Leakage-Resilient Signatures with Graceful Degradation

We investigate new models and constructions which allow leakage-resilient signatures secure against existential forgeries, where the signature is much shorter than the leakage bound. Current models of leakage-resilient signatures against existential forgeries demand that the adversary cannot produce a new valid message/signature pair (

m

,

σ

) even after receiving some

λ

bits of leakage on the signing key. If ∣ 

σ

 ∣ ≤ 

λ

, then the adversary can just choose to leak a valid signature

σ

, and hence signatures must be larger than the allowed leakage, which is impractical as the goal often is to have large signing keys to allow a lot of leakage.

We propose a new notion of leakage-resilient signatures against existential forgeries where we demand that the adversary cannot produce

$n = \lfloor \lambda / \vert \sigma \vert \rfloor + 1$

distinct valid message/signature pairs (

m

1

,

σ

1

), …, (

m

n

,

σ

n

) after receiving

λ

bits of leakage. If

λ

 = 0, this is the usual notion of existential unforgeability. If 1 < 

λ

 < ∣ 

σ

 ∣, this is essentially the usual notion of existential unforgeability in the presence of leakage. In addition, for

λ

 ≥ ∣ 

σ

 ∣ our new notion still guarantees the best possible, namely that the adversary cannot produce more forgeries than he could have leaked, hence graceful degradation.

Besides the game-based notion hinted above, we also consider a variant which is more simulation-based, in that it asks that from the leakage a simulator can “extract” a set of

n

 − 1 messages (to be thought of as the messages corresponding to the leaked signatures), and no adversary can produce forgeries not in this small set. The game-based notion is easier to prove for a concrete instantiation of a signature scheme. The simulation-based notion is easier to use, when leakage-resilient signatures are used as components in larger protocols.

We prove that the two notion are equivalent and present a generic construction of signature schemes meeting our new notion and a concrete instantiation under fairly standard assumptions. We further give an application, to leakage-resilient identification.