Author Bernard van Gastel
License Apache License 2.0
Library for polymorphic pseudonimisation and encryption. Same library in different languages:
This library implements the PEP encryption based on ElGamal using Curve25519, and operations on these encrypted messages. A message
M can be encrypted for a receiver which has public key
Y associated with it, belonging to secret key
y with (with being a generator for the used curve). This encryption is random: every time a different random
r is used, resulting in different ciphertexts (encrypted messages). We represent this encryption function as . Decrypt a ciphertext using secret key by calculating .
The library supports three operations on ciphertext
in = , encrypting message for public key with random :
rerandomize(in, s) = out: scrambles a ciphertext with a random
outcan be decrypted by the same secret key
y, both resulting in the same decrypted message
M. However, the binary form of
outdiffers. Spec: input is transformed to by performing ;
reshuffle(in, n) = out: modifies a ciphertext
in(an encrypted form of
M), so that after decryption of
outthe decrypted message will be equal to
n*M. Spec: input is transformed to by performing .
rekey(in, k) = out: if
incan be decrypted by secret key
outcan be decrypted by secret key
k*y. Decryption will both result in message
M. Spec: input is transformed to by performing .
rekey(in, k) and
reshuffle(in, n) can be combined in a slighly more efficient
rks(in, k, n).
There are also zero knowledge proof version of these operations. These are needed so that a party can prove to another party that it has applied the operation on the input data, without revealing the factors used in the operation.
When distributing trust over multiple central servers, these zero knowledge proofs are essential, so that a malfunctioning server can not violate security guarantees of the system. If server B has a secret factor
n, server A can check with these zero knowledge proofs that server B has applied for example a reshuffle with factor
N () to a specific message. Server A does not learn anything about
For pseudonimisation, the core operation is reshuffle with
n. It modifies a main pseudonym with a factor
n that is specific to a user (or user group) receiving the pseudonym. After applying a user specific factor
n, a pseudonym is called a local pseudonym. The factor
n is typically tied to the access group of a user.
Using only a reshuffle is insufficient, as the pseudonym is still encrypted with the public key
Y (which can be decrypted by the secret key
y). To allow a user to decrypt the encrypted pseudonym, a rekey with
k is needed, in combination with a protocol to hand the user the secret key
k*y. The factor
k is typically tied to the current session of a user.
To make pseudonyms harder to trace, rerandomize is applied frequently. This way a binary compare of the encrypted pseudonym will not leak any information.
This library is using the Ristretto encoding on Curve25519. There are a number of arithmetic rules for scalars and group elements: group elements can be added and subtracted from each other. Scalars support addition, subtraction, and multiplication. Division can be done by multipling with the inverse (using
s.invert() for non-zero scalar
s). A scalar can be converted to a group element (by multiplying with the special generator
G), but not the other way around. Group elements can also be multiplied by a scalar.
Group elements have an almost 32 byte range (top bit is always zero, and some other values are invalid). Therefore, not all AES-256 keys (using the full 32 bytes range) are valid group elements. But all group elements are valid AES-256 keys. Group elements can be generated by
GroupElement::from_hash(..). Scalars are also 32 bytes, and can be generated with
Scalar::from_hash(..). We ensure that scalars are never zero, to avoid a multiply/division by zero problem.
The zero knowledge proofs are offline Schnorr proofs, based on a Fiat-Shamir transform. The hashing algorithm used is SHA512.
Build using cargo:
Run using cargo:
cargo run --bin peppy --features build-binary
cargo install libpep --features build-binary
Based on the article by Eric Verheul and Bart Jacobs, Polymorphic Encryption and Pseudonymisation in Identity Management and Medical Research. In Nieuw Archief voor Wiskunde (NAW), 5/18, nr. 3, 2017, p. 168-172. This article does not contain the zero knowledge proofs.