QARMA explained

QARMA (from Qualcomm ARM Authenticator^[1]) is a lightweight tweakable block cipher primarily known for its use in the ARMv8 architecture for protection of software as a cryptographic hash for the Pointer Authentication Code. The cipher was proposed by Roberto Avanzi in 2016. Two versions of QARMA are defined: QARMA-64 (64-bit block size with a 128-bit encryption key) and QARMA-128 (128-bit block size with a 256-bit key). The design of the QARMA was influenced by PRINCE and MANTIS. The cipher is intended for fully-unrolled hardware implementations with low latency (like memory encryption). Unlike the XTS mode, the address can be directly used as a tweak and does not need to be whitened with the block encryption first.

Architecture

QARMA is an Even–Mansour cipher using three stages, with whitening keys w⁰ and w¹ XORed in between:

1. permutation F is using core key k⁰ and parameterized by a tweak T. It has r rounds inside (r = 7 for QARMA-64, r = 11 for QARMA-128);
2. "central" permutation C is using key k¹ and is designed to be reversible via a simple key transformation (contains two central rounds);
3. the third permutation is an inverse of the first (r more rounds).

All keys are derived from the master encryption key K using specialisation:

• K is partitioned into halves as w⁰ Concatenation k⁰, each will have halfsize bits;
• for encryption w¹ = (w⁰ >>> 1) + (w⁰ >> (halfsize-1));
• for encryption k¹ = k⁰;
• for decryption, the same design can be used as long as k⁰+α is used as a core key, k¹ = Q•k⁰, w¹ and w⁰ are swapped. α here is a special constant and Q a special involutary matrix. This construct is similar to the alpha reflection in PRINCE.

The data is split into 16 cells (4-bit nibbles for QARMA-64, 8-bit bytes for QARMA-128). Internal state also contains 16 cells, arranged in a 4x4 matrix, and is initialized by plaintext (XORed with w⁰). In each round of

\digamma , the state is transformed via operations \tau, M, S :\tau is ShuffleCells, a MIDORI permutation of cells ([0, 11, 6, 13, 10, 1, 12, 7, 5, 14, 3, 8, 15, 4, 9, 2]);M is MixColumns: each column is multiplied by a fixed matrix M;S is SubCells: each cell is transformed using an S-box.The tweak for each round is updated using h, \omega :h is a cell permutation from MANTIS ([6, 5, 14, 15, 0, 1, 2, 3, 7, 12, 13, 4, 8, 9, 10, 11]);\omega is an LFSR applied to each of the cells with numbers [0, 1, 3, 4, 8, 11, 13]. For QARMA-64, the LFSR is (b3, b2, b1, b0) ⇒ (b0 + b1, b3, b2, b1), for QARMA-128, (b7, b6, ..., b0) ⇒ (b0 + b2, b7, b6, ..., b1),The rounds of \overline \digamma consist of inverse operations \overline \tau, \overline M, \overline S, \overline h, \overline \omega .Central rounds, in addition to two rounds (\tau, M, S and \overline \tau, \overline M, \overline S ), include multiplication of the state by an involutary matrix Q.

Sources

• The QARMA Block Cipher Family. 10.13154/tosc.v2017.i1.4-44. IACR Transactions on Symmetric Cryptology (ToSC). 2016. 8 March 2017. https://tosc.iacr.org/index.php/ToSC/article/view/583. 17. 4–44. Roberto. Avanzi. 1. https://web.archive.org/web/20200513144451/https://eprint.iacr.org/2016/444.pdf. May 13, 2020.
• Web site: Zong . Rui . Dong . Xiaoyang . Meet-in-the-Middle Attack on QARMA Block Cipher . iacr.org . . 10 June 2022. 2016.
• Kaur . Jasmin . Kermani . Mehran Mozaffari . Azarderakhsh . Reza . Hardware Constructions for Lightweight Cryptographic Block Cipher QARMA With Error Detection Mechanisms . IEEE Transactions on Emerging Topics in Computing . 1 January 2022 . 10 . 1 . 514–519 . 2376-4562 . 10.1109/TETC.2020.3027789 . 226665710 . free .
• Li . Rongjia . Jin . Chenhui . Meet-in-the-Middle Attacks on Reduced-Round QARMA-64/128 . The Computer Journal . 4 May 2018 . 61 . 8 . 1158–1165 . 0010-4620 . 1460-2067 . 10.1093/comjnl/bxy045 .
• Yang . Dong . Qi . Wen-feng . Chen . Hua-jin . Impossible Differential Attack on QARMA Family of Block Ciphers . Cryptology ePrint Archive . 2018.

External links

• Public-domain Python implementation of QARMA-64
• Open-source (MIT license) implementation of QARMA-64 in C

Notes and References

1. https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/qameleon-spec.pdf Qameleon v. 1.0: A Submission to the NIST Lightweight Cryptography Standardization Process