Documentation improvements, code cleaned up

Here we ship a number of improvements we did when we were evaluating the library to use for our project.

Summary of changes:

Cleared up single-mode naming as well as removed G and Mu parameters from Paillier keys. We always use G = N + 1 (threshold version is not secure with another choice of G by the way), N is the only one parameter needed for a public key. Also, Mu is needed only for decrypting and can be computed from Lambda and N so there is no need to keep it in the private key.
Added documentation to <Key, Enc, Dec> single-mode functions with an important note that p and q supplied to CreatePrivateKey must be either of equal length or gcd(pq, (p-1)(q-1)) = 1 which is assured if both primes are of equal length. This requirement is mentioned both in [KL 08] and [DJN 10].
Removed single-mode PrivateKey's String() method and cached N^2 value from PublicKey. It's better to have no code encouraging to turn key into a string and printing it somewhere, especially that string contained private Lambda parameter. Computing N^2 is just a really small piece of encryption/decryption work and if we decide we need to tweak performance, we will need a different approach anyway. Removing it from PublicKey lets to keep this structure clean.
Removed G parameter from ThresholdKey. G is always equal to N+1, only then threshold scheme is safe.
Added documentation explaining how ThresholdKey is generated, how message is encrypted and decrypted, how zero-knowledge proof is constructed.
Made internal functions not being exported.
Removed dead code.
Added test ensuring threshold version is a homomorphic encryption scheme.
Explained how do we handle negative Lambda parameter values when decrypting (modular multiplicative inverse).

[KL 08]: Jonathan Katz, Yehuda Lindell, (2008) Introduction to Modern Cryptography: Principles and Protocols, Chapman & Hall/CRC

[DJN 10]: Ivan Damgard, Mads Jurik, Jesper Buus Nielsen, (2010) A Generalization of Paillier’s Public-Key System with Applications to Electronic Voting Aarhus University, Dept. of Computer Science, BRICS

Wow, thanks a lot for that PR. I'll verify everything and merge it as soon as I get home.

Cheers,

Didier

On Tue, Jun 5, 2018, 9:55 AM pdyraga notifications@github.com wrote:

Here we ship a number of improvements we did when we were evaluating the library to use for our project.

Summary of changes:

Cleared up single-mode naming as well as removed G and Mu parameters from Paillier keys. We always use G = N + 1 (threshold version is not secure with another choice of G by the way), N is the only one parameter needed for a public key. Also, Mu is needed only for decrypting and can be computed from Lambda and N so there is no need to keep it in the private key.

Added documentation to <Key, Enc, Dec> single-mode functions with an important note that p and q supplied to CreatePrivateKey must be either of equal length or gcd(pq, (p-1)(q-1)) = 1 which is assured if both primes are of equal length. This requirement is mentioned both in [KL 08] and [DJN 10].

Removed single-mode PrivateKey's String() method and cached N^2 value from PublicKey. It's better to have no code encouraging to turn key into a string and printing it somewhere, especially that string contained private Lambda parameter. Computing N^2 is just a really small piece of encryption/decryption work and if we decide we need to tweak performance, we will need a different approach anyway. Removing it from PublicKey lets to keep this structure clean.

Removed G parameter from ThresholdKey. G is always equal to N+1, only then threshold scheme is safe.

Added documentation explaining how ThresholdKey is generated, how message is encrypted and decrypted, how zero-knowledge proof is constructed.

Made internal functions not being exported.

Removed dead code.

Added test ensuring threshold version is a homomorphic encryption scheme.

Explained how do we handle negative Lambda parameter values when decrypting (modular multiplicative inverse).

[KL 08]: Jonathan Katz, Yehuda Lindell, (2008) Introduction to Modern Cryptography: Principles and Protocols, Chapman & Hall/CRC

[DJN 10]: Ivan Damgard, Mads Jurik, Jesper Buus Nielsen, (2010) A Generalization of Paillier’s Public-Key System with Applications to Electronic Voting Aarhus University, Dept. of Computer Science, BRICS

You can view, comment on, or merge this pull request online at:

https://github.com/didiercrunch/paillier/pull/2 Commit Summary

Fixed test for LCM

Added test for Lambda parameter computation

Cleared up Paillier scheme API

Do not cache N^2 value in PublicKey

G parameter moved from PublicKey to ThresholdKey

Removed PrivateKey's String() method

Comment about G value moved to ThresholdKey

Merge pull request #1 from keep-network/evaluate-and-fix

Explained how do we compute D from Chinese Remainder Theorem

Added documentation to the threshold Paillier key generator

Do not export internal threshold generator functions

Improved documentation for a secret share computation fn

Small improvements to the threshold key generator tests

G parameter removed from ThresholdKey

Do not export internal ThresholdKey functions

Improved documentation for ThresholdKey functions

Removed unused ThresholdKey.divide function

Added test ensuring threshold Paillier is a partially homomorphic system

Added documentation describing how partial decryptions are combined

Removed unneeded return statements from tests

Added documentation to code evaluating ZKP

Removed G parameter serialization code for ThresholdKey

Explained how Fiat-Shamir heuristic works on a high level

ThresholdKeyGenerator self-ref renamed from this to tkg

ThresholdKey self-ref renamed from this to tk

ThresholdPrivateKey self-ref renamed from this to tpk

PartialDecryptionZKP self-ref renamed from this to pd

ThresholdKey renamed to ThresholdPublicKey

Shortened name of the partial decryption verification function

Explained how do we handle negative lambda parameter value

Merge pull request #3 from keep-network/threshold-rabbit-hole

File Changes

M encoding.go https://github.com/didiercrunch/paillier/pull/2/files#diff-0 (46)

M encoding_test.go https://github.com/didiercrunch/paillier/pull/2/files#diff-1 (18)

M paillier.go https://github.com/didiercrunch/paillier/pull/2/files#diff-2 (86)

M paillier_test.go https://github.com/didiercrunch/paillier/pull/2/files#diff-3 (52)

M thresholdkey.go https://github.com/didiercrunch/paillier/pull/2/files#diff-4 (314)

M thresholdkey_generator.go https://github.com/didiercrunch/paillier/pull/2/files#diff-5 (211)

M thresholdkey_generator_test.go https://github.com/didiercrunch/paillier/pull/2/files#diff-6 (70)

M thresholdkey_test.go https://github.com/didiercrunch/paillier/pull/2/files#diff-7 (114)

Patch Links:

https://github.com/didiercrunch/paillier/pull/2.patch

https://github.com/didiercrunch/paillier/pull/2.diff

— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub https://github.com/didiercrunch/paillier/pull/2, or mute the thread https://github.com/notifications/unsubscribe-auth/AC4UlMtEy5J-vakIE69VlS-0Oe4bNLivks5t5o3VgaJpZM4Ua4Ab .

didiercrunch / paillier

Documentation improvements, code cleaned up #2

[DJN 10]: Ivan Damgard, Mads Jurik, Jesper Buus Nielsen, (2010) A Generalization of Paillier’s Public-Key System with Applications to Electronic Voting Aarhus University, Dept. of Computer Science, BRICS