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APPENDIX
Digital Signatures
In a nutshell, a digital signature scheme uses a mes-
sage M and an asymmetric key-pair key(sk
sig
, pk
sig
)
to produce a digital signature σ by using M and the
private key sk
sig
from asymmetric key-pair. A verifier
can use the signature σ, the message M and the public
key pk
sig
from asymmetric key-pair to check the in-
tegrity (σ has been issued for M) and the authenticity
(σ was produced by the holder of the corresponding
signing key sk
sig
) of the signature.
In a more formal way, a digital signature scheme
(DSS) is a set (K, S,V ) of poly-times algorithms. The
first algorithm DSS
K
takes a security parameter k to
generate an asymmetric key-pair DSS
K
(sk
sig
, pk
sig
)
where the private key is sk
sig
and the public key is
pk
sig
. The second algorithm DSS
S
is the signing
algorithm. This signing algorithm uses a message
M ∈ {0,1}
∗
and a private key sk
sig
as input data and
outputs a signature σ = DSS
S
(sk
sig
,m). The third al-
gorithm DSS
V
is the verification algorithm. This ve-
rification algorithm uses the message M ∈ {0,1}
∗
,
a public key pk
sig
, and a signature σ as input data
and outputs a single bit b = RS
V
(σ,M, pk
sig
), b ∈
{true, f alse} that indicates if the signature σ is va-
lid for M or not. Also, in a practical implementation
the message M is not directly used as input data in
DSS
S
and DSS
V
but rather H(M), where H is a cryp-
tographic hash function.
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