Use of Predictable Algorithm in Random Number Generator

Description

Demonstrations

The following examples help to illustrate the nature of this weakness and describe methods or techniques which can be used to mitigate the risk.

Note that the examples here are by no means exhaustive and any given weakness may have many subtle varieties, each of which may require different detection methods or runtime controls.

Example One

Suppose a cryptographic function expects random value to be supplied for the crypto algorithm.

During the implementation phase, due to space constraint, a cryptographically secure random-number-generator could not be used, and instead of using a TRNG (True Random Number Generator), a LFSR (Linear Feedback Shift Register) is used to generate a random value. While an LFSR will provide a pseudo-random number, its entropy (measure of randomness) is insufficient for a cryptographic algorithm.

Example Two

The example code is taken from the PRNG inside the buggy OpenPiton SoC of HACK@DAC'21 [REF-1370]. The SoC implements a pseudo-random number generator using a Linear Feedback Shift Register (LFSR).

An example of LFSR with the polynomial function P(x) = x

+x

+x

+1 is shown in the figure.

reg in_sr, entropy16_valid;
reg [15:0] entropy16;

assign entropy16_o = entropy16;
assign entropy16_valid_o = entropy16_valid;

always @ (*)
begin

  in_sr = ^ (poly_i [15:0] & entropy16 [15:0]);

end

A LFSR's input bit is determined by the output of a linear function of two or more of its previous states. Therefore, given a long cycle, a LFSR-based PRNG will enter a repeating cycle, which is predictable.

See Also