Decentralized Certificate Authority

Bargav JayaramanHannah Li

1

Review - Creating a Certificate

Identity

Ownership

class/type of certificate

With private key

2

example.com Certificate Authority

Motivation

3

2011 Comodo and DigiNotar

The certificates are only as trustworthy as the weakest CA...

OR

Background - Digital Signature Algorithm (DSA)

4

ECDSA Signature Algorithm Random Number

k

Private Key

d

Hash(message)

Public Key qDigital Signature

(r,s)

Background - Elliptic Curve DSA

5

ECDSA Signature Algorithm

Parameters = (p, b, G, n, h)

Public Key: Q = d * G

Signature: (x, y) = k * Gr = x mod n

s = k-1(Hash(m) + rd)

Sample Curve

d= CA private keyk = Random numberm = info to be signed

Background - Secure Multiparty Computation

6

Input: X Input: Y

Output: f(X, Y)

Computation

Alice Bob

Alice generates the Circuit Bob evaluates the Circuit

Framework ==> OblivC + Absentminded Crypto

7

Generic Computation

obliv int x, y, z;

feedOblivInt(&x, io->x, 1);feedOblivInt(&y, io->y, 2);

Z = x + y;

revealOblivInt(&io->z, z, 0);

Absentminded Crypto provides ‘big number’ arithmetic over OblivC!

Use obig keyword for big numbers..

Decentralized CA using MPC

8

MPC

ECDSA Signature Algorithm

Certificate Signing Request

Certificate

CA Organization

example.com

MPC

Implementation in C

99

ECDSA Signature Algorithm(Secp192k1 192-bit EC parameters)

Random Number k(Generated via C’s

GMP library)

Private Key d(Generated via C’s

GMP library)

Hash(message)(SHA256 of template

TBSCertificate)

Public Key qDigital Signature (r,s)

To Be Signed Certificate

Experiments3-4 hours to perform certificate signing using ‘secp192k1’ elliptic curve.

Computation Bottleneck: Curve Point-multiplication!

10

pointMultiplication(G, k): N ← G Q ← 0 for i from 0 to m do if ki = 1 then Q ← pointAdd(Q, N) N ← pointDouble(N) return Q

pointAdd(P, Q): pointDouble(P):

Signature: (x, y) = k * Gr = x mod n

s = k-1(Hash(m) + rd)

Conclusion

Decentralized CA is feasible in practice

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Certificate Signing takes around 3-4 hours, which can be optimized

Deployment in open source tool OpenSSL