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Journals / International Journal of Information Security Science / 2026 / Volume: 15 Issue: 1

LadderPrime: Exception-Free, Twist-Insensitive, and Constant-Time Ladder for Prime-Order Elliptic Curves

Hüseyin Hışıl(University of Wollongong)0000-0002-1019-2187
Nuri Furkan Pala(IZMIR INSTITUTE OF TECHNOLOGY)0009-0003-9504-9340
Pages
—
Publication Date
2026-03-19
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Essential cryptographic protocols such as DH and qDSA can be instantiated over LadderPrime.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce LadderPrime, an exception-free scalar-point multiplication algorithm, which works on the Kummer line of an elliptic curve given by the equation B*y^2=x^3+A*x^2+ax+b.
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Key Findings & Data:LadderPrime operates only on two coordinates and computes the correct output for all input points, all scalars, and all elliptic curves of characteristic > 2.
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Conclusion & Impact:Essential cryptographic protocols such as DH and qDSA can be instantiated over LadderPrime.
🔬Design:Research Article
📍Scope:2015 Verileri
⚙️Variables:elliptic curve cryptography · Diffie-Hellman key exchange · twist-secure curves

Abstract

We introduce LadderPrime, an exception-free scalar-point multiplication algorithm, which works on the Kummer line of an elliptic curve given by the equation B*y^2=x^3+A*x^2+ax+b. LadderPrime operates only on two coordinates and computes the correct output for all input points, all scalars, and all elliptic curves of characteristic > 2. This is achieved by an alternative set of differential-addition formulas which can handle not only generic points but also the problematic point (0 : Z) for Montgomery ladder. The main structure of LadderPrime is analogous to the scalar-point multiplication in Bernstein’s X25519 Diffie-Hellman key exchange (DH) specification. Unlike, X25519 which uses the non-prime order (h = 8) elliptic Curve25519, LadderPrime is able to work with prime order (h = 1) (and non-prime order) elliptic curves. When used with a prime order elliptic curve, LadderPrime does not need the initial raising of base point to a prime order subgroup. In other words, LadderPrime eliminates the need for masking lower bits of the scalar. LadderPrime also eliminates the need for Hamburg’s "Decaf" (CRYPTO 2015) and later refined "Ristretto" methods. Essential cryptographic protocols such as DH and qDSA can be instantiated over LadderPrime.

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Cite This Article

Hışıl, H., Pala, N. F. (2026). LadderPrime: Exception-Free, Twist-Insensitive, and Constant-Time Ladder for Prime-Order Elliptic Curves. International Journal of Information Security Science, Volume: 15 Issue: 1. https://doi.org/10.55859/ijiss.1867564

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