Selection of Sampling Keys for Cryptographic Tests

The keys of modern cryptographic algorithms have an enormous size, so the testing of the algorithm performance for all key combinations, will take practically an infinite time. To avoid this, the sampling method is used, where a much smaller number of keys is tested and then the estimation of the algorithm performance for all the keys is calculated with a predetermined sampling error. For each sampling key, an output sample of the algorithm must be generated and tested. Therefore, in order to have sampling results as close as possible to the real performance of the algorithm, the key question is whether the selection of the keys should be random or it must follow some rules. If the selection of the keys is completely random, there is a high probability that the tests will not find some "weak" or "equivalent" keys, which give non-random or similar outputs and therefore reduce the total number of active keys. But if the sampling keys are selected with some specific criteria, there is a much greater probability of detecting any weak or equivalent key. In this study an optimal key selection methodology is proposed, which combines the random and the non-random key selection. Keywords: Cryptography, Data encryption, Communication security, Computer security, Data security, Information security.

Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings

ElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in ‘Neural Computing & Applications’. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.

Cryptanalysis of an Image Cipher using Multi entropy Measures and the Countermeasures

The use of same keys or equivalent keys should not be occurred in cryptographic communications because a cipher system utilising such keys to secure messages can be attacked even it possesses excellent cryptographic characteristics for extracting intelligible information from encrypted messages. Identification of crypts formed with such keys is an important task of traffic analysis of cryptographic communications to check the applicability of two-messages-on-same-key (TMSK) attack. To avoid its applicability, adequate safeguards are required. In the paper, we cryptanalyze stream encryption based cipher system and propose an intelligent identification methodology using multi-entropy measures and soft decision criteria for identification of encrypted images of same or equivalent keys. Experimental test results show that the crypts formed with same keys can be identified successfully with high precision. We also present the countermeasures against TMSK attack.

On the Security of a Latin-Bit Cube-Based Image Chaotic Encryption Algorithm

In this paper, the security analysis of an image chaotic encryption algorithm based on Latin cubes and bit cubes is given. The proposed algorithm adopts a first-scrambling-diffusion- second-scrambling three-stage encryption scheme. First, a finite field is constructed using chaotic sequences. Then, the Latin cubes are generated from finite field operation and used for image chaotic encryption. In addition, according to the statistical characteristics of the diffusion image in the diffusion stage, the algorithm also uses different Latin cube combinations to scramble the diffusion image for the second time. However, the generation of Latin cubes in this algorithm is independent of plain image, while, in the diffusion stage, when any one bit in the plain image changes, the corresponding number of bits in the cipher image follows the change with obvious regularity. Thus, the equivalent secret keys can be obtained by chosen plaintext attack. Theoretical analysis and experimental results indicate that only a maximum of 2 . 5 × w × h 3 + 6 plain images are needed to crack the cipher image with w × h resolution. The size of equivalent keys deciphered by the method proposed in this paper are much smaller than other general methods of cryptanalysis for similar encryption schemes.

Side-Channel Attacks on Post-Quantum Signature Schemes based on Multivariate Quadratic Equations

In this paper, we investigate the security of Rainbow and Unbalanced Oil-and-Vinegar (UOV) signature schemes based on multivariate quadratic equations, which is one of the most promising alternatives for post-quantum signature schemes, against side-channel attacks. We describe correlation power analysis (CPA) on the schemes that yield full secret key recoveries. First, we identify a secret leakage of secret affine maps S and T during matrix-vector products in signing when Rainbow is implemented with equivalent keys rather than random affine maps for optimal implementations. In this case, the simple structure of the equivalent keys leads to the retrieval of the entire secret affine map T. Next, we extend the full secret key recovery to the general case using random affine maps via a hybrid attack: after recovering S by performing CPA, we recover T by mounting algebraic key recovery attacks. We demonstrate how this leakage on Rainbow can be practically exploited on an 8-bit AVR microcontroller using CPA. Consequently, our CPA can be applied to Rainbow-like multi-layered schemes regardless of the use of the simple-structured equivalent keys and UOV-like single layer schemes with the implementations using the equivalent keys of the simple structure. This is the first result on the security of multivariate quadratic equations-based signature schemes using only CPA. Our result can be applied to Rainbow-like multi-layered schemes and UOV-like single layer schemes submitted to NIST for Post-Quantum Cryptography Standardization.