CWI Cryptology Group

Abstract: This paper introduces the structured generic-group model, an extension of Shoup’s generic-group model (from Eurocrypt 1997) to capture algorithms that take advantage of some non-generic structure of the group. We show that any discrete-log algorithm in a group of prime order that exploits the structure of at most a fraction of group elements, in a way that we precisely define, must run in time . As an application, we prove a tight subexponential-time lower bound against discrete-log algorithms that exploit the multiplicative structure of smooth integers, but that are otherwise generic. This lower bound applies to a broad class of index-calculus algorithms. We prove similar lower bounds against algorithms that exploit the structure of small integers, smooth polynomials, and elliptic-curve points.

Abstract: We present a number of observations on TEA-3, a stream cipher used in TETRA radio networks that was kept secret until recently. While the same also holds for the six other TETRA encryption algorithms, we pick TEA-3 to start with, as (i) it is not obviously weakened as TEA-{1,4,7} but (ii) in contrast to TEA-2 it is approved for extra-European emergency service, and (iii) as already noted by [MBW23] the TEA-3 design surprisingly contains a non-bijective S-box. Most importantly, we show that the 80-bit non-linear feedback shift register operating on the key decomposes into a cascade of two 40-bit registers. Although this hints at an intentional weakness at first glance, we are not able to lift our results to a practical attack. Other than that, we show how the balanced non-linear feedback functions used in the state register of TEA-3 can be constructed.

Abstract: Fiat-Shamir signatures replace the challenge in interactive identification schemes by a hash value over the commitment, the message, and possibly the signer's public key. This construction paradigm is well known and widely used in cryptography, for example, for Schnorr signatures and CRYSTALS-Dilithium. There is no ``general recipe'' for constructing Fiat-Shamir signatures regarding the inputs and their order for the hash computation, though, since the hash function is usually modeled as a monolithic random oracle. In practice, however, the hash function is based on the Merkle-Damgård or the sponge design. Our work investigates whether there are advisable or imprudent input orders for hashing in Fiat-Shamir signatures. We examine Fiat-Shamir signatures with plain and nested hashing using Merkle-Damgård or sponge-based hash functions. We analyze these constructions in both classical and quantum settings. As part of our investigations, we introduce new security properties following the idea of quantum-annoyance of Eaton and Stebila (PQCrypto 2021), called annoyance for user exposure and signature forgeries. These properties ensure that an adversary against the hash function cannot gain a significant advantage when attempting to extend a successful attack on a single signature forgery to multiple users or to multiple forgeries of a single user. Instead, the adversary must create extra forgeries from scratch. Based on our analysis, we derive a simple rule: When using Fiat-Shamir signatures, one should hash the commitment before the message; all other inputs may be ordered arbitrarily.