Table 3 Comprehensive statistical testU01 results on 6DHCM outputs and security implications.

From: Fusion cryptography for secure medical data transmission using mathematical quantum computing operations

Test suite

No. of tests

Tests passed

Focus of tests

Security implications

SmallCrush

10

10

Basic uniformity and randomness properties; tests for simple patterns, bit-level uniformity

Passing ensures no trivial patterns or biases; implies no easy distinguishers or weak points exploitable by statistical or linear attacks.

Crush

96

95

Advanced tests for autocorrelation, linear complexity, and distribution of bit patterns

High linear complexity and low autocorrelation indicate strong diffusion and confusion; prevents attackers from exploiting correlations or linear weaknesses in the key stream.

BigCrush

160

158

Most stringent battery with tests for complex dependencies, overlaps, and large-scale structural randomness

Passing these tests demonstrates resistance to sophisticated statistical attacks, including differential and higher-order correlation attacks; also ensures unpredictability critical against quantum adversaries.

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