Streaming prime processing
Finite candidate windows are processed without constructing a dense representation of the entire search range.
Pythagorean Sieve Enterprise RSA-Oriented & ECC-Oriented Engineering Technologies
Pythagorean Sieve Enterprise / RSA
Bounded-memory prime processing for RSA-oriented engineering.
A proprietary C++ technology line for streaming prime-candidate processing, multiprecision factor generation and complete RSA key-material verification.
Technology profile
Structured for controlled, reproducible evaluation.
The RSA-oriented line develops the Pythagorean Sieve into a bounded-memory processing architecture. It supports distant finite windows, rejection-only prefiltering, multiprecision probable-prime generation and consistency checking of the resulting RSA material. Lean and OpenSSL-backed profiles make it possible to distinguish the proprietary arithmetic path from auxiliary external validation and interoperability.
Why this architecture
Predictable memory, distant-range access and native streaming.
The RSA-oriented technology is intended for applications in which predictable memory use, native streaming, direct access to distant numerical ranges and controlled prime-candidate generation are more important than a universal claim of maximum throughput.
Unlike dense interval-based approaches, the modular index formulation decouples working-memory requirements from the magnitude of the numerical range being examined. Processing may begin from an arbitrary index without materializing or traversing all preceding intervals, while candidates can be emitted incrementally and computation can stop as soon as the requested result has been obtained.
The Enterprise implementation complements this architecture with finite-window acceleration through IPM, high-bound multiprecision filtering through MPW and the MPS1 small-prime moduli cache. Separate Lean and OpenSSL-backed profiles allow the proprietary low-RSS core to be evaluated independently from BIGNUM validation, interoperability checks and PEM serialization.
Multiprecision generation
Independent prime factors are generated with controlled bit length, retry behavior and configurable primality validation.
Complete key material
The pipeline constructs and checks the modulus, totient-related values, private exponent and CRT components.
Interoperability profile
Optional OpenSSL-backed verification and PEM handling support integration-oriented review without redefining the lean core.
Resource awareness
The design emphasizes bounded working memory, controlled logging and reproducible operational measurement.
Integration surface
A stable shared-library interface supports binary evaluation and platform-specific integration studies.
Enterprise acceleration layers
Distinct paths for finite windows and high-bound workflows.
The selectors preserve the public processing semantics while choosing an implementation path appropriate to the requested numerical regime.
LayerPurposeSelection boundary
IPMFinite odd 64-bit batch windowsExplicit or conservative backend=auto selection
MPWWindowed multiprecision prefilterSelected high-bound candidate workflows
MPS1Cached small-prime moduliReduces repeated multiprecision remainder work
Scalar pathsReference-compatible filteringRetained as the conservative/default boundary
Processing architecture
From an index range to verified RSA key material.
The public architecture can be described as a sequence of bounded stages. Optimized kernels, internal policies and implementation details remain proprietary.
Select a finite range beginning at the required numerical position.
Apply modular, IPM or multiprecision prefilter paths according to the selected profile.
Submit surviving candidates to configurable multiprecision probable-prime testing.
Generate distinct factors with the requested bit-length and retry requirements.
Compute the modulus, private exponent and CRT-related components.
Run internal consistency checks and, where enabled, OpenSSL validation and PEM serialization.
RSA-oriented construction
Independent factors, complete mathematical key material.
The controlled profile generates independent candidates p and q, validates them internally, checks distance and exponent compatibility and can optionally cross-check the factors through OpenSSL BIGNUM.
N = pqλ(N) = lcm(p − 1, q − 1)d ≡ e−1 (mod λ(N))
The construction also computes the CRT parameters dP, dQ and qinv. A key handle is issued only after the essential invariants have passed.
Execution profiles
Separate dependency and validation boundaries.
CapabilityLeanOpenSSL-backed + PEM
Proprietary candidate and RSA pathGenerates p/q and validates complete mathematical RSA materialSame proprietary construction path
Random generationNative system RNGs with std::random_device fallbackOpenSSL RAND_bytes
OpenSSL/libcrypto dependencyNoneRequired
BIGNUM cross-validationNot usedOptional p/q cross-validation
PEM and metadata outputNot usedOpt-in through a validated handle
Evaluation objectiveLow-dependency, low-RSS coreValidation and interoperability
RSA validation boundary
Checks performed before material is accepted.
A key handle is issued only after the essential bit-length, independence, primality, exponent, modulus and CRT invariants pass. Optional BIGNUM validation and PEM or metadata output do not replace the mandatory internal checks, and reports exclude secret values.
Expected candidate and modulus bit lengthsIndependent generation and inequality of p and qProbable-prime validation of both factorsConsistency of N = p × qPublic/private exponent relationshipCRT component consistencyOptional OpenSSL BIGNUM cross-checkNo-secret operational reporting
Deployment-oriented assessment
Assess the resource boundary before broader integration.
Binary-only Footprint Evaluation and Integration Kits provide separate Embedded Lean and Edge OpenSSL boundaries. Authorized evaluators can inspect dependencies, reproduce the supplied resource evidence and perform compile, link and API-integration checks without disclosure of the proprietary implementation.
This separation makes the memory, dependency and interoperability boundaries assessable before broader product-integration or deployment decisions are made.
Potential RSA deployment value
Small resident memory can matter at system scale.
The RSA-oriented value proposition combines a low-RSS Lean workflow, a compact embedded workspace and an optional OpenSSL-backed interoperability profile. The benefit is determined by the customer's actual deployment rather than by a universal speed claim.
A smaller per-process resident set may support more concurrent workers within a fixed memory budget.
Workspace measured in only a few kilobytes can make technical assessment possible on constrained targets where resource margins are decisive.
Lean and OpenSSL-backed profiles let an organization evaluate only the validation, serialization and dependency boundary its deployment requires.
Bounded memory, streaming output and early stop can reduce over-provisioning and make batch or service capacity more predictable.
RSA hosted benchmark evidence
Resource profiles and same-target algorithmic comparisons.
Canonical resource profiling and scalar-versus-auto same-target testing are separate campaigns. They are reported in separate tables below; Binary Footprint measurements follow in their own section.
Hosted measurement and timing-diagnostic interpretation are summarized in the Technical FAQ.
01 · Canonical resource profile
Complete workflow wall time and peak RSS.
Ten independent runs per series; the OpenSSL-backed measurements include BIGNUM cross-validation of p and q.
ModulusLean median · RSSOpenSSL median · RSS
RSA-20480.355 s · 3808 KB0.140–0.920 s · 3764–3816 KB0.345 s · 7980 KB0.140–1.190 s · 7704–8004 KB
RSA-30721.190 s · 3894 KB0.340–2.920 s · 3748–3940 KB1.950 s · 7850 KB0.920–6.310 s · 7792–7996 KB
RSA-40966.045 s · 3798 KB0.560–9.910 s · 3576–3856 KB5.115 s · 7964 KB1.620–25.780 s · 7788–8112 KB
RSA-8192 high-bound≈29.80 s · ≈3936 KB12.61–126.91 s · 3760–3976 KB52.075 s · 7972 KB12.620–205.490 s · 7904–8112 KB
02 · Same-target comparisonScalar versus
Scalar versus mp_prefilter=auto.
Both methods process the same initial p and q targets and preserve equal search-attempt counts.
ConfigurationScalar medianAuto median · speedup
RSA-2048 standard-bound0.220418 s0.178506 s · 1.229×
RSA-3072 standard-bound1.172450 s1.020870 s · 1.176×
RSA-4096 standard-bound2.167550 s1.916860 s · 1.130×
RSA-8192 standard-bound15.437800 s14.802600 s · 1.041×
RSA-8192 high-bound46.053000 s20.142600 s · 2.281×
The high-bound configuration uses small_prime_bound=4000000, window_marker_chunk_size=4096 and auto/windowed prefiltering.
User CPU time remained close to wall time, with zero or near-zero system CPU time and zero major page faults.
Ten-run comparison with primesieve reproduced all tested finite-64-bit counts. Primesieve remained faster for dense enumeration; the Enterprise path used about 62% lower median peak RSS in distant-range cases near 1018.
RSA Binary Footprint evidence
Static workspace, library code and assessed stack by RSA profile.
This Embedded Lean evidence is reported independently from hosted process RSS and OpenSSL-backed execution.
The Embedded Lean boundary has no libcrypto or libssl dependency.
Fixed workspace progression from RSA-2048 through RSA-8192 high-bound.
Functional execution, dependency audit, binary hygiene, package retest, manifest and SHA-256 integrity accompany the supplied kits.
Binary Footprint scope and hosted-versus-embedded interpretation are summarized in the Technical FAQ.
Technical brochure