# Cooperative Secret Sharing Using QR Codes and Symmetric Keys

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## Abstract

**:**

## 1. Introduction

- The objective of the proposed protocol is to encrypt and conceal shares within QR codes to be able to distribute the shares via public channels without raising suspicion. While there are a number of existing techniques for hiding a secret within a QR code, the purpose of many of these methods is for data hiding and not for secret sharing [5,6,7,8,9]. Hence, cooperation between a threshold number of participants to recover the secret is not incorporated in these techniques.
- There are some drawbacks with existing QR code secret sharing approaches that are based on visual cryptography. For example, the QR code sizes that are used may have to be very large [10]. This may be useful in situations where decryption necessitates no computation; however, large QR codes are impractical and are likely to raise suspicion as these are not commonly used in public. Other approaches result in QR codes that are valid, but do not look like normal QR codes because each module is divided into smaller sub-modules in order to enable secret sharing [11].
- There are also existing (n, n) QR code secret sharing approaches where normal looking QR codes are used [12,13]. However, (n, n) secret sharing requires that all participants must be present to recover the secret. The proposed protocol is for (k, n) secret sharing, where k can be < n. In other words, while a threshold number of participants is required to recover the secret, this threshold does not have to be all the participants.
- Unlike our previous work in Chow et al. [14], in which the purpose was to use a single non-suspicious QR code to broadcast a secret to a group of authorized participants where each participant can obtain the secret themselves, the protocol proposed in this paper provides a mechanism for a shared secret using QR codes. This means that each participant can only obtain his/her respective share, which does not reveal the secret, and must cooperate with other participants before the secret can be recovered.

## 2. Background

#### 2.1. Secret Sharing

**Definition**

**1.**

#### 2.2. Quick Response Codes

## 3. Related Work

## 4. Protocol and Adversarial Models

#### 4.1. Protocol Model

#### 4.2. Adversarial Model

## 5. Secret Sharing Protocol Using QR codes

#### 5.1. Encryption and Concealment Phase

**Definition**

**2.**

- ${C}_{i}\leftarrow $ Enc(${k}_{pu{b}_{i}}$, ${S}_{i}$): This algorithm takes a share, ${S}_{i}$, and encrypts it using a group member’s public key, ${k}_{pu{b}_{i}}$. This results in the encrypted message, ${C}_{i}$.
- ${M}_{i}\leftarrow {C}_{i}\oplus {k}_{sym}$: This process ‘XOR’s the encrypted message, ${C}_{i}$, with a symmetric key, ${k}_{sym}$, to produce the encrypted hidden message, ${M}_{i}$, which is to be embedded in a QR code.
- $CoverQ{R}_{i}\leftarrow $ Gen(${P}_{i}$): Taking a public message, ${P}_{i}$, this algorithm generates a cover QR code, $CoverQ{R}_{i}$.
- $Q{R}_{i}\leftarrow Emb(CoverQ{R}_{i},{M}_{i})$: This process embeds the encrypted hidden message, ${M}_{i}$, into the cover QR code, $CoverQ{R}_{i}$, to produce a QR code, $Q{R}_{i}$.

#### 5.2. Extraction and Decryption Phase

**Definition**

**3.**

- ${M}_{i}\leftarrow $ Ext($Q{R}_{i})$): Given the QR code with the conceal information, $Q{R}_{i}$, this algorithm extracts the encrypted hidden message, ${M}_{i}$, from it.
- ${C}_{i}\leftarrow {M}_{i}\oplus {k}_{sym}$: By ‘XOR’ing the encrypted hidden message, ${M}_{i}$, with the symmetric key, ${k}_{sym}$, the encrypted message, ${C}_{i}$, can be obtained.
- ${S}_{i}\leftarrow $ Dec(${k}_{pri{v}_{i}},{C}_{i}$): This process obtains the share ${S}_{i}$ by decrypting the encrypted message, ${C}_{i}$, using the private key, ${k}_{pri{v}_{i}}$.

#### 5.3. Cooperative Phase

## 6. Analysis and Discussion

#### 6.1. Implementation Guidelines

#### 6.2. Security

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**2.**

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Arrangement of the data and error correction codewords within a Version 4 QR code, with error correction level H.

**Figure 4.**Example of embedding a hidden QR code message within a cover QR code; (

**a**) QR code containing a message to be embedded; (

**b**) codeword modules of the QR code presented in (

**a**); (

**c**) cover QR code containing a public message; (

**d**) resulting QR code containing a public message and an embedded hidden message; (

**e**) differences in modules between the QR codes shown in (

**c**,

**d**).

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## Share and Cite

**MDPI and ACS Style**

Chow, Y.-W.; Susilo, W.; Tonien, J.; Vlahu-Gjorgievska, E.; Yang, G.
Cooperative Secret Sharing Using QR Codes and Symmetric Keys. *Symmetry* **2018**, *10*, 95.
https://doi.org/10.3390/sym10040095

**AMA Style**

Chow Y-W, Susilo W, Tonien J, Vlahu-Gjorgievska E, Yang G.
Cooperative Secret Sharing Using QR Codes and Symmetric Keys. *Symmetry*. 2018; 10(4):95.
https://doi.org/10.3390/sym10040095

**Chicago/Turabian Style**

Chow, Yang-Wai, Willy Susilo, Joseph Tonien, Elena Vlahu-Gjorgievska, and Guomin Yang.
2018. "Cooperative Secret Sharing Using QR Codes and Symmetric Keys" *Symmetry* 10, no. 4: 95.
https://doi.org/10.3390/sym10040095