm) of the public
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key *K*<sub>*B*</sub><sup>*p**u**b**l**i**c*</sup>.
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key *K<sub>B</sub><sup>public</sup>*.
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9. Bob's device replies to Alice's device with an
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9. Bob's device replies to Alice's device with an
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`m.key.verification.accept` message.
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`m.key.verification.accept` message.
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10. Alice's device receives Bob's message and stores the commitment hash
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10. Alice's device receives Bob's message and stores the commitment hash
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for later use.
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for later use.
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11. Alice's device creates an ephemeral Curve25519 key pair
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11. Alice's device creates an ephemeral Curve25519 key pair
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(*K*<sub>*A*</sub><sup>*p**r**i**v**a**t**e*</sup>, *K*<sub>*A*</sub><sup>*p**u**b**l**i**c*</sup>)
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(*K<sub>A</sub><sup>private</sup>*, *K<sub>A</sub><sup>public</sup>*)
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and replies to Bob's device with an `m.key.verification.key`,
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and replies to Bob's device with an `m.key.verification.key`,
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sending only the public key
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sending only the public key
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*K*<sub>*A*</sub><sup>*p**u**b**l**i**c*</sup>.
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*K<sub>A</sub><sup>public</sup>*.
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12. Bob's device receives Alice's message and replies with its own
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12. Bob's device receives Alice's message and replies with its own
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`m.key.verification.key` message containing its public key
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`m.key.verification.key` message containing its public key
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*K*<sub>*B*</sub><sup>*p**u**b**l**i**c*</sup>.
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*K<sub>B</sub><sup>public</sup>*.
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13. Alice's device receives Bob's message and verifies the commitment
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13. Alice's device receives Bob's message and verifies the commitment
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hash from earlier matches the hash of the key Bob's device just sent
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hash from earlier matches the hash of the key Bob's device just sent
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and the content of Alice's `m.key.verification.start` message.
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and the content of Alice's `m.key.verification.start` message.
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14. Both Alice and Bob's devices perform an Elliptic-curve
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14. Both Alice and Bob's devices perform an Elliptic-curve
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Diffie-Hellman
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Diffie-Hellman
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(*E**C**D**H*(*K*<sub>*A*</sub><sup>*p**r**i**v**a**t**e*</sup>, *K*<sub>*B*</sub><sup>*p**u**b**l**i**c*</sup>)),
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(*ECDH(K<sub>A</sub><sup>private</sup>*, *K<sub>B</sub><sup>public</sup>*)),
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using the result as the shared secret.
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using the result as the shared secret.
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15. Both Alice and Bob's devices display a SAS to their users, which is
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15. Both Alice and Bob's devices display a SAS to their users, which is
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derived from the shared key using one of the methods in this
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derived from the shared key using one of the methods in this
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@ -711,13 +711,13 @@ to convert to decimal numbers (resulting in 3 numbers between 0 and 8191
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inclusive each). Add 1000 to each calculated number.
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inclusive each). Add 1000 to each calculated number.
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The bitwise operations to get the numbers given the 5 bytes
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The bitwise operations to get the numbers given the 5 bytes
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*B*<sub>0</sub>, *B*<sub>1</sub>, *B*<sub>2</sub>, *B*<sub>3</sub>, *B*<sub>4</sub>
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*B<sub>0</sub>*, *B<sub>1</sub>*, *B<sub>2</sub>*, *B<sub>3</sub>*, *B<sub>4</sub>*
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would be:
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would be:
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- First: (*B*<sub>0</sub> ≪ 5|*B*<sub>1</sub> ≫ 3) + 1000
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- First: (*B<sub>0</sub>* ≪ 5|*B<sub>1</sub>* ≫ 3) + 1000
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- Second:
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- Second:
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((*B*<sub>1</sub>&0*x*7) ≪ 10|*B*<sub>2</sub> ≪ 2|*B*<sub>3</sub> ≫ 6) + 1000
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((*B<sub>1</sub>*&0x7) ≪ 10|*B<sub>2</sub>* ≪ 2|*B<sub>3</sub>* ≫ 6) + 1000
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- Third: ((*B*<sub>3</sub>&0*x*3*F*) ≪ 7|*B*<sub>4</sub> ≫ 1) + 1000
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- Third: ((*B<sub>3</sub>*&0x3F) ≪ 7|*B<sub>4</sub>* ≫ 1) + 1000
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The digits are displayed to the user either with an appropriate
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The digits are displayed to the user either with an appropriate
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separator, such as dashes, or with the numbers on individual lines.
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separator, such as dashes, or with the numbers on individual lines.
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