Using the new VPMADD instructions for the new post quantum key encapsulation mechanism SIKE

This paper demonstrates the use of new processor instructions VPMADD, intended to appear in the coming generation of Intel processors (codename "Cannon Lake"), in order to accelerate the newly proposed key encapsulation mechanism (KEM) named SIKE. SIKE is one of the submissions to the NIST standardization process on post-quantum cryptography, and is based on pseudo-random walks in supersingular isogeny graphs. While very small keys are the main advantage of SIKE, its extreme computational intensiveness makes it one of the slowest KEM proposals. Performance optimizations are needed. We address here the "Level 1" parameters that target 64-bit quantum security, and deemed sufficient for the NIST standardization effort. Thus, we focus on SIKE503 that operates over F p2 with a 503-bit prime p. These short operands pose a significant challenge on using VPMADD effectively. We demonstrate several optimization methods to accelerate F-p, F-p2, and the elliptic curve arithmetic, and predict a potential speedup by a factor of 1.72x.

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Novak Kaluderovic

Post-quantum cryptography is a branch of cryptography which deals with cryptographic algorithms whose hardness assumptions are not based on problems known to be solvable by a quantum computer, such as the RSA problem, factoring or discrete logarithms.This thesis treats two such algorithms and provides theoretical and practical attacks against them.The first protocol is the generalised Legendre pseudorandom function - a random bit generator computed as the Legendre symbol of the evaluation of a secret polynomial at an element of a finite field. We introduce a new point of view on the protocol by analysing the action of the group of Möbius transformations on the set of secret keys (secret polynomials).We provide a key extraction attack by creating a table which is cubic in the number of the function queries, an improvement over the previous algorithms which only provided a quadratic yield. Furthermore we provide an ever stronger attack for a new set of particularly weak keys.The second protocol that we cover is SIKE - supersingular isogeny key encapsulation.In 2017 the American National Institute of Standards and Technology (NIST) opened a call for standardisation of post-quantum cryptographic algorithms. One of the candidates, currently listed as an alternative key encapsulation candidate in the third round of the standardisation process, is SIKE.We provide three practical side-channel attacks on the 32-bit ARM Cortex-M4 implementation of SIKE.The first attack targets the elliptic curve scalar multiplication, implemented as a three-point ladder in SIKE. The lack of coordinate randomisation is observed, and used to attack the ladder by means of a differential power analysis algorithm.This allows us to extract the full secret key of the target party with only one power trace.The second attack assumes coordinate randomisation is implemented and provides a zero-value attack - the target party is forced to compute the field element zero, which cannot be protected by randomisation. In particular we target both the three-point ladder and isogeny computation in two separate attacks by providing maliciously generated public keys made of elliptic curve points of irregular order.We show that an order-checking countermeasure is effective, but comes at a price of 10% computational overhead. Furthermore we show how to modify the implementation so that it can be protected from all zero-value attacks, i.e., a zero-value is never computed during the execution of the algorithm.Finally, the last attack targets a point swapping procedure which is a subroutine of the three-point ladder. The attack successfully extracts the full secret key with only one power trace even if the implementation is protected with coordinate randomisation or order-checking. We provide an effective countermeasure --- an improved point swapping algorithm which protects the implementation from our attack.

EPFL2022

Side-channel attacks on SIKE

Natacha Yolande Emmanuel Marie Linard de Guertechin

This thesis presents, firstly, an introduction to the current state of the art in isogeny-based cryptography, and secondly, a side-channel differential power analysis of SIKE—an isogeny-based key exchange algorithm—in semi-static mode. These attacks have been realized on an ARM implementation of SIKEp434 in the pqm4 library which is itself based on the reference implementation of the SIKE submission to the NIST post-quantum standardization process. We have analyzed the power consumption of an STM32F3 board which features an ARM Cortex-M4 microcontroller through Pearson’s correlation in the Hamming Weight model. We investigated an information leak of the 3-points Ladder involved in the decapsulation mechanism of SIKEp434. As this function was used to compute P + [m]Q where m is Bob’s private key and P, Q are two public points on a known elliptic curve, we showed that we can recover every bit of Bob’s private key by exploiting the power consumption as a bit distinguisher through a correlation with the result of an ADDS assembly instruction. A proof of leakage of the ADDS instruction of ARM has been demonstrated in this thesis. Ideas for countermeasures to prevent this attack are discussed.

2020

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Novak Kaluderovic

EPFL2022