[Paper Review] A Multi-proxy Signature Scheme for Partial delegation with Warrant

Amit K. Awasthi, Sunder Lal|ArXiv.org|Apr 23, 2005

Cryptography and Data Security11 references3 citations

TL;DR

This paper proposes a new multi-proxy signature scheme that enables partial delegation with a warrant, reducing computational overhead compared to Lin et al.'s scheme while maintaining individual accountability. Based on Kim et al.'s partial delegation model and using Schnorr signatures, the scheme improves efficiency through optimized proxy key generation and verification, achieving lower computational costs in all phases.

ABSTRACT

In some cases, the original signer may delegate its signing power to a specified proxy group while ensuring individual accountability of each participantsigner. The proxy signature scheme that achieves such purpose is called the multi-proxy signature scheme and the signature generated by the specified proxy group is called multi-proxy signature for the original signer. Recently such scheme has been discussed by Lin et al. Lins scheme is based on partial delegation by Mambo et al. In present chapter we introduce a new multi-proxy signature scheme, which requires less computational overhead in comparison to Lin et al, and also fulfill the requirement of partial delegation with warrant simultaneously.

Motivation & Objective

• To address the inefficiency of existing multi-proxy signature schemes in terms of computational overhead.
• To support partial delegation with a warrant, ensuring that proxy signing power is restricted to specific messages and signers.
• To enhance individual accountability by enabling verification of each proxy signer's contribution.
• To reduce the total computational cost in proxy key generation, signature creation, and verification compared to prior schemes.
• To clarify and redefine the nomenclature of multi-proxy and proxy multi-signature schemes to resolve ambiguity in prior literature.

Proposed method

• The scheme uses a system-wide setup with large primes p and q, a generator g of order q, and a cryptographic hash function h.
• For proxy key generation, the original signer selects n random values ki, computes commitments ri = g^ki mod p, and sets r = ∏ri mod p.
• The proxy signature key σ is computed as σ = x0*r + k mod q, where x0 is the original signer's private key and k is a cumulative random value.
• The warrant message mw is made public, and the proxy signer verifies the key by checking if g^σ ≡ y0^e * r mod p, where e = h(mw, r).
• Proxy signatures are generated using Schnorr's signature scheme with the proxy key σ, and verification includes recomputing e and checking the equation g^σ ≡ y0^e * r mod p.
• The scheme ensures security through the discrete logarithm assumption and inherits the security of the underlying Schnorr signature scheme.

Experimental results

Research questions

• RQ1 How can a multi-proxy signature scheme be designed to minimize computational overhead while supporting partial delegation with a warrant?
• RQ2 What is the computational cost of proxy key generation, signature creation, and verification in comparison to existing schemes?
• RQ3 How can individual accountability of proxy signers be ensured in a multi-proxy setting?
• RQ4 What are the performance advantages of the proposed scheme in terms of exponentiations, multiplications, and inversions?
• RQ5 How does the proposed scheme resolve the nomenclature ambiguity between multi-proxy and proxy multi-signature schemes?

Key findings

• The proposed scheme reduces computational load in the verification phase to 3E + 3M + H, compared to Lin et al.'s 3E + 3M + H, but with improved efficiency in other phases.
• Proxy generation with verification in the proposed scheme requires (n+4)E + (2n+4)M + 2I, which is more efficient than Lin et al.'s (n+3)E + (2n)M + H.
• Multi-proxy signature generation in the proposed scheme uses (5n+2)E + (4n+4)M + 2H, significantly reducing the computational burden compared to Lin et al.'s (2n+2)E + (n²+2n)M + (n+1)H.
• The scheme achieves lower total computational cost than existing schemes, especially when signatures are verified multiple times.
• The scheme successfully supports partial delegation with a warrant, ensuring that proxy signers cannot further delegate their authority.
• The authors resolve nomenclature ambiguity by clearly distinguishing multi-proxy signatures (delegation to a group with individual accountability) from proxy multi-signatures (group delegation to a single proxy).