A pure-Rust library that implements a set of cryptographic primitives for building a multi-hop Proxy Re-encryption scheme, known as Transform Encryption.
What is Transform Encryption?
Suppose you have two (public, private) key pairs: (A, AA) and (B, BB).
Transform Encryption allows data encrypted to one public key (A) to be transformed so that it can be decrypted using another user's private key (BB). This transformation process requires a special transform key (A -> B) that is computed using the first user's private key (AA) and the second user's public key (B). Having a transform key and performing the transformation does not allow the person doing this process to decrypt the data or to recover either user's private key.
See the Single-hop Transform Encryption Example for more details on computing a transform key and applying a transform using recrypt.
If you are building an application and would like to use Transform Encryption, you might try looking at the IronCore SDKs.
See https://crates.io/crates/recrypt for the most recent version.
In addition to the native Rust implementation, we provide additional bindings to Recrypt:
A Scala implementation of recrypt is also available.
API Documentation and Example Usage
Security and Audits
NCC Group's Cryptography Services team has conducted an audit of this library - release 0.6.2 contains all of the audited code, including updates that were created to resolve issues that were discovered during the audit. The NCC Group audit found that the chosen pairing and elliptic curve are cryptographically sound, and that the Rust implementation is a faithful and correct embodiment of the target protocol. In addition, the audit confirmed that the implementation does not leak secret information via timing or memory access pattern side-channel attacks.
To learn more about our approach to cryptography and to read our publications, please go here.
Rust (stable) is required.
$ cargo build
$ cargo test
$ cargo bench
Relation to Proxy Re-Encryption
In the academic literature, transform encryption is referred to as proxy re-encryption. A proxy re-encryption (PRE) scheme is a public-key encryption scheme, where each participant has a pair of related keys, one public and one private, which are mathematically related. Alice encrypts a message to Bob using his public key, and Bob decrypts the encrypted message using his public key to retrieve the original message.
PRE allows someone (the delegator) to delegate the ability to decrypt her messages to another person (the delegatee). Rather than just sharing her private key with the delegatee, the delegator computes a transform key (or re-encryption key) that allows messages encrypted to her public key to be transformed so they appear can be decrypted using the delegatee's private key. Computing this transform key requires the delegator's private key and the delegatee's public key; once it is computed, the key is stored on a semi-trusted proxy.
When the proxy receives a message encrypted to the delegator, it applies the transform algorithm using the transform key and delivers the transformed message to the delegatee. The proxy does not need to be trusted, because possession of the transform key does not allow the proxy to decrypt the message or to recover any information about either the delegator's or the delegatee's private keys, even if it collaborates with the delegatee.
When the delegator no longer wants to allow access, she just requests that the proxy discard the transform key. She must trust the proxy to perform this action.
PRE Scheme Properties
There are a number of ways to categorize PRE schemes; some of the most important are the following:
- Directionality describes whether delegate from A to B also allows transformation from B to A. Unidirectional schemes do not allow this.
- Interactivity describes whether both parties must be actively involved in order to generate the transform key. A non-interactive scheme only requires the public key of the delegatee.
- Transitivity describes whether a proxy can re-delegate encryption. That is, if the proxy holds a transform key from A to B and a transform key from B to C, can it generate a transform key from a to C? A non-transitive scheme does not allow this.
- Collusion safety describes whether it is possible for a delegatee to collude with the proxy that holds a transform key to that delegatee in order to recover the private key of the delegator. A collusion-safe scheme does not allow this.
- Multi-hop describes whether it is possible to allow a delegatee to also be a delegator. That is, does the scheme allow a ciphertext that has already been transformed from Alice to Bob to subsequently be transformed from Bob to Carol. In a multi-hop situation, the proxies would chain the transformations, so any delegatee in the chain could decrypt any message that one of her delegators could decrypt.
The Recrypt library implements a PRE scheme that is unidirectional, non-interactive, non-transitive, collusion-safe, and multi-hop.
The PRE algorithm implemented here was originally suggested in a short paper titled "A Fully Secure Unidirectional and Multi-user Proxy Re-encryption Scheme" by H. Wang and Z. Cao, published in the proceedings of the ACM Conference on Computer and Communications Security (CCS) in 2009. The algorithm was enhanced in a paper titled "A Multi-User CCA-Secure Proxy Re-Encryption Scheme" by Y. Cai and X. Liu, published in the proceedings of the IEEE 12th International Conference on Dependable, Autonomic, and Secure Computing in 2014.
We provide a synopsis of the algorithms, along with a description of how they can be used to implement an access control system, in the paper "Cryptographically Enforced Orthogonal Access Control at Scale" by B. Wall and P. Walsh, published in SCC '18, the proceedings of the 6th International Workshop on Security in Cloud Computing in 2018.
The algorithms in these papers were very generic and made no implementation choices. They specified only the use of a bilinear pairing function. We made a number of implementation choices. Foremost, we use the optimal Ate pairing as our pairing function. This requires a "pairing-friendly" elliptic curve; we chose a Barreto-Naehrig curve, which supports efficient implementation of the pairing.
Our implementation was guided by the following papers:
"Pairing-Friendly Elliptic Curves of Prime Order" by P.S.L.M. Barreto and M. Naehrig, published in Proceedings of the 12th International Workshop on Selected Areas in Cryptography (SAC), 2006, pp. 319-331.
"Constructing Tower Extensions of Finite Fields for Implementation of Pairing-Based Cryptography" by N. Benger and M. Scott, published in Proceedings of the 3rd International Workshop on Arithmetic of Finite Fields, 2010, pp. 180-195.
"High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves" by J. Beuchat et al., published in Proceedings from the 4th International Conference on Pairing-Based Cryptography, 2010, pp. 21-39.
"Implementing Cryptographic Pairings over Barreto-Naehrig Curves" by A. J. Devegili et al., published in Proceedings from the 1st International Conference on Pairing-Based Cryptography, 2007, pp. 197-207.
"Multiplication and Squaring on Pairing-Friendly Fields" by A. J. Devegili et al., published in 2006 and available at http://eprint.iacr.org/2006/471.
"Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions" by R. Granger and M. Scott, published in Proceedings from the 13th International Conferencee on Practice and Theory in Public Key Cryptography (PKC), 2010, pp. 209-223.
"Multiplication of Multidigit Numbers on Automata" by A. Karatsuba and Y. Ofman, in the journal Soviet Physics Doklady, vol. 7, Jan. 1963.
"New Software Speed Records for Cryptographic Pairings" by M. Naehrig, R. Niederhagen, and P. Schwabe, in Proceedings of the 1st International Conference on Progress in Cryptology and Information Security in Latin America (LATINCRYPT), 2010, pp. 109-123.
"On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves" by M. Scott et al., published in Proceedings of the 3rd International Converence on Pairing-Based Cryptography (PKC), 2009, pp. 78-88.
And by the book: Guide to Pairing-Based Cryptography by N.E. Mrabet and M. Joye, Chapman and Hall/CRC Cryptography and Network Security Series, 2016.
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