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

  • * Corresponding author: Sebati Ghosh

    * Corresponding author: Sebati Ghosh 
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  • 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.

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

    Citation:

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

    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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