Key-length analysis of double random phase encoding

Kazuya Nakano; Masafumi Takeda; Hiroyuki Suzuki

doi:10.1364/AO.56.004474

Applied Optics
Vol. 56,
Issue 15,
pp. 4474-4479
(2017)
•https://doi.org/10.1364/AO.56.004474

Key-length analysis of double random phase encoding

Kazuya Nakano, Masafumi Takeda, and Hiroyuki Suzuki

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Kazuya Nakano, Masafumi Takeda, and Hiroyuki Suzuki, "Key-length analysis of double random phase encoding," Appl. Opt. 56, 4474-4479 (2017)

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Abstract

Double random phase encoding (DRPE) is a classical optical symmetric-key encryption method. DRPE prevents the key length from being determined because of its redundancy between encryption and decryption, unlike digital symmetric-key cryptographies. In our study, we numerically analyzed the key length of DRPE based on key-space analysis. We estimated the key length of DRPE by calculating the inverse value of the cumulative probability of the normal distribution that was estimated from samples of DRPE and then discuss security against brute-force attacks.

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Corrections

Kazuya Nakano, Masafumi Takeda, and Hiroyuki Suzuki, "Key-length analysis of double random phase encoding: publisher’s note," Appl. Opt. 56, 4917-4917 (2017)
https://opg.optica.org/ao/abstract.cfm?uri=ao-56-17-4917

18 May 2017: A correction was made to Table 3.

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Key Space $Q^{N \times N}$	$W$	$p$ -Value
$256^{64 \times 64}$	0.989	0.561
$256^{128 \times 128}$	0.989	0.603
$256^{256 \times 256}$	0.989	0.603
$256^{512 \times 512}$	0.990	0.898

Key Space $Q^{N \times N}$	Population Mean $μ$
Key Space $Q^{N \times N}$	Lower	Upper
$256^{64 \times 64}$	$- 2.88 \times 10^{- 5}$	$- 1.56 \times 10^{- 5}$
$256^{128 \times 128}$	$2.03 \times 10^{- 5}$	$2.27 \times 10^{- 5}$
$256^{256 \times 256}$	$8.73 \times 10^{- 6}$	$8.79 \times 10^{- 6}$
$256^{512 \times 512}$	$3.82 \times 10^{- 6}$	$3.83 \times 10^{- 6}$

Key Space $Q^{N \times N}$	Population Mean $μ$
Key Space $Q^{N \times N}$	Lower	Upper
$64^{256 \times 256}$	$- 1.06 \times 10^{- 4}$	$- 3.00 \times 10^{- 5}$
$128^{256 \times 256}$	$1.07 \times 10^{- 5}$	$2.04 \times 10^{- 5}$
$256^{256 \times 256}$	$8.73 \times 10^{- 6}$	$8.79 \times 10^{- 6}$
$512^{256 \times 256}$	$- 6.84 \times 10^{- 6}$	$- 6.78 \times 10^{- 6}$

Key Space $Q^{N \times N}$	Population Standard Deviation $σ$
Key Space $Q^{N \times N}$	Lower	Upper
$256^{64 \times 64}$	$5.78 \times 10^{- 2}$	$5.80 \times 10^{- 2}$
$256^{128 \times 128}$	$2.47 \times 10^{- 2}$	$2.48 \times 10^{- 2}$
$256^{256 \times 256}$	$3.91 \times 10^{- 3}$	$3.92 \times 10^{- 3}$
$256^{512 \times 512}$	$1.95 \times 10^{- 3}$	$1.96 \times 10^{- 3}$

Key Space $Q^{N \times N}$	Population Standard Deviation $σ$
Key Space $Q^{N \times N}$	Lower	Upper
$64^{256 \times 256}$	$1.39 \times 10^{- 1}$	$1.39 \times 10^{- 1}$
$128^{256 \times 256}$	$4.98 \times 10^{- 2}$	$4.99 \times 10^{- 2}$
$256^{256 \times 256}$	$3.91 \times 10^{- 3}$	$3.92 \times 10^{- 3}$
$512^{256 \times 256}$	$3.93 \times 10^{- 3}$	$3.94 \times 10^{- 3}$

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Applied Optics