The Dalos Elliptic Curve

At a glance

Curve family	Twisted Edwards Curve (TEC)
Formal name	TEC_S1600_Pr1605p2315_m26
Common name	Dalos
Used for	Ouronet accounts (Standard + Smart)
Safe scalar size	1600 bits per account
Possible accounts per Codex	2¹⁶⁰⁰ ≈ 10⁴⁸¹
Address encoding	160 glyphs from the Dalos Character Set
Reference impl.	DALOS_Crypto/Elliptic/Parameters.go (Go), `@stoachain/dalos-crypto` (TypeScript)

The curve equation, at a glance

Curve parameters

Prime field `P`	2¹⁶⁰⁵ + 2315 (1606-bit prime defining the finite field the curve lives in)
Subgroup order `Q`	2¹⁶⁰³ + 1258387060301909514024042379046449850251725029634697115619073843890705481440046740552204199635883885272944914904655483501916023678206167596650367826811846862157534952990004386839463386963494516862067933899764941962204635259228497801901380413 (1604-bit prime — the order of the generator's subgroup; private-key scalars are reduced mod this)
Trace `T`	−5033548241207638056096169516185799401006900118538788462476295375562821925760186962208816798543535541091779659618621934007664094712824670386601471307247387448630139811960017547357853547853978067448271735599059767848818541036913991207605519336 (curve trace — relates to cofactor via R · Q = P + 1 − T)
Cofactor `R`	Computed via `R = (P + 1 − T) / Q` (small cofactor required for safe Schnorr)
`a` coefficient	1
`d` coefficient	−26
Safe scalar `S`	1600 bits (size of the private-key search space, after cofactor accounting)

Dalos's specific coefficients (a = 1, d = −26) over a 1606-bit prime field give it the strongest security margin of any elliptic curve currently in production use anywhere in cryptocurrency. The frozen parameters above are the canonical reference — any implementation that deviates produces incompatible keys.

Used for every Ouronet account

Every Ouronet account in your Codex — Standard (Ѻ.xxx) and Smart (Σ.xxx) — has a private key that lives on the Dalos curve. The 160-glyph address you see is the Dalos-Character-Set encoding of the account's public key.

• Standard Ouronet Accounts (Ѻ.) — single-key accounts. The Dalos private key signs operations directly.
• Smart Ouronet Accounts (Σ.) — multi-branch authorization. The Dalos private key is one component; the account also has a sovereign guard and an optional governor branch for more sophisticated authorization patterns.

Each Ouronet account is independent — its own Dalos private key, its own Payment Key (the StoaChain k:account that backs gas costs), its own address. A Codex can hold thousands of such accounts and the Dalos space (2¹⁶⁰⁰ ≈ 10⁴⁸¹ possible keys) is wildly larger than anything any user would ever need.

Entropy scale

Dalos was sized specifically to be the heaviest practical elliptic curve in production:

• 1600 bits = roughly 6× the safe-scalar size of Ed25519 (~252 bits)
• Practical brute-force attack effort: 2⁸⁰⁰ operations (the birthday bound for elliptic-curve discrete-log via Pollard's rho)
• Total Ouronet account space: 2¹⁶⁰⁰ ≈ 10⁴⁸¹ — comfortably more than the cube of the atom count of the observable universe

The cost is signature size and verification time. Dalos signatures are several hundred bytes; verification takes milliseconds rather than microseconds. For an identity-and-account layer this is an acceptable trade for a permanence ceiling that nothing else in cryptocurrency approaches.

Dalos vs Apollo — when each is used

Property	Apollo	Dalos
Safe scalar	1024 bits	1600 bits
Used for	Codex Identity (1 per Codex, 2 halves)	Ouronet accounts (many per Codex)
Prefix glyph	`₱.` Standard, `Π.` Smart	`Ѻ.` Standard, `Σ.` Smart
Total per Codex	2²⁰⁴⁸ ≈ 10⁶¹⁶	2¹⁶⁰⁰ ≈ 10⁴⁸¹ (per account; unlimited count)
Signature verification	Off-chain only (Apollo not Pact-native)	Off-chain; on-chain via Pact native verifier for the chain-side ED25519 Payment Key
Design intent	Identity (permanent handle)	Operational accounts (frequent use)

Note that the Codex Identity space is larger than the per-account Dalos space (10⁶¹⁶ vs 10⁴⁸¹) — by design. The identity layer needs more cryptographic margin than any individual account because identity is meant to be permanent, while accounts can be rotated. Apollo's 2×1024 architecture also gives the identity layer a Guardian-style cosign model that single-key accounts don't have.

Schnorr signatures on Dalos

Like Apollo, Dalos uses Schnorr signatures. Each signature is a pair (R, s) with verification s·G = R + e·P. The math is the same as Apollo; only the curve parameters differ.

Dalos signatures are also off-chain-verified in user-facing contexts (the Mnemosyne web app, OuronetUI, AncientHoldings, etc.). On StoaChain itself, Dalos signatures don't reach the Pact runtime — chain operations are authorized by the Ouronet account's Payment Key, which is a Stoa-native ED25519 keypair (k: account format). Dalos and the Payment Key are linked at account-creation time and together form what we call an "Ouronet account" in the user-facing sense.

Where Dalos seed words come from

A Dalos account can be created from any of these inputs:

• Random (system-generated; user never sees the seed)
• A bitstring (1600 bits raw binary)
• A base-10 scalar (a big number, up to ~482 digits)
• A base-49 scalar (the curve's natural base — most compact)
• Seed words from the Dalos Character Set (the human-friendly path)
• A 40×40 bitmap (1600 pixels = 1600 bits, paste or scan)

All six are equivalent — they're different encodings of the same 1600 bits of entropy. The dalos-crypto package handles conversion between them; you can supply any format the user provides.

The Dalos Character Set →

The 256-glyph alphabet, including how Dalos seed words are composed.

The Apollo Elliptic Curve →

The 1024-bit twin used for Codex Identity.

Reference implementation: github.com/StoaChain/DALOS_Crypto