# American Institute of Mathematical Sciences

November  2019, 13(4): 705-732. doi: 10.3934/amc.2019042

## $\textsf{DWCDM+}$: A BBB secure nonce based MAC

 1 Indian Statistical Institute, Kolkata, India 2 NTT Secure Platform Laboratories, NTT Corporation, Japan

* Corresponding author

Received  November 2018 Revised  January 2019 Published  June 2019

Fund Project: This is an extended version of the article accepted in IACR-CRYPTO 2018. Section 3, section 4 and section 5 contains the substantial changes from our article accepted in IACR-CRYPTO 2018. Mridul Nandi is supported by R.C.Bose Centre for Cryptology and Security

In CRYPTO 2016, Cogliati and Seurin have proposed a nonce-based MAC called Encrypted Wegman-Carter with Davies-Meyer (
 $\textsf{EWCDM}$
), from an
 $n$
-bit block cipher
 $\textsf{E}$
and an
 $n$
-bit almost xor universal hash function
 $\textsf{H}$
as
 $\textsf{E}_{K_2}\bigl(\textsf{E}_{K_1}(N)\oplus N\oplus \textsf{H}_{K_h}(M)\bigr),$
for a nonce
 $N$
and a message
 $M$
that provides roughly
 $2n/3$
-bit MAC security. However, obtaining the similar security using a single block cipher key was posed as an open research problem. In this paper, we present Decrypted Wegman-Carter with Davies-Meyer (
 $\textsf{DWCDM+}$
) construction based on a single block cipher key that provides
 $2n/3$
-bit MAC security from an
 $n$
-bit block cipher
 $\textsf{E}$
and an
 $n$
-bit
 $k$
-regular (
 $\forall k \leq n$
), almost xor universal hash function
 $\textsf{H}$
as
 $\textsf{E}^{-1}_{K}\bigl(\textsf{E}_{K}(N)\oplus N \oplus \textsf{H}_{K_h}(M)\bigr).$
 $\textsf{DWCDM+}$
is structurally very similar to its predecessor
 $\textsf{EWCDM}$
except that the facts that (i) the number of block cipher keys reduced from
 $2$
to
 $1$
and (ⅱ) the outer encryption call is replaced by a decryption one. To make the construction truely single-keyed, here we derive the hash key
 $K_h$
as the block cipher output of a fixed string
 $0^{n-2} \| 10$
as long as the hash key is of
 $n$
bits. We show that if the nonce space is restricted to
 $(n-1)$
bits,
 $\textsf{DWCDM+}$
is secured roughly up to
 $2^{2n/3}$
MAC queries (
 $2^{n/2}$
MAC queries) and
 $2^n$
verification queries against nonce respecting (nonce misuse resp.) adversaries.
Citation: Nilanjan Datta, Avijit Dutta, Mridul Nandi, Kan Yasuda. $\textsf{DWCDM+}$: A BBB secure nonce based MAC. Advances in Mathematics of Communications, 2019, 13 (4) : 705-732. doi: 10.3934/amc.2019042
##### References:

show all references

##### References:
$\textsf{DWCDM+}$ construction with an n-bit block cipher EK and n-bit keyed hash function HL where L = EK(0n−2║10).
Birthday bound MAC attack against $\textsf{DWCDM+}$ if full nonce space is used.
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