Ascon (cipher)

Ascon is a family of lightweight authenticated ciphers that had been selected by US National Institute of Standards and Technology (NIST) for future standardization of the lightweight cryptography.

History
Ascon was developed in 2014 by a team of researchers from Graz University of Technology, Infineon Technologies, Lamarr Security Research, and Radboud University. The cipher family was chosen as a finalist of the CAESAR Competition in February 2019.

NIST had announced its decision on February 7, 2023 with the following intermediate steps that would lead to the eventual standardization:
 * Publication of NIST IR 8454 describing the process of evaluation and selection that was used;
 * Preparation of a new draft for public comments;
 * Public workshop to be held on June 21-22, 2023.

Design
The design is based on a sponge construction along the lines of SpongeWrap and MonkeyDuplex. This design makes it easy to reuse Ascon in multiple ways (as a cipher, hash, or a MAC). As of February 2023, the Ascon suite contained seven ciphers, including:
 * Ascon-128 and Ascon-128a authenticated ciphers;
 * Ascon-Hash cryptographic hash;
 * Ascon-Xof extendable-output function;
 * Ascon-80pq cipher with an "increased" 160-bit key.

The main components have been borrowed from other designs:
 * substitution layer utilizes a modified S-box from the $χ$ function of Keccak;
 * permutation layer functions are similar to the $$\Sigma$$ of SHA-2.

Parameterization
The ciphers are parameterizable by the key length k (up to 128 bits), "rate" (block size) r, and two numbers of rounds a, b. All algorithms support authenticated encryption with plaintext P and additional authenticated data A (that remains unencrypted). The encryption input also includes a public nonce N, the output - authentication tag T, size of the ciphertext C is the same as that of P. The decryption uses N, A, C, and T as inputs and produces either P or signals verification failure if the message has been altered. Nonce and tag have the same size as the key K (k bits).

In the CAESAR submission, two sets of parameters were recommended:

Padding
The data in both A and P is padded with a single bit with the value of 1 and a number of zeros to the nearest multiple of $r$ bits. As an exception, if A is an empty string, there is no padding at all.

State
The state consists of 320 bits, so the capacity $$c=320-r$$. The state is initialized by an initialization vector IV (constant for each cipher type, e.g., hex 80400c0600000000 for Ascon-128) concatenated with K and N.

Transformation
The initial state is transformed by applying $a$ times the transformation function $p$ ($$p^a$$). On encryption, each word of A || P is XORed into the state and the $p$ is applied $b$ times ($$p^b$$). The ciphertext C is contained in the first $r$ bits of the result of the XOR. Decryption is near-identical to encryption. The final stage that produces the tag T consists of another application of $$p^a$$; the special values are XORed into the last $c$ bits after the initialization, the end of A, and before the finalization.

Transformation $p$ consists of three layers:
 * $$p_C$$, XORing the round constants;
 * $$p_S$$, application of 5-bit S-boxes;
 * $$p_L$$, application of linear diffusion.

Test vectors
Hash values of an empty string (i.e., a zero-length input text) for both the XOF and non-XOF variants. Ascon-Hash("") 0x 7346bc14f036e87ae03d0997913088f5f68411434b3cf8b54fa796a80d251f91 Ascon-HashA("") 0x aecd027026d0675f9de7a8ad8ccf512db64b1edcf0b20c388a0c7cc617aaa2c4 Ascon-Xof("", 32) 0x 5d4cbde6350ea4c174bd65b5b332f8408f99740b81aa02735eaefbcf0ba0339e Ascon-XofA("", 32) 0x 7c10dffd6bb03be262d72fbe1b0f530013c6c4eadaabde278d6f29d579e3908d

Even a small change in the message will (with overwhelming probability) result in a different hash, due to the avalanche effect. Ascon-Hash("The quick brown fox jumps over the lazy dog") 0x 3375fb43372c49cbd48ac5bb6774e7cf5702f537b2cf854628edae1bd280059e Ascon-Hash("The quick brown fox jumps over the lazy dog.") 0x c9744340ed476ac235dd979d12f5010a7523146ee90b57ccc4faeb864efcd048