PKSig - Public-Key Signatures

This module provides the base class for implementing Public-Key Signature (digital signature) schemes in the Charm cryptographic library.

Overview

Public-Key Signatures (digital signatures) allow a signer to generate a signature on a message using their private key, which anyone can verify using the corresponding public key. Signatures provide three fundamental security properties:

• Authentication: Proof that the message originated from the claimed signer

• Integrity: Assurance that the message wasn’t modified after signing

• Non-repudiation: The signer cannot deny having signed the message

Core Algorithms:

• KeyGen: Generate a public/private key pair

• Sign: Create a signature on a message using the private key

• Verify: Check if a signature is valid for a message and public key

Common Constructions:

• RSA Signatures: Based on the RSA problem

• DSA/ECDSA: Based on discrete logarithm in prime/elliptic curve groups

• Schnorr: Efficient DL-based signatures, basis for many modern schemes

• BLS: Short signatures from bilinear pairings

Security Properties

PKSig schemes in Charm support the following security definitions:

Security Definition	Description
EU_CMA	Existential Unforgeability under Chosen Message Attack. The standard security notion. An adversary with access to a signing oracle cannot produce a valid signature on any new message.
wEU_CMA	Weak existential unforgeability. A relaxed notion that may allow re-randomization of existing signatures or other forms of malleability.
sEU_CMA	Strong existential unforgeability. Even producing a different valid signature on an already-signed message counts as a forgery. Required for some applications like preventing signature replay.

Underlying Assumptions:

• DL (Discrete Logarithm) - Schnorr, DSA

• RSA - RSA signatures

• CDH/DDH - Various pairing-based signatures

• Lattice assumptions - Post-quantum signatures

Typical Use Cases

1. Code Signing

   Software vendors sign executables and packages to prove authenticity and integrity. Users verify signatures before installation to ensure software hasn’t been tampered with.

   # Developer signs the software
   software_hash = hash(executable_bytes)
   signature = pksig.sign(public_key, secret_key, software_hash)
   
   # User verifies before installing
   is_authentic = pksig.verify(vendor_public_key, signature, software_hash)
   if is_authentic:
       install(executable_bytes)
   

2. Document Signing

   Legal contracts, certificates, and official documents with cryptographic authentication. Provides legally binding digital signatures in many jurisdictions.

3. Blockchain Transactions

   Users sign transactions to authorize transfers of digital assets. The signature proves ownership of the sending account without revealing the private key.

Example Schemes

The following PKSig implementations are available in Charm:

Schnorr Signatures:

• charm.schemes.pksig.pksig_schnorr91 - SchnorrSig: Classic Schnorr signature scheme based on discrete logarithm.

from charm.core.math.integer import integer
from charm.schemes.pksig.pksig_schnorr91 import SchnorrSig

# Setup with safe primes
p = integer(156816585111264668689583680968857341596876961491501655859473581156994765485015490912709775771877391134974110808285244016265856659644360836326566918061490651852930016078015163968109160397122004869749553669499102243382571334855815358562585736488447912605222780091120196023676916968821094827532746274593222577067)
q = integer(78408292555632334344791840484428670798438480745750827929736790578497382742507745456354887885938695567487055404142622008132928329822180418163283459030745325926465008039007581984054580198561002434874776834749551121691285667427907679281292868244223956302611390045560098011838458484410547413766373137296611288533)

pksig = SchnorrSig()
pksig.params(p, q)

# Key generation
(public_key, secret_key) = pksig.keygen()

# Sign
msg = "hello world."
signature = pksig.sign(public_key, secret_key, msg)

# Verify
is_valid = pksig.verify(public_key, signature, msg)
assert is_valid == True

Other PKSig Schemes:

• charm.schemes.pksig.pksig_dsa - DSA: Digital Signature Algorithm

• charm.schemes.pksig.pksig_ecdsa - ECDSA: Elliptic Curve DSA

• charm.schemes.pksig.pksig_bls04 - BLS01: Short BLS signatures

• charm.schemes.pksig.pksig_cl03 - Sig_CL03: Camenisch-Lysyanskaya signatures

• charm.schemes.pksig.pksig_waters - WatersSig: Waters signatures

• charm.schemes.pksig.pksig_rsa_hw09 - RSA-based signatures

Adapters:

• charm.adapters.pksig_adapt_naor01 - Convert IBE schemes to signatures

API Reference

Base class for public-key signatures

Notes: This class implements an interface for a standard public-key signature scheme. A public key signature consists of three algorithms: (keygen, sign, verify).

class PKSig.PKSig

Bases: SchemeBase

checkProperty(schemeObj, _reqProps)

getProperty()

keygen(securityparam)

printProperties()

setProperty(secDef=None, assumption=None, messageSpace=None, secModel=None, **kwargs)

sign(pk, sk, message)

updateProperty(scheme, secDef=None, assumption=None, messageSpace=None, secModel=None, **kwargs)

verify(pk, message, sig)

See Also

• charm.toolbox.PKEnc - Public-key encryption

• charm.toolbox.IBSig - Identity-based signatures

• charm.toolbox.integergroup - Integer groups for DL-based signatures

• charm.toolbox.ecgroup - Elliptic curve groups for ECDSA