KCDSA

KCDSA (Korean Certificate-based Digital Signature Algorithm) is a digital signature algorithm created by a team led by the Korea Internet & Security Agency (KISA). It is an ElGamal variant, similar to the Digital Signature Algorithm and GOST R 34.10-94. The standard algorithm is implemented over $GF(p)$ , but an elliptic curve variant (EC-KCDSA) is also specified.

KCDSA requires a collision-resistant cryptographic hash function that can produce a variable-sized output (from 128 to 256 bits, in 32-bit increments). HAS-160, another Korean standard, is the suggested choice.

Domain parameters

$p$ : a large prime such that $|p|=512+256i$ for $i=0,1,\dots ,6$ .
$q$ : a prime factor of $p-1$ such that $|q|=128+32j$ for $j=0,1,\dots ,4$ .
$g$ : a base element of order $q$ in $\operatorname {GF} (p)$ .

User parameters

$x$ : signer's private signature key such that $x\in Z_{q}$ .
$y$ : signer's public verification key computed by $y=g^{{\bar {x}}}{\pmod {p}},$ where ${\bar {x}}=x^{{-1}}{\pmod {q}}$ .
$z$ : a hash-value of Cert Data, i.e., $z=h({\text{Cert Data}})$ .

Signing

Signer randomly picks an integer $k\in Z_{q}$ and computes $w=g^{k}\mod {p}$
Then computes the first part: $r=h(w)$
Then computes the second part: $s=x(k-r\oplus h(z\parallel m)){\pmod {q}}$
If $s=0$ , the process must be repeated from the start.
The signature is $(r,s)$

Verifying

Verifier checks that $0\leq r<2^{|q|}$ and $0<s<q$ and rejects the signature as invalid if not.
Verifier computes $e=r\oplus h(z\parallel m)$
Then he checks if $r=h(y^{s}\cdot g^{e}\mod {p})$

External links

KCDSA specification and analysis

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