Brute Force the Log

Hit the Target

The row that equals the public value reveals the toy exponent.

highlighted = computed this step

The target appears

The table eventually reaches value 8, exactly the public value.

y=8y=8
Hit the targetThe tiny discrete-log rows are recomputed from p, g, and the target public value.Hit the target - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8

Read the hit row

The hit is at x=6, so the toy secret exponent is recovered.

x=6x=6
Hit the targetThe tiny discrete-log rows are recomputed from p, g, and the target public value.Hit the target - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8

Check the equality

Raising 5 to x=6 modulo 23 gives 8.

56 mod 23=85^6\bmod{}23=8
Hit the targetThe tiny discrete-log rows are recomputed from p, g, and the target public value.Hit the target - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8

Summary

The brute-force table turns the tiny public value back into the secret exponent.

recovered x=6\text{recovered }x=6
Hit the targetThe tiny discrete-log rows are recomputed from p, g, and the target public value.Hit the target - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8