Security Arguments for Digital Signatures and Blind Signatures

By David Pointcheval, Jacques Stern. Journal of Cryptology, 2015

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VDAS: Verifiable data aggregation scheme for Internet of Things (2017, background): “From the Forking lemma [27], if C has a replay with the same random tape but a different respond of h2, AI will output a new effective forged signature σ′ = 〈R, V ′〉.”
Mona: Secure Multi-Owner Data Sharing for Dynamic Groups in the Cloud (2013, methodology): “According to the Forking Lemma [21] , by using the oracle replay technique, the attacker A obtains two valid signatures ðM; 0 ; c; 1 Þ and ðM; 0 ; c 0 ; 0 1 Þ as follows: 0 ¼ ðT 1 ; T 2 ; T 3 ; c; R 1 ; R 2 ; R 3 ; R 4 ; R 5 Þ c ¼ fðM; T 1 ; T 2 ; T 3 ; R 1 ; R 2 ; R 3 ; R 4 ; R 5 Þ c 0 ¼ f 0 ðM; T ”
Secure Anonymous Key Distribution Scheme for Smart Grid (2016, background): “5) Analysis: According to forking lemma [34], adversary”
An Efficient Conditional Privacy-Preserving Authentication Scheme for Vehicular Sensor Networks Without Pairings (2016, methodology): “Analysis: By using Forking Lemma [38], [39], once A can construct two valid signatures (Ri, Vi = h2 × ri + SIDi mod q) and (Ri, V ′ i = h ′ 2 × ri + SIDi mod q), such that h2 = h2, B can successfully derive the value SIDi from these two valid signatures (Ri, Vi = h2 × ri + SIDi mod q) and (Ri, V ′ i”
Compact Multi-Signatures for Smaller Blockchains (2018, methodology): “The forking lemma of Pointcheval and Stern [46] is commonly used to prove the security of schemes based on Schnorr signatures [48] in the random-oracle model.”