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We analyze the handshake protocol of the Transport Layer Security (TLS) protocol, version 1.3. We address both the full TLS 1.3 handshake (the one round-trip time mode, with signatures for authentication and (elliptic curve) Diffie–Hellman ephemeral ((EC)DHE) key exchange), and the abbreviated resumption/“PSK” mode which uses a pre-shared key for authentication (with optional (EC)DHE key exchange and zero round-trip time key establishment). Our analysis in the reductionist security framework uses a multi-stage key exchange security model, where each of the many session keys derived in a single TLS 1.3 handshake is tagged with various properties (such as unauthenticated versus unilaterally authenticated versus mutually authenticated, whether it is intended to provide forward security, how it is used in the protocol, and whether the key is protected against replay attacks). We show that these TLS 1.3 handshake protocol modes establish session keys with their desired security properties under standard cryptographic assumptions. [ABSTRACT FROM AUTHOR]

In this work, we retake an old idea that Koblitz presented in his landmark paper (Koblitz, in: Proceedings of CRYPTO 1991. LNCS, vol 576, Springer, Berlin, pp 279–287, 1991), where he suggested the possibility of defining anomalous elliptic curves over the base field F 4 . We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. We also introduce two ordinary Koblitz-like elliptic curves defined over F 4 that are equipped with efficient endomorphisms. To the best of our knowledge, these endomorphisms have not been reported before. In order to achieve a fast reduction procedure, we adopted a redundant trinomial strategy that embeds elements of the field F 4 m , with m a prime number, into a ring of higher order defined by an almost irreducible trinomial. We also suggest a number of techniques that allow us to take full advantage of the native vector instructions of high-end microprocessors. Our software library achieves the fastest timings reported for the computation of the timing-protected scalar multiplication on Koblitz curves, and competitive timings with respect to the speed records established recently in the computation of the scalar multiplication over binary and prime fields. [ABSTRACT FROM AUTHOR]

Transport Layer Security (TLS) is the most important cryptographic protocol in use today. However, finding a cryptographic security proof for the complete, unaltered protocol has proven to be a challenging task. We give the first such proof in the standard model for the core cryptographic protocol underlying TLS cipher suites based on ephemeral Diffie-Hellman key exchange (TLS-DHE). This includes the cipher suite TLS_DHE_DSS_WITH_3DES_EDE_CBC_SHA, which is mandatory in TLS 1.0 and TLS 1.1. It is impossible to prove the TLS Handshake secure in the classical security models of Bellare-Rogaway and Canetti-Krawczyk. The reason for this is that the final Finished messages of the TLS Handshake are encrypted with the session key, which provides an opportunity to distinguish real keys from random values. Therefore we start with proving the security of a truncated version of the TLS Handshake protocol, which has also been considered in previous work on TLS, and give the first proof of this variant in the standard model. Then we define the new notion of authenticated and confidential channel establishment (ACCE), which allows the monolithic analysis of protocols for which a modular security proof is not possible. We show that the combination of the TLS-DHE Handshake protocol and the TLS Record Layer encryption is secure in this model. Since the conference publication of this paper, the notion of ACCE has found many further applications, for example to the analysis of further TLS cipher suites (Krawczyk et al., Crypto 2013; Li et al., PKC 2014), advanced mechanisms like secure renegotiation of TLS session keys (Giesen et al., CCS 2013), and other practical protocols like EMV channel establishment (Brzuska et al., CCS 2013), SSH (Bergsma et al., CCS 2014), and QUIC (Lychev et al., S&P 2015). [ABSTRACT FROM AUTHOR]