# BL0K: A New Stage of Privacy-Preserving Scope for Location-Based Services

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- We propose a framework called BL0K that creates an entirely new encryption communication procedure in the problem domains (malicious server) and a secure application for use in resource-constrained schemes such as mobile devices.
- (2)
- BL0K is capable of reducing the amount of exposed data during an attack, hence BL0K can be used to lessen data leakage.
- (3)
- BL0K can be used to make the outputs of the algorithm appear completely randomized. Thus, increasing the general performance level that would also increase the level of privacy.
- (4)
- We evaluated the performance of BL0K framework: using a dataset close to the real-world queries by comparing its performance with the BLOT in terms of privacy (entropy), and the reported performance improvements increased to 93% (averaging 25% to 30%).

## 2. Related Work

#### 2.1. Privacy of Bloom Filter

_{1}, ∆

_{2}, and ∆

_{3}are used to build an SBF, as shown in Figure 1, where the hash functions 1, 2, and 3 are used to link all elements to the filter, except for the first 10 elements of the SBF [33].

#### 2.2. Privacy of Zero Knowledge and Localization

_{1}and N

_{N}; M

_{1}and M

_{M}) and is even a portion of the two distinct strings of terms, whereas the holders of the location a

_{i}and b

_{i}show the relations of M

_{i}and N

_{i}, correspondingly. The module in M

_{i}cannot be exposed after the instantiation of the placeholder “S (M/a) (N/b)”, which is often revealed to be true. After this, zero-knowledge profits can then be regarded as successful. For instance, zero knowledge zk

_{check}(a

_{1}; b

_{1}) _a

_{2}(sign (m;k); m; vk(k)) tends to prove that the information of a signature can be successfully verified with a key vk(k) [43]. ZKP tends to vary from the traditional cryptography, where they tend to authenticate and secure the privacy of communication in contemporary applications such as LBS. The numerous benefits of ZKP often supercede the embryonic techniques of security and confidentiality since they can confirm a particular user and still ensure that the user is unidentified [44]. Although ZKP is mainly desirable for defending the confidentiality of a user and the content of a message, computer-assisted support in modeling the security protocols is not available. However, for these intentions, this protocol is still vulnerable [45]. Garg et al. [46] proposed a new category for localization method in wireless sensor networks using localization algorithms that contained based on multiple key features such as Anchor Based, Anchor Less, Range Based, and Range-Free.

## 3. Preliminaries

#### 3.1. Deficiency of BLOT

#### 3.2. Zero-Knowledge Plan within LBS

- (1)
- Proof of an assertion: Provided by the protocol regarding LBS information with probability p.
- (2)
- Probability: By increasing the queries, probability q can be increased exponentially close to 1.0.
- (3)
- Leakage: No information is leaked by any query, except with negligible probability.
- (4)
- Malicious LBS server: Using probability q, it is possible to detect a malicious LBS server.

^{−N})

^{k}. Traditionally, the verifier V is referred to as Victor, and the prover P is referred to as Peggy. In the LBS case, the verifier is the user (receiver), and the prover is the LBS provider (sender).

#### 3.3. Bloom Filter Plan within LBS

- (1)
- User/server: The user and SNS can send a particular query if there is something in the LBS server’s range.
- (2)
- Query list: The original server can locate one bit of data from the query list, while SNS can locate none.
- (3)
- Server range: Set of objects in the range of the server will need to be itemized.
- (4)
- Malicious LBS server: A malicious LBS server can be able to detect with probability q.
- (5)
- Probability: Probability q can be increased close to 1 by increasing the queries.

^{N}), where p refers to a genuine false positive. Apart from a negligible probability caused by the inverse HK, malicious servers cannot receive information from any exchange.

#### 3.4. Overview of BL0K in LBS and Research Design

#### 3.5. Security for LBS: The BL0K Protocol

#### 3.6. BL0K System Architecture

#### 3.7. ZKP Standard

^{2}≡ y mod n. The problem is constructive: if x exists, then the algorithm must produce it. There is no known polynomial time algorithm that can solve this problem. In this formulation, the key material is p and q and the plaintext is x. It can be proven that the intractability of this problem is equivalent to the intractability of factorization.

^{−1}must also be polynomial time computable, and it must comply with the following: g

^{−1}(g(x)) = x and g(g

^{−1}(y)) = y for all plaintexts x and for all encoded integers y. This requirement is easy to meet. Length-encoded values with padding, as defined by RFC1321 for example, can be used. It is not intended that g or its inverse contain any key material. It is an advantage for both V and P that the complete algorithms for g and g

^{−1}are made publicly available. Standard encoding methods consider time as linear. For the rest of this document, we refer to s and g(s) interchangeably.

- (1)
- PEGGY STEP: Peggy generates primes p and q, such that p ≡ 3 mod 4 and q ≡ 3 mod 4. She computes n = pq and sends n to Victor. The values p and q are the “auxiliary secret” referred to above.
- (2)
- VICTOR STEP: Victor chooses a random integer x and computes w = (xs)
^{4}mod n. He then sends w to Peggy. Note that because of the intractability assumption, it is not possible to recover a single bit of (xs)^{2}or (xs) from w. Good practice suggests that Victor uses a new value of x for each ZKP interaction (LBX transaction). - (3)
- PEGGY STEP: Peggy can now compute the principal square root y
_{1}of w mod p and the principal square root y_{2}of w mod q. Using Fermat’s Little Theorem [61], these values are:$${y}_{1}={w}^{(p+1)/2}$$$${y}_{2}=\text{}{w}^{(q+1)/2}$$Peggy then uses the Chinese Remainder Theorem [62] to construct a value y such that y ≡ y_{1}mod p and y ≡ y_{2}mod q. It follows that (xs)^{2}≡ y mod n. Peggy now needs to find m—the multiplicative inverse of s^{2}mod n. Euclid’s algorithm tells us that m exists and is computable in linear time if and only if gcd(s^{2}, n) = 1. This will be true, except with negligible probability. Peggy then computes m and observes that m(xs)^{2}≡ x^{2}≡ my mod n. Peggy sends my to Victor. - (4)
- VICTOR STEP: Victor computes x
^{2}mod n and observes that this is equal to the value just received from Peggy, namely my. First, consider that this is a probabilistic algorithm. The likelihood of success is 1 − 2^{−b}where b = log2(n). This may increase arbitrarily using larger values of p and q. Secondly, in Step 3, Peggy did not need s^{2}; she only needed m, the multiplicative inverse of s^{2}mod n. By the first assumption, it is computationally intractable to recover any part of s from m. (his is why a fourth power was used rather than a second power. The value m can be safely be stored in a database referring to the quantity c, or some abstract token that refers to c. If the encryption was performed on a device, then it could be arranged that the encryption mechanism returns m and a token that points to c. Finally, we must discuss the issue of Fermat Liars and “approximately prime” values. Fermat’s Little Theorem states that if p is prime, then a^{p−1}≡ 1 mod p for all such that 1 ≤ a < p. If n is composite, then a^{n−1}≡ 1 mod n, where n is referred to as a Fermat Liar or an approximately prime integer. For example, n = 221 is a Fermat Liar for a = 38. This is why the auxiliary secrets p and q must be prime, and not approximately prime. Any primary algorithm that runs on p and q must ensure that they are truly prime. Since p and q are computed offline, this does not affect the runtime performance of the system.

## 4. BL0K Technique

#### 4.1. BL0K Querying Users’ Locations

#### 4.2. BL0K Algorithm

#### Zero Knowledge with Bloom Filter Scenario (BL0K)

- Step 1: Initialization of ZKP as shown in Algorithm 1:

^{A}that can calculate J(A). It also has a secret ID. Before step 2, we have two files to update: one for BF updating and this function updates the BF with the data in a text file “DataListforBF.txt,” and one for SNS backing store with the data and its locations as (SHA32 bit) code.

Algorithm 1: BL0K Algorithm. |

- Step 2: Prover has an ID
^{A}that can calculate J(A) = f(Id(A)) mod n. It also has a secret ID and the secret data (A) = J(A)^{−s}. - Step 3: Prover generates primes p and q such that p ≡ 3 mod 4 and q ≡ 3 mod 4. Prover computes n = pq and sends n to Victor.
- Step 4: The actual protocol BL0K begins from this step. Prover sends its identity ID J(A) after Prover selects a random secret r and x = r
^{v}mod n to Verifier. - Step 5: Verifier sends a random challenge to Prover after Verifier selects a random challenge e in {1, 2, ..., v}.
- Step 6: Prover can compute then sends the following response to Verifier: y= r · secret(A)
^{e}mod n. - Step 7: Verifier receives y, constructs J(A) = f(Id(A)) mod n, computes z = J(A)
^{e}y^{v}, and accepts this round if z = x mod n. - Step 8: The (GQ) zero-knowledge protocol has complete its work.
- Step 9: Verifier checks if the Prover is verified or not. If verified, the query send data query to Prover to obtain the location if data is present in bloom filter; otherwise, send a message “data not found”!
- Step 10: The BL0K protocol is completed.

## 5. BL0K Performance Measures

#### Attack Model

## 6. Calculate the Performance Entropy for BL0K

## 7. Performance Results

#### 7.1. Connection Performance

#### 7.2. Computing Performance

#### 7.3. Simulation Result for Computing Performance

#### 7.4. Computing Performance Measurement

## 8. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

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**Figure 1.**Spatial bloom filter (SBF). (

**a**) Two BF elements joined to ∆

_{1}are processed through the use of the hash functions, leading to six one-value elements that can then be written into the SBF. The same method can be used in (

**b**) and (

**c**).

**Figure 2.**Zero Knowledge protocol example [50].

**Figure 9.**Performance entropy comparison of BL0K offers has better entropy than BLOT because the BLOT uses a lot of anonymous messages for increasing security, but in BL0K is achieved by using the zero-knowledge proof algorithm. No multiple or redundant information or queries sent on the network.

Symbol | Description |
---|---|

Verifier | Mobile device user |

Prover | Location-based servers |

SNS | The social network server |

CT | Wi-Fi tower |

BF | Bloom filter |

ZKP | Zero Knowledge Proof |

Symbol | Description |
---|---|

ID^{A} | User A should be unique-identifier |

PubMO^{A} | The Public-modulus |

Pube^{A} | The Public-exponent |

ID^{CT} | Wi-Fi tower’s-identifier |

Pub^{Key} | Public key/coding-encoding |

Skey^{(AES)} | Symmetric key/coding-encoding |

Information | Size of Information (Bits) |
---|---|

J(A) | 64 |

SNS to the user (X) | 64 |

User to SNS (e) | 32 |

SNS to the user (Y) | 64 |

User to LBS and back (Location) | 32 |

Protocol | Computation Time | Connection in Time (s) |
---|---|---|

BMobishare | 1.75 s | 1.5 |

BLOT | 10 ms | 0 |

BL0K | 7.8 ms | 0 |

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Albelaihy, A.; Thayananthan, V. BL0K: A New Stage of Privacy-Preserving Scope for Location-Based Services. *Sensors* **2019**, *19*, 696.
https://doi.org/10.3390/s19030696

**AMA Style**

Albelaihy A, Thayananthan V. BL0K: A New Stage of Privacy-Preserving Scope for Location-Based Services. *Sensors*. 2019; 19(3):696.
https://doi.org/10.3390/s19030696

**Chicago/Turabian Style**

Albelaihy, Abdullah, and Vijey Thayananthan. 2019. "BL0K: A New Stage of Privacy-Preserving Scope for Location-Based Services" *Sensors* 19, no. 3: 696.
https://doi.org/10.3390/s19030696