# TriviA and uTriviA: two fast and secure authenticated encryption schemes

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## Abstract

In this paper, we propose two hardware optimized authenticated encryption schemes: TriviA-v2 and uTriviA. Both TriviA-v2, an efficient hardware optimization of TriviA-0-v1, and uTriviA are based on (i) a stream cipher for generating keys for the ciphertext and the tag, and (ii) a pairwise independent hash to compute the tag. *We have adopted one of the ISO-standardized stream ciphers for lightweight cryptography, namely * Trivium *, to obtain our underlying stream cipher*. The main structure of TriviA-v2 remains same as TriviA-0-v1, except some changes in the internal functions. The stream cipher used both in TriviA-v2 and uTriviA has a 384-bit state, slightly larger than Trivium, and can accommodate a 128-bit secret key and IV. TriviA-v2 uses a *pairwise independent hash which is an adaptation of the * EHC or “Encode-Hash-Combine” hash that requires the optimum number of field multiplications and hence requires small hardware footprint. uTriviA uses a *pairwise independent hash which is an adaptation of the * HC or “Hash-Combine” hash which is close to EHC but does not use any encode function. We prove that TriviA-v2 construction has at least 128-bit security for privacy and 124-bit security of authenticity under the assumption that the underlying stream cipher produces a pseudorandom bit stream. The uTriviA construction achieves at least 128-bit security for privacy and 93-bit security of authenticity under the same assumption. We have implemented the designs in synthesizable RTL. Pre-layout synthesis using 65 nm standard cell technology reveals that TriviA-v2 is able to achieve a high throughput of 65.9 Gbps for an area of 21.2 KGE, whereas TriviA-0-v1 achieved a much higher hardware area. The uTriviA design achieves a hardware area of only 16.74 KGE, which is lowest among all the TriviA variants but with a lower throughput of 36.76 Gbps. Finally, we provide a brief comparison between the three constructions TriviA-0-v1, TriviA-v2 and uTriviA and the other standard implementations in terms of hardware area-efficiency metric.

## Keywords

Trivium Stream cipher Authenticated encryption Pairwise independent EHC TriviA uTriviA## Notes

### Acknowledgments

We would like to thank the reviewers for their detailed comments and suggestions for the betterment of our paper. Their suggestion regarding the choice of the primitive polynomial \(p_{32}(x)\) helped us to increase the area–throughput ratio for TriviA-v1, TriviA-v2 and uTriviA. We are thankful to that.

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