Twin-Schnorr: A Security Upgrade for the Schnorr Identity-Based Identification Scheme

Table 2

Comparison of the identification protocol with other discrete logarithm IBI schemes.

Scheme	U	E	MG	MZ	IMP-AA/CA
OKDL-IBI (Bellare et al., 2004 [4])	3	8	5	2	DLP
BNN-IBI (Bellare et al., 2004 [4])	2	5	2	1	OMDLP
Beth-IBI (Bellare et al., 2004 [4])	2	4	2	3	Unknown
Schnorr-IBI (Heng, 2004 [6])	2	6	3		DLP
Tight-Schnorr-IBI (Tan et al., 2011 [8])	2	6	3	1	DDHP
Twin-Schnorr-IBI	3	9	6	2	DLP

U: usk components, E: exponentiation, MG: multiplication in , MZ: multiplication in , IMP-AA/CA: security assumption against impersonation under active and concurrent attack, DLP: discrete logarithm problem, OMDL: one-more discrete logarithm problem, and DDHP: decisional Diffie-Hellman problem, .