On the correlation and sensitivity of so far statistical randomness tests based on runs

Abstract—Random numbers play a very important role in cryptography. More precisely, almost cryptographic primitives are ensured their security based on random values such as random key, nonces, salts... Therefore, the assessment of randomness according to statistical tests is really essential for measuring the security of cryptographic algorithms. In this paper, we focus on so far randomness tests based on runs in the literature. First, we have proved in detail that the expected number of gaps (or blocks) of length in a random sequence of length is . Secondly, we have evaluated correlation of some tests based on runs so far using Pearson coefficient method [5, 6] and Fail-Fail ratio one [7, 8]. Surprisingly, the Pearson coefficient method do not show any strong linear correlation of these runs-based tests but the Fail-Fail ratio do. Then, we have considered the sensitivity of these runs tests with some basic transformations. Finally, we have proposed some new runs tests based on the sensitivity results and applied evaluations to some random sources. Tóm tắt—Số ngẫu nhiên đóng một vai trò quan trọng trong mật mã. Cụ thể, độ an toàn của hầu hết các nguyên thủy mật mã đều được đảm bảo dựa trên các giá trị ngẫu nhiên như khóa, nonce, salt… Do đó, việc đánh giá tính ngẫu nhiên dựa trên các kiểm tra thống kê là thực sự cần thiết để đo độ an toàn cho các thuật toán mật mã. Trong bài báo này, chúng tôi tập trung vào các kiểm tra ngẫu nhiên dựa vào run trong các tài liệu. Đầu tiên, chúng tôi chứng minh chi tiết rằng kỳ vọng số các gap (khối) độ dài trong một chuỗi ngẫu nhiên độ dài là . Sau đó, chúng tôi đánh giá mối tương quan của một số kiểm tra dựa vào run bằng phương pháp hệ số Pearson [5, 6] và tỷ số Fail-Fail [7, 8]. Đáng ngạc nhiên là phương pháp hệ số Pearson không cho thấy bất kỳ mối tương quan tuyến tính mạnh nào của các kiểm tra dựa vào run, trong khi đó tỷ số Fail-Fail lại chỉ ra. Tiếp theo, chúng tôi xem xét độ nhạy của các kiểm tra run này với một số phép biến đổi cơ bản. Cuối cùng, chúng tôi đề xuất một số kiểm tra run mới dựa trên các kết quả độ nhạy và đánh giá áp dụng chúng cho một số nguồn ngẫu nhiên.

Một số cải tiến cho các kiểm tra thống kê tính ngẫu nhiên sử dụng so khớp mẫu

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Mối liên hệ giữa tính nhận biết tiền ảnh và một số tính chất mật mã khác của hàm băm

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Fast Software Implementation of Serial Test and Approximate Entropy Test of Binary Sequence

In many cryptographic applications, random numbers and pseudorandom numbers are required. Many cryptographic protocols require using random or pseudorandom numbers at various points, e.g., for auxiliary data in digital signatures or challenges in authentication protocols. In NIST SP800-22, the focus is on the need for randomness for encryption purposes and describes how to apply a set of statistical randomness tests. These tests can be used to evaluate the data generated by cryptographic algorithms. This paper will study the fast software implementation of the serial test and the approximate entropy test and propose two types of fast implementations of these tests. The first method is to follow the basic steps of these tests and replace bit operations with byte operations. Through this method, compared with the implementation of Fast NIST STS, the efficiency of the serial test and approximate entropy test is increased by 2.164 and 2.100 times, respectively. The second method is based on the first method, combining the statistical characteristics of subsequences of different lengths and further combining the two detections with different detection parameters. In this way, compared to the individual implementation of these tests, the efficiency has been significantly improved. Compared with the implementation of Fast NIST STS, the efficiency of this paper is increased by 4.078 times.

Testing the randomness of shares in color visual cryptography

The concept of black-and-white visual cryptography with two truly random shares, previously applied to color images, was improved by mixing the contents of the segments of each coding image and by randomly changing a specified number of black pixels into color ones. This was done in such a way that the changes of the contents of the decoded image were as small as possible. These modifications made the numbers of color pixels in the shares close to balanced, which potentially made it possible for the shares to be truly random. The true randomness was understood as that the data pass the suitably designed randomness tests. The randomness of the shares was tested with the NIST randomness tests. Part of the tests passed successfully, while some failed. The target of coding a color image in truly random shares was approached, but not yet reached. In visual cryptography, the decoding with the unarmed human eye is of primary importance, but besides this, simple numerical processing of the decoded image makes it possible to greatly improve the quality of the reconstructed image, so that it becomes close to that of the dithered original image.

Magniber v2 Ransomware Decryption: Exploiting the Vulnerability of a Self-Developed Pseudo Random Number Generator

With the rapid increase in computer storage capabilities, user data has become increasingly important. Although user data can be maintained by various protection techniques, its safety has been threatened by the advent of ransomware, defined as malware that encrypts user data, such as documents, photographs and videos, and demands money to victims in exchange for data recovery. Ransomware-infected files can be recovered only by obtaining the encryption key used to encrypt the files. However, the encryption key is derived using a Pseudo Random Number Generator (PRNG) and is recoverable only by the attacker. For this reason, the encryption keys of malware are known to be difficult to obtain. In this paper, we analyzed Magniber v2, which has exerted a large impact in the Asian region. We revealed the operation process of Magniber v2 including PRNG and file encryption algorithms. In our analysis, we found a vulnerability in the PRNG of Magniber v2 developed by the attacker. We exploited this vulnerability to successfully recover the encryption keys, which was by verified the result in padding verification and statistical randomness tests. To our knowledge, we report the first recovery result of Magniber v2-infected files.

Lightweight Image Encryption: A Chaotic ARX Block Cipher

Nowadays, lightweight cryptography attracts academicians, scientists and researchers to concentrate on its requisite with the increasing usage of low resource devices. In this paper, a new lightweight image encryption scheme is proposed using the Lorenz 3D super chaotic map. This encryption scheme is an addition–rotation–XOR block cipher designed for its supremacy, efficacy and speed execution. In this addition–rotation–XOR cipher, the equation for Lorenz 3D chaotic map is iteratively solved to generate double valued signals in a speedy manner using the Runge–Kutta and Euler methods. The addition, rotation and diffusion sequences are generated from the double valued signals, and the source pixels of the 8-bit plain test images are manipulated with the addition, rotation and diffusion of the bytes. Finally, the cipher images are constructed from the manipulated pixels and evaluated with various statistical as well as randomness tests. The results from various tests prove that the proposed chaotic addition–rotation–XOR block image cipher is efficient in terms of randomness and speed.

Cryptosystems using an improving hiding technique based on latin square and magic square

<p>Hackers should be prevented from disclosing sensitive data when sent from one device to another over the network. Therefore, the proposed method was established to prevent the attackers from exploiting the vulnerabilities of the redundancy in the ciphertext and enhances the substitution and permutation operations of the encryption process .the solution was performed by eliminates these duplicates by hiding the ciphertext into a submatrix 4 x4 that chooses randomly from magic square 16x16 in each ciphering process. Two techniques of encrypted and hiding were executed in the encryption stage by using a magic square size 3 × 3 and Latin square size 3 × 3 to providing more permutation and also to ensure an inverse matrix of decryption operation be available. In the hiding stage, the ciphertext was hidden into a 16×16 matrix that includes 16 sub-magic squares to eliminate the duplicates in the ciphertext. Where all elements that uses were polynomial numbers of a finite field of degree Galois Fields GF ( ). The proposed technique is robust against disclosing the repetition encrypted data based on the result of Avalanche Effect in an accepted ratio (62%) and the results of the output of the proposed encryption method have acceptable randomness based on the results of the p-values (0.629515) of the National Institute of Standards and Technology (NIST) randomness tests. The work can be considered significant in the field of encrypting databases because the repetition of encrypted data inside databases is considered an important vulnerability that helps to guess the plaintext from the encrypted text.</p>

Maintaining the Integrity of Encrypted Data by Using the Improving Hash Function Based on GF 28

The issue of protecting the information from penetration has become an important issue. The system that depends on the encryption ensures the confidentiality of the information non-disclosure of sensitive information but does not ensure the integrity of data from destruction and change. In this paper, a proposed system is designed to protect the confidentiality and integrity of data from penetration, disclosure, and destruction. The proposed system based on the polynomial numbers of GF (𝟐𝟖) is achieved by improving the encryption approach using the idea of the magic square and the linear equation system also uses improving the digital signature method for ensuring that data is not changed or modified. The system has higher encryption and decryption throughput (548.924Kb /sec), (548.924 Kb /sec) and acceptable value 0.759294 of the randomness data according to the NIST randomness tests as well as a high confusion and diffusion in cipher text based on the ratio of Avalanche effect test.