GCM Security Bounds Reconsidered

A constant of $2^{22}$ appears in the security bounds of the Galois/Counter Mode of Operation, GCM. In this paper, we first develop an algorithm to generate nonces that have a high counter-collision probability. We show concrete examples of nonces with the counter-collision probability of about $2^{20.75}/2^{128}$. This shows that the constant in the security bounds, $2^{22}$, cannot be made smaller than $2^{19.74}$ if the proof relies on ``the sum bound.\u27\u27 We next show that it is possible to avoid using the sum bound, leading to improved security bounds of GCM. One of our improvements shows that the constant of $2^{22}$ can be reduced to 32

Limits on Authenticated Encryption Use in TLS

This technical note presents limits on the security (as a function of the number of plaintext bytes encrypted and the number of forgery attempts made by an adversary) for the main Authenticated Encryption schemes available in TLS 1.2 and the draft of TLS 1.3. These limits are derived from security proofs for the considered schemes available in the literature. Our intention is to provide considered technical input to on-going discussions in the TLS Working Group of the IETF concerning, amongst other things, the necessity of adding a key update feature to the TLS 1.3 specification

Optimal Forgeries Against Polynomial-Based MACs and GCM

Polynomial-based authentication algorithms, such as GCM and Poly1305, have seen widespread adoption in practice. Due to their importance, a significant amount of attention has been given to understanding and improving both proofs and attacks against such schemes. At EUROCRYPT 2005, Bernstein published the best known analysis of the schemes when instantiated with PRPs, thereby establishing the most lenient limits on the amount of data the schemes can process per key. A long line of work, initiated by Handschuh and Preneel at CRYPTO 2008, finds the best known attacks, advancing our understanding of the fragility of the schemes. Yet surprisingly, no known attacks perform as well as the predicted worst-case attacks allowed by Bernstein\u27s analysis, nor has there been any advancement in proofs improving Bernstein\u27s bounds, and the gap between attacks and analysis is significant. We settle the issue by finding a novel attack against polynomial-based authentication algorithms using PRPs, and combine it with new analysis, to show that Bernstein\u27s bound, and our attacks, are optimal

Authenticated Encryption with Small Stretch (or, How to Accelerate AERO)

Standard form of authenticated encryption (AE) requires the ciphertext to be expanded by the nonce and the authentication tag. These expansions can be problematic when messages are relatively short and communication cost is high. To overcome the problem we propose a new form of AE scheme, MiniAE, which expands the ciphertext only by the single variable integrating nonce and tag. An important feature of MiniAE is that it requires the receiver to be stateful not only for detecting replays but also for detecting forgery of any type. McGrew and Foley already proposed a scheme having this feature, called AERO, however, there is no formal security guarantee based on the provable security framework. We provide a provable security analysis for MiniAE, and show several provably-secure schemes using standard symmetric crypto primitives. This covers a generalization of AERO, hence our results imply a provable security of AERO. Moreover, one of our schemes has a similar structure as OCB mode of operation and enables rate-1 operation, i.e. only one blockcipher call to process one input block. This implies that the computation cost of MiniAE can be as small as encryption-only schemes

The Multi-User Security of Authenticated Encryption: AES-GCM in TLS 1.3

We initiate the study of multi-user (mu) security of authenticated encryption (AE) schemes as a way to rigorously formulate, and answer, questions about the randomized nonce mechanism proposed for the use of the AE scheme GCM in TLS 1.3. We (1) Give definitions of mu ind (indistinguishability) and mu kr (key recovery) security for AE (2) Characterize the intent of nonce randomization as being improved mu security as a defense against mass surveillance (3) Cast the method as a (new) AE scheme RGCM (4) Analyze and compare the mu security of both GCM and RGCM in the model where the underlying block cipher is ideal, showing that the mu security of the latter is indeed superior in many practical contexts to that of the former, and (5) Propose an alternative AE scheme XGCM having the same efficiency as RGCM but better mu security and a more simple and modular design

Gleeok: A Family of Low-Latency PRFs and its Applications to Authenticated Encryption

In this paper, we propose a new family of low-latency pseudorandom functions (PRFs), dubbed Gleeok. Gleeok utilizes three 128-bit branches to achieve a 256-bit key size while maintaining low latency. The first two branches are specifically designed to defend against statistical attacks, especially for differential attacks, while the third branch provides resilience against algebraic attacks. This unique design enables Gleeok to offer ultralow latency while supporting 256-bit keys, setting it apart from existing ciphers dedicated to low-latency requirements. In addition, we propose wide-block variants having three 256-bit branches. We also present an application of Gleeok to short-input authenticated encryption which is crucial for memory encryption and various realtime communication applications. Furthermore, we present comprehensive hardware implementation results that establish the capabilities of Gleeok and demonstrate its competitiveness against related schemes in the literature. In particular, Gleeok achieves a minimum latency of roughly 360 ps with the NanGate 15 nm cell library and is thus on par with related low-latency schemes that only feature 128-bit keys while maintaining minimal overhead when equipped in an authenticated mode of operation

Pholkos -- Efficient Large-state Tweakable Block Ciphers from the AES Round Function

With the dawn of quantum computers, higher security than $128$ bits has become desirable for primitives and modes. During the past decade, highly secure hash functions, MACs, and encryption schemes have been built primarily on top of keyless permutations, which simplified their analyses and implementation due to the absence of a key schedule. However, the security of these modes is most often limited to the birthday bound of the state size, and their analysis may require a different security model than the easier-to-handle secret-permutation setting. Yet, larger state and key sizes are desirable not only for permutations but also for other primitives such as block ciphers. Using the additional public input of tweakable block ciphers for domain separation allows for exceptionally high security or performance as recently proposed modes have shown. Therefore, it appears natural to ask for such designs. While security is fundamental for cryptographic primitives, performance is of similar relevance. Since 2009, processor-integrated instructions have allowed high throughput for the AES round function, which already motivated various constructions based on it. Moreover, the four-fold vectorization of the AES instruction sets in Intel\u27s Ice Lake architecture is yet another leap in terms of performance and gives rise to exploit the AES round function for even more efficient designs. This work tries to combine all aspects above into a primitive and to build upon years of existing analysis on its components. We propose Pholkos, a family of (1) highly efficient, (2) highly secure, and (3) tweakable block ciphers. Pholkos is no novel round-function design, but utilizes the AES round function, following design ideas of Haraka and AESQ to profit from earlier analysis results. It extends them to build a family of primitives with state and key sizes of $256$ and $512$ bits for flexible applications, providing high security at high performance. Moreover, we propose its usage with a $128$-bit tweak to instantiate high-security encryption and authentication schemes such as SCT, ThetaCB3, or ZAE. We study its resistance against the common attack vectors, including differential, linear, and integral distinguishers using a MILP-based approach and show an isomorphism from the AES to Pholkos-$512$ for bounding impossible-differential, or exchange distinguishers from the AES. Our proposals encrypt at around $1$--$2$ cycles per byte on Skylake processors, while supporting a much more general application range and considerably higher security guarantees than comparable primitives and modes such as PAEQ/AESQ, AEGIS, Tiaoxin346, or Simpira