Secret Sharing in RSA (#99)

* 📦 Add cryptography package

- Demotes hypothesis and typish to dev package

* ✨Replace ElGamal with RSA for Auxiliary Key

* 🐛Missing TearDown in Decryption tests

* 📝Update Documentation for Auxiliary Encrypt/Decrypt override

Pipfile

@@ -7,18 +7,19 @@ verify_ssl = true
 black = "*"
 coverage = "*"
 docutils = "*"
+hypothesis = "==5.15.1"
 mkdocs = "*"
 mypy = "*"
 pydeps = "*"
 pydocstyle = "*"
 pylint = "*"
 pytest = "*"
+typish = '*'
 
 [packages]
-hypothesis = "==5.15.1"
 numpy = '==1.18.2'
 jsons = '==1.1.2'
-typish = '*'
+cryptography = "*"
 
 [requires]
 python_version = "3.8"

docs/1_Key_Ceremony.md

@@ -34,26 +34,29 @@ This is a detailed description of the entire Key Ceremony Process
 
 1. The ceremony details are decided upon. These include a `number_of_guardians` and `quorum` of guardians required for decryption.
 2. Each guardian creates a unique `id` and `sequence_order`.
-3. Each guardian must generate their `auxiliary key pair`.
+3. Each guardian must generate their `auxiliary key pair`.\*
 4. Each guardian must give the other guardians their `auxiliary public key` directly or through a mediator.
 5. Each guardian must check if all `auxiliary public keys` are received.
 6. Each guardian must generate their `election key pair` _(ElGamal key pair)_. This will generate a corresponding Schnorr `proof` and `polynomial` used for generating `election partial key backups` for sharing.
 7. Each guardian must give the other guardians their `election public key` directly or through a mediator.
 8. Each guardian must check if all `election public keys` are received.
-9. Each guardian must generate `election partial key backup` for each other guardian. The guardian will use their `polynomial` and the designated guardian's `sequence_order` to create the value. The backup will be encrypted with the designated guardian's `auxiliary public key`
+9. Each guardian must generate `election partial key backup` for each other guardian. The guardian will use their `polynomial` and the designated guardian's `sequence_order` to create the value. The backup will be encrypted with the designated guardian's `auxiliary public key`\*
 10. Each guardian must send each encrypted `election partial key backup` to the designated guardian directly or through a `mediator`.
 11. Each guardian checks if all encrypted `election partial key backups` have been received by their recipient guardian directly or through a mediator.
-12. Each recipient guardian decrypts each received encrypted `election partial key backup` with their own `auxiliary private key`
+12. Each recipient guardian decrypts each received encrypted `election partial key backup` with their own `auxiliary private key`\*
 13. Each recipient guardian verifies each `election partial key backup` and sends confirmation of verification
     - If the proof verifies, continue
     - If the proof fails
-      1. Sender guardian publishes the `election partial key backup` value sent to recipient as a `election partial key challenge` where the value is **unencrypted** to all the other guardians \*
+      1. Sender guardian publishes the `election partial key backup` value sent to recipient as a `election partial key challenge` where the value is **unencrypted** to all the other guardians \*\*
       2. Alternate guardian (outside sender or original recipient) attempts to verify key
          - If the proof verifies, continue
          - If the proof fails again, the accused (sender guardian) should be evicted and process should be restarted with new guardian.
 14. On receipt of all verifications of `election partial private keys` by all guardians, generate and publish `joint key` from election public keys
 
-\* **Note:** _The confidentiality of this value is now gone, but since the two Guardians are in the dispute, at least one is misbehaving and could be revealing this data._
+
+\* **Note:** _The auxiliary encrypt and decrypt functions can be overridden to allow different encryption mechanisms other than the default._
+
+\*\* **Note:** _The confidentiality of this value is now gone, but since the two Guardians are in the dispute, at least one is misbehaving and could be revealing this data._
 
 ## Files
 

src/electionguard/auxiliary.py

@@ -0,0 +1,43 @@
+from typing import Callable, Optional, NamedTuple
+
+from .types import GUARDIAN_ID
+
+MESSAGE = str
+PUBLIC_KEY = str
+SECRET_KEY = str
+ENCRYPTED_MESSAGE = str
+
+
+class AuxiliaryKeyPair(NamedTuple):
+    """A tuple of a secret key and public key."""
+
+    secret_key: SECRET_KEY
+    """The secret or private key"""
+    public_key: PUBLIC_KEY
+
+
+class AuxiliaryPublicKey(NamedTuple):
+    """A tuple of auxiliary public key and owner information"""
+
+    owner_id: GUARDIAN_ID
+    """
+    The unique identifier of the guardian
+    """
+
+    sequence_order: int
+    """
+    The sequence order of the auxiliary public key (usually the guardian's sequence order)
+    """
+
+    key: PUBLIC_KEY
+    """
+    A string representation of the Auxiliary public key.  
+    It is up to the external `AuxiliaryEncrypt` function to know how to parse this value
+    """
+
+
+AuxiliaryEncrypt = Callable[[MESSAGE, PUBLIC_KEY], Optional[ENCRYPTED_MESSAGE]]
+"""A callable type that represents the auxiliary encryption scheme."""
+
+AuxiliaryDecrypt = Callable[[ENCRYPTED_MESSAGE, SECRET_KEY], Optional[MESSAGE]]
+"""A callable type that represents the auxiliary decryption scheme."""

src/electionguard/guardian.py

@@ -23,8 +23,6 @@
     combine_election_public_keys,
     CeremonyDetails,
     CoefficientValidationSet,
-    default_auxiliary_decrypt,
-    default_auxiliary_encrypt,
     ElectionJointKey,
     ElectionKeyPair,
     ElectionPartialKeyBackup,
@@ -35,12 +33,13 @@
     generate_election_key_pair,
     generate_election_partial_key_backup,
     generate_election_partial_key_challenge,
-    generate_elgamal_auxiliary_key_pair,
+    generate_rsa_auxiliary_key_pair,
     PublicKeySet,
     verify_election_partial_key_backup,
     verify_election_partial_key_challenge,
 )
 from .logs import log_warning
+from .rsa import rsa_encrypt, rsa_decrypt
 from .types import GUARDIAN_ID
 from .utils import get_optional
 
@@ -179,7 +178,7 @@ def generate_auxiliary_key_pair(
         self,
         generate_auxiliary_key_pair: Callable[
             [], AuxiliaryKeyPair
-        ] = generate_elgamal_auxiliary_key_pair,
+        ] = generate_rsa_auxiliary_key_pair,
     ) -> None:
         """
         Generate auxiliary key pair
@@ -277,7 +276,7 @@ def guardian_election_public_keys(
         return ReadOnlyDataStore(self._guardian_election_public_keys)
 
     def generate_election_partial_key_backups(
-        self, encrypt: AuxiliaryEncrypt = default_auxiliary_encrypt
+        self, encrypt: AuxiliaryEncrypt = rsa_encrypt
     ) -> bool:
         """
         Generate all election partial key backups based on existing public keys
@@ -292,6 +291,11 @@ def generate_election_partial_key_backups(
             backup = generate_election_partial_key_backup(
                 self.object_id, self._election_keys.polynomial, auxiliary_key, encrypt
             )
+            if backup is None:
+                log_warning(
+                    f"guardian; {self.object_id} could not generate election partial key backups: failed to encrypt"
+                )
+                return False
             self._backups_to_share.set(auxiliary_key.owner_id, backup)
 
         return True
@@ -328,9 +332,7 @@ def all_election_partial_key_backups_received(self) -> bool:
 
     # Verification
     def verify_election_partial_key_backup(
-        self,
-        guardian_id: GUARDIAN_ID,
-        decrypt: AuxiliaryDecrypt = default_auxiliary_decrypt,
+        self, guardian_id: GUARDIAN_ID, decrypt: AuxiliaryDecrypt = rsa_decrypt,
     ) -> Optional[ElectionPartialKeyVerification]:
         """
         Verify election partial key backup value is in polynomial
@@ -449,7 +451,7 @@ def compensate_decrypt(
         elgamal: ElGamalCiphertext,
         extended_base_hash: ElementModQ,
         nonce_seed: ElementModQ = None,
-        decrypt: AuxiliaryDecrypt = default_auxiliary_decrypt,
+        decrypt: AuxiliaryDecrypt = rsa_decrypt,
     ) -> Optional[Tuple[ElementModP, ChaumPedersenProof]]:
         """
         Compute a compensated partial decryption of an elgamal encryption 
@@ -474,7 +476,14 @@ def compensate_decrypt(
             )
             return None
 
-        decrypted_value = decrypt(backup.encrypted_value, self._auxiliary_keys)
+        decrypted_value = decrypt(
+            backup.encrypted_value, self._auxiliary_keys.secret_key
+        )
+        if decrypted_value is None:
+            log_warning(
+                f"compensate decrypt guardian {self.object_id} failed decryption for {missing_guardian_id}"
+            )
+            return None
         partial_secret_key = get_optional(int_to_q(int(decrypted_value)))
 
         # 𝑀_{𝑖,l} = 𝐴^P𝑖_{l}

src/electionguard/key_ceremony.py

@@ -1,10 +1,12 @@
 from dataclasses import dataclass
-from typing import (
-    Callable,
-    List,
-    NamedTuple,
-)
+from typing import List, Optional, NamedTuple
 
+from .auxiliary import (
+    AuxiliaryKeyPair,
+    AuxiliaryDecrypt,
+    AuxiliaryEncrypt,
+    AuxiliaryPublicKey,
+)
 from .data_store import DataStore
 from .election_polynomial import (
     compute_polynomial_coordinate,
@@ -18,9 +20,10 @@
     elgamal_keypair_random,
 )
 from .group import int_to_q, rand_q, ElementModP, ElementModQ
+from .rsa import rsa_keypair, rsa_decrypt, rsa_encrypt
 from .schnorr import SchnorrProof, make_schnorr_proof
-from .types import GUARDIAN_ID
 from .serializable import Serializable
+from .types import GUARDIAN_ID
 from .utils import get_optional
 
 ElectionJointKey = ElementModP
@@ -35,48 +38,6 @@ class CeremonyDetails(NamedTuple):
     quorum: int
 
 
-class AuxiliaryKeyPair(NamedTuple):
-    """A tuple of a secret key and public key."""
-
-    secret_key: str
-    """The secret or private key"""
-    public_key: str
-
-
-class AuxiliaryPublicKey(NamedTuple):
-    """A tuple of auxiliary public key and owner information"""
-
-    owner_id: GUARDIAN_ID
-    """
-    The unique identifier of the guardian
-    """
-
-    sequence_order: int
-    """
-    The sequence order of the auxiliary public key (usually the guardian's sequence order)
-    """
-
-    key: str
-    """
-    A string representation of the Auxiliary public key.  
-    It is up to the external `AuxiliaryEncrypt` function to know how to parse this value
-    """
-
-
-AuxiliaryEncrypt = Callable[[str, AuxiliaryPublicKey], str]
-"""
-A Genric callable type that represents an encryption/decryption scheme.
-"""
-
-# FIX_ME ISSUE #47: Default Auxiliary Encrypt is temporary placeholder
-default_auxiliary_encrypt = lambda unencrypted, key: unencrypted
-
-AuxiliaryDecrypt = Callable[[str, AuxiliaryKeyPair], str]
-
-# FIX_ME ISSUE #47: Default Auxiliary Decrypt is temporary placeholder
-default_auxiliary_decrypt = lambda encrypted, key_pair: encrypted
-
-
 class ElectionKeyPair(NamedTuple):
     """A tuple of election key pair, proof and polynomial"""
 
@@ -187,6 +148,15 @@ def generate_elgamal_auxiliary_key_pair() -> AuxiliaryKeyPair:
     )
 
 
+def generate_rsa_auxiliary_key_pair() -> AuxiliaryKeyPair:
+    """
+    Generate auxiliary key pair using RSA
+    :return: Auxiliary key pair
+    """
+    rsa_key_pair = rsa_keypair()
+    return AuxiliaryKeyPair(rsa_key_pair.private_key, rsa_key_pair.public_key)
+
+
 def generate_election_key_pair(
     quorum: int, nonce: ElementModQ = None
 ) -> ElectionKeyPair:
@@ -207,8 +177,8 @@ def generate_election_partial_key_backup(
     owner_id: GUARDIAN_ID,
     polynomial: ElectionPolynomial,
     auxiliary_public_key: AuxiliaryPublicKey,
-    encrypt: AuxiliaryEncrypt = default_auxiliary_encrypt,
-) -> ElectionPartialKeyBackup:
+    encrypt: AuxiliaryEncrypt = rsa_encrypt,
+) -> Optional[ElectionPartialKeyBackup]:
     """
     Generate election partial key backup for sharing
     :param owner_id: Owner of election key
@@ -220,7 +190,9 @@ def generate_election_partial_key_backup(
     value = compute_polynomial_coordinate(
         auxiliary_public_key.sequence_order, polynomial
     )
-    encrypted_value = encrypt(str(value.to_int()), auxiliary_public_key)
+    encrypted_value = encrypt(str(value.to_int()), auxiliary_public_key.key)
+    if encrypted_value is None:
+        return None
     return ElectionPartialKeyBackup(
         owner_id,
         auxiliary_public_key.owner_id,
@@ -253,7 +225,7 @@ def verify_election_partial_key_backup(
     verifier_id: GUARDIAN_ID,
     backup: ElectionPartialKeyBackup,
     auxiliary_key_pair: AuxiliaryKeyPair,
-    decrypt: AuxiliaryDecrypt = default_auxiliary_decrypt,
+    decrypt: AuxiliaryDecrypt = rsa_decrypt,
 ) -> ElectionPartialKeyVerification:
     """
     Verify election partial key backup contain point on owners polynomial
@@ -263,9 +235,12 @@ def verify_election_partial_key_backup(
     :param decrypt: Decryption function using auxiliary key
     """
 
-    decrypted_value = decrypt(backup.encrypted_value, auxiliary_key_pair)
+    decrypted_value = decrypt(backup.encrypted_value, auxiliary_key_pair.secret_key)
+    if decrypted_value is None:
+        return ElectionPartialKeyVerification(
+            backup.owner_id, backup.designated_id, verifier_id, False
+        )
     value = get_optional(int_to_q(int(decrypted_value)))
-
     return ElectionPartialKeyVerification(
         backup.owner_id,
         backup.designated_id,