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Pedersen DKG Materials

Memo
#pedersen-dkg#dkg#threshold-cryptography#cryptography

Visual materials used in Pedersen DKG란?. These diagrams show how each participant creates a local polynomial, broadcasts coefficient commitments, exchanges and verifies shares, then aggregates final shares and a group public key.

Polynomial Form

When the threshold is t, each participant i samples a degree t - 1 polynomial:

fi(x)=∑j=0t−1ci,jxjf_i(x) = \sum_{j=0}^{t-1} c_{i,j} x^j

The constant term is that participant’s local secret contribution:

ci,0=ski=fi(0)c_{i,0} = sk_i = f_i(0)

For three participants:

f1(x)=∑j=0t−1c1,jxjf_1(x) = \sum_{j=0}^{t-1} c_{1,j} x^j f2(x)=∑j=0t−1c2,jxjf_2(x) = \sum_{j=0}^{t-1} c_{2,j} x^j f3(x)=∑j=0t−1c3,jxjf_3(x) = \sum_{j=0}^{t-1} c_{3,j} x^j

Local Polynomial Shares

Participant 1

Participant 1 DKG polynomial

Participant 2

Participant 2 DKG polynomial

Participant 3

Participant 3 DKG polynomial

Local Contributions

Each DKG node creates its own secret contribution

Group Polynomial

Three DKG participant polynomials combine into a group polynomial whose y-intercept is the group secret

Round 1 Commitments

Round 1 commitment broadcast

Round 2 Share Exchange

DKG nodes commit, verify, and exchange shares

Round 2 Share Verification

Round 2 share verification flow

Final Shares

Aggregate verified shares into final shares and one public key