Strong authentication

on smart wireless devices

V. Mora-Afonso / P. Caballero-Gil / J. Molina-Gil

Heads Up

proposal to protect communications combining IBC for Bluetooth communication with the promising NFC technology for secure authentication.

Layout

Brief introduction
State of the art
Let's dive into IBE
Our proposal
Conclusions

Motivation

Smartphones are everywhere
All kind of environments
Computing, power and battery limitations.

Identity Based Cryptography

Any piece of text as public key
Shorter encryption keys
No certificates
No CRLs
Less computational complexity

Near Field Communication

Short-range high frequency wireless communications
Enables simple and safe interactions
Contactless transitions. Tap & connect

State of the art

Encryption of messages sent within different social providers
Access control through Zero-Knowledge proof authentication
Encryption of phone calls

Identity-Based Cryptography

Piece of information linked to node as public key
Proposed by Shamir but did not come up with specific solution
Private Key Generator (PKG) with master secret key

Bilinear maps

Bilinear: $e(aP,bQ) = e(P,Q)^{ab} \forall P,Q \in G_1$ Non-degenerate: $e(P,P)$ is a generator of $G_2$. In other words $e(P,P)\not=1$ Computable: Give $P,Q \in G_1$ there is an efficient algorithm to compute $e(P,Q)$

Pairing over elliptic curves

Tate pairing
Weil pairing
Miller's algorithm

Security based on assumptions of hard problems in Elliptic Curves

Computational Diffie-Hellman. No efficient algorithm exists to compute $abP$ from $P,aP,bP \in G_1$ for some $a,b \in {Z \ast}_q$ Weak Diffie-Hellman. No efficient algorithm exists to compute $sQ$ from $P,Q,sP\in G_1 and$ $s \in {Z \ast}_q $ Billinear Diffie-Hellman. No efficient algorithm exists to compute $e(P,P)^{abc}$ from $P,aP,bP,cP \in G_1$ where $a,b,c \in {Z \ast}_q$ Decisional Billinear Diffie-Hellman. No efficient algorithm exsits to decide if $r=e(P,P)^{abc}$ given $P,aP,bP,cP \in G_1, r \in G_2 and a,b,c \in {Z \ast}_q$

Boneh-Franklin scheme

Setup stage. Generation of the master secret key and a set of public parameters
Extract stage. Generation of a user's private key
Encrypt stage. A user wants to encrypt a message M to send the resulting ciphertext C to the user with identity ID
Decrypt state. A user that recieves C uses its private key to obtain the original message M

Our proposal

Bluetooth lacks of user friendliness
Too much time to pair two unknown devices
NFC is a breath of fresh air
There are some security problems with its ciphers

The situation

Two users A and B want to securely share information through the bluetooth of their smartphones. They are both registered to a TTP PKG server.

Pairing phase

Communication phase

Implementation details

Elliptic curve $y^2=x^3 + 1$ over $F_p$ for primes $p$ congruent to 11 modulo 12
Use of the group $E(F_p)$ with points (x,y) and the group $E({F_p}^2)$
Tate pairing and Miller's algorithm for its computation

Windows Phone 8

Nokia Lumia 920
First implementations a little bit dissapointing
Message size Time to encrypt Time to decrypt 128 7497.198 ms 7368.289 ms 512 7498.221 ms 6998.858 ms
App to encrypt emails published as a result of this work

MacOs and iOs

Use of the Pairing Based Cryptography Library
Performance boost
Encryption time around 60ms

Conclusions

It was proposed a communication protocol which use NFC for pairing and IBE for securing communications
Implement the proposal in different platforms and testing environments
In-depth analysis of its security
Signcryption and applications in everyday life

Strong authentication – on smart wireless devices – Motivation

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Strong authentication – on smart wireless devices – Motivation

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