${\sf {FAST}}$: Disk encryption and beyond

Debrup Chakraborty; Sebati Ghosh; Cuauhtemoc Mancillas López; Palash Sarkar

doi:10.3934/amc.2020108

Article Contents

2022, Volume 16, Issue 1: 185-230. Doi: 10.3934/amc.2020108

This issue Previous Article Optimal antiblocking systems of information sets for the binary codes related to triangular graphs Next Article

${\sf {FAST}}$: Disk encryption and beyond

1.
Indian Statistical Institute, 203, B.T. Road, Kolkata, India 700108
2.
Computer Science Department, CINVESTAV-IPN, Mexico, D.F., 07360, Mexico

^* Corresponding author: Sebati Ghosh
^* Corresponding author: Sebati Ghosh

Received: February 2020

Early access: September 2020

Published: February 2022

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Abstract

This work introduces ${\sf {FAST}}$ which is a new family of tweakable enciphering schemes. Several instantiations of ${\sf {FAST}}$ are described. These are targeted towards two goals, the specific task of disk encryption and a more general scheme suitable for a wide variety of practical applications. A major contribution of this work is to present detailed and careful software implementations of all of these instantiations. For disk encryption, the results from the implementations show that ${\sf {FAST}}$ compares very favourably to the IEEE disk encryption standards XCB and EME2 as well as the more recent proposal AEZ. ${\sf {FAST}}$ is built using a fixed input length pseudo-random function and an appropriate hash function. It uses a single-block key, is parallelisable and can be instantiated using only the encryption function of a block cipher. The hash function can be instantiated using either the Horner's rule based usual polynomial hashing or hashing based on the more efficient Bernstein-Rabin-Winograd polynomials. Security of ${\sf {FAST}}$ has been rigorously analysed using the standard provable security approach and concrete security bounds have been derived. Based on our implementation results, we put forward ${\sf {FAST}}$ as a serious candidate for standardisation and deployment.

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Mathematics Subject Classification: 11T71, 68P25, 94A60.

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Figure 1. The hash functions $ \mathbf{H} $ and $ \mathbf{G} $

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Table 1. Encryption and decryption algorithms for ${\sf FAST}$

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Table 2. A two-round Feistel construction required in Table 1

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Table 3. Computations of ${\sf {vecHorner}}$ and ${\sf {vecHash2L}}$. The string $ 1^n $ denotes the element of $ { \mathbb{F} } $ whose binary representation consists of the all-one string. Here $ \eta $ is a positive integer $ \geq 3 $ and $ \mathfrak{d}(\eta) $ denote the degree of $ {\sf {BRW}}_{\tau}(X_1, \ldots, X_\eta) $, where $ X_1, \ldots, X_\eta \in { \mathbb{F} } $

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Table 4. Game $ G_{{\sf {real}}} $

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Table 5. Game $ G_{{\sf {int}}} $

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Table 6. Game $ G_{{\sf {rnd}}} $

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Table 7. Comparison of different tweakable enciphering schemes according to computational efficiency. [BC] denotes the number of block cipher calls; [M] denotes the number of field multiplications; [D] denotes the number of doubling ('multiplication by $ \alpha $') operations;

type	scheme	[BC]	[M]	[D]
enc-mix-enc	CMC [23]	$ 2m+1 $	–	–
	EME2$ ^* $ [20]	$ 2m+1+m/n $	–	2
	AEZ [25]	$ (5m+4)/2 $	–	$ \frac{m-2}{4} $
	FMix [7]	$ 2m+1 $	–	–
hash-enc-hash	XCB [27]	$ m+1 $	$ 2(m+3) $	–
	HCTR [38]	$ m $	$ 2(m+1) $	–
	HCHfp [14]	$ m+2 $	$ 2(m-1) $	–
	TET [21]	$ m+1 $	$ 2m $	$ 2(m-1) $
	HEH-BRW[36]	$ m+1 $	$ 2+2\lfloor(m-1)/2\rfloor $	$ 2(m-1) $
	$ {\sf {TESX}} $ with BRW [37]	$ m+1 $	$ 4+2\lfloor(m-1)/2\rfloor $	$ 2(m-1) $
	$ {\sf {FAST}}[{\sf {Fx}}_m, {\sf Horner}] $	$ m+1 $	$ 2m+1 $	–
	$ {\sf {FAST}}[{\sf {Fx}}_m, {\sf {BRW}}] $	$ m+1 $	$ 2+2\lfloor(m-1)/2\rfloor $	–

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Table 8. Comparison of different tweakable enciphering schemes according to practical and implementation simplicity. [BCK] denotes the number of block cipher keys; and [HK] denotes the number of blocks in the hash key

type	scheme	[BCK]	[HK]	dec module	parallel
enc-mix-enc	CMC [23]	1	-	reqd	no
	EME2$ ^* $ [20]	1	2	reqd	yes
	AEZ [25]	1	2	not reqd	yes
	FMix [7]	1	-	not reqd	no
hash-enc-hash	XCB [27]	3	2	reqd	yes
	HCTR [38]	1	1	reqd	yes
	HCHfp [14]	1	1	reqd	yes
	TET [21]	2	3	reqd	yes
	HEH-BRW[36]	1	1	reqd	yes
	$ {\sf {TESX}} $ with BRW [37]	1	2	not reqd	yes
	$ {\sf {FAST}}[{\sf {Fx}}_m, {\sf Horner}] $	1	-	not reqd	yes
	$ {\sf {FAST}}[{\sf {Fx}}_m, {\sf {BRW}}] $	1	-	not reqd	yes
Note: for both Tables 7 and 8, the block size is $n$ bits, the tweak is a single $n$-bit block and the number of blocks $m\geq 3$ in the message is fixed.

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Table 9. Comparison of the cycles per byte measure of ${\sf {FAST}}$ with those of XCB, EME2 and AEZ in the setting of $ {\sf {Fx}}_{256} $

scheme	Skylake	Kabylake
XCB	1.92	1.85
EME2	2.07	1.99
AEZ	1.74	1.70
$ {\sf {FAST}}[{\sf {Fx}}_{256}, {\sf {Horner}}] $	1.63	1.56
$ {\sf {FAST}}[{\sf {Fx}}_{256}, {\sf {BRW}}] $	1.24	1.19

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Table 10. Report of cycles per byte measure for the setting of ${\sf {Gn}}$ for $ {\sf {FAST}}[{\sf {Gn}}, \mathfrak{k}, {\sf {vecHorner}}] $ and $ {\sf {FAST}}[{\sf {Gn}}, \mathfrak{k}, 31, {\sf {vecHash2L}}] $

		Skylake			Kabylake
msg len	$ \mathfrak{k} $	$ {\sf {vecHorner}} $	$ {\sf {vecHash2L}} $	$ {\sf {vecHash2L}} $	$ {\sf {vecHorner}} $	$ {\sf {vecHash2L}} $	$ {\sf {vecHash2L}} $
(bytes)			(delayed)	(normal)		(delayed)	(normal)
	2	1.51	1.38	1.59	1.42	1.32	1.56
512	3	1.40	1.38	1.39	1.32	1.31	1.35
	4	1.34	1.37	1.36	1.26	1.31	1.33
	2	1.53	1.34	1.48	1.42	1.27	1.42
1024	3	1.45	1.34	1.34	1.35	1.27	1.30
	4	1.40	1.33	1.32	1.29	1.27	1.30
	2	1.57	1.30	1.35	1.45	1.24	1.30
4096	3	1.54	1.29	1.31	1.43	1.24	1.27
	4	1.51	1.29	1.30	1.40	1.24	1.26
	2	1.57	1.27	1.32	1.45	1.22	1.27
8192	3	1.56	1.27	1.30	1.44	1.22	1.25
	4	1.54	1.27	1.30	1.43	1.22	1.25

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