Fiat Crypto

What Is Fiat Crypto?

Fiat Crypto, commonly written as Fiat-Crypto or Fiat Cryptography, is an open-source system for generating efficient and formally verified cryptographic arithmetic code.

It is designed to turn high-level mathematical descriptions into low-level implementations that come with machine-checked correctness proofs.

The project focuses mainly on arithmetic used in elliptic-curve cryptography, digital signatures, key exchange, authentication, and other cryptographic systems.

Cryptocurrency software depends heavily on this type of arithmetic because blockchain transactions are authorized with digital signatures and verified using mathematical operations over finite fields.

Fiat Crypto is not a cryptocurrency, token, blockchain, stablecoin, wallet, trading platform, or fiat-backed digital asset.

Its name uses “fiat” in the programming-language sense of deriving software from specifications rather than in the monetary sense of government-issued currency.

The official Fiat-Crypto repository describes the project as a system for synthesizing correct-by-construction code for cryptographic primitives.

The project was developed through research connected with the Programming Languages and Verification group at the Massachusetts Institute of Technology.

Its central goal is to reduce the risk of subtle arithmetic mistakes in security-critical cryptographic software.

Why Is Cryptographic Arithmetic Difficult?

Many cryptographic algorithms are easy to express as mathematical equations but difficult to implement efficiently on real computer processors.

A mathematical specification may operate on integers containing hundreds of bits.

Ordinary processors usually operate on much smaller fixed-size values such as 32-bit or 64-bit machine words.

Developers must divide a large number into several smaller pieces and carefully manage carries, borrows, multiplication results, and modular reductions.

A single incorrect carry or missing reduction can produce a wrong signature, reject a valid transaction, accept an invalid value, or expose secret information.

The fastest implementations are often written as long sequences of low-level arithmetic operations.

These routines can be difficult for human reviewers to understand and test completely.

Traditional testing can show that code works for selected inputs.

It cannot prove that the implementation works for every possible valid input.

Fiat Crypto addresses this problem by generating code from mathematical specifications while producing machine-checkable evidence that the generated arithmetic follows those specifications.

What Does Correct by Construction Mean?

Correct by construction means that correctness is built into the process used to create the software.

A developer begins with a mathematical description of the desired operation.

The system transforms that description through a sequence of proven compilation and optimization steps.

Each verified step preserves the meaning of the original operation.

The final arithmetic routine is therefore connected to the high-level specification through formal proofs.

This approach differs from writing optimized code manually and attempting to prove it correct afterward.

It can also reduce the amount of repetitive proof work required when supporting a new prime modulus or processor word size.

The research paper Simple High-Level Code for Cryptographic Arithmetic describes the project’s use of short high-level programs and machine-checked functional-correctness proofs.

What Is Formal Verification?

Formal verification uses mathematical logic to prove that software satisfies precisely stated properties.

A proof assistant checks each proof according to a small set of trusted logical rules.

Fiat Crypto uses the Coq proof assistant for its specifications, proofs, compiler components, and code-generation process.

Coq allows developers to define mathematical objects, write programs, state theorems, and construct proofs that the system checks mechanically.

A successful proof does not depend only on running a collection of test cases.

It establishes the proven property for every input covered by the formal specification and assumptions.

Formal verification does not prove every imaginable property of a complete cryptocurrency application.

It proves the particular statements that developers have defined within the verified model.

How Does Fiat Crypto Work?

Fiat Crypto begins with a high-level description of modular arithmetic.

The developer specifies information such as the prime modulus, processor word size, limb arrangement, implementation strategy, and operations to generate.

The system represents the arithmetic inside Coq.

It then applies verified transformations that simplify expressions, calculate safe numeric bounds, eliminate unnecessary operations, and lower the program toward machine-word arithmetic.

The transformed program becomes a straight-line, C-like internal representation.

A backend converts that representation into a target programming language or another verified intermediate language.

The generated functions can include addition, subtraction, multiplication, squaring, carrying, conditional selection, and byte conversion.

The resulting code can be included in a larger cryptographic library after appropriate review, integration, compilation, and testing.

What Is Modular Arithmetic?

Modular arithmetic performs calculations while treating numbers that differ by a multiple of a modulus as equivalent.

A clock provides a simple example because 13:00 and 1:00 represent the same position on a 12-hour clock.

Cryptographic modular arithmetic uses much larger moduli, often large prime numbers.

Assume calculations use modulus 17.

The value 20 is equivalent to 3 because subtracting 17 leaves 3.

The expression can be written as

.

Elliptic-curve systems repeatedly perform addition, subtraction, multiplication, squaring, and inversion modulo a large prime.

Fiat Crypto specializes these operations for a selected modulus.

What Is a Finite Field?

A finite field is a finite set of values with well-defined addition, subtraction, multiplication, and division operations.

Cryptographic systems commonly use fields based on integers modulo a large prime.

The values range from zero to one less than the prime.

Every nonzero value has a multiplicative inverse inside the field.

Elliptic-curve points are defined using coordinates whose arithmetic takes place in a finite field.

Digital signature and key-agreement systems therefore depend on correct finite-field operations.

Fiat Crypto primarily helps generate the low-level routines that perform this field arithmetic.

What Is a Limb?

A limb is one machine-sized portion of a larger integer.

A 256-bit field element may be represented using four 64-bit limbs.

Another implementation may use five limbs containing about 51 bits each.

Leaving unused bits in each limb can provide space for carries and intermediate results.

The best limb arrangement depends on the modulus, processor, multiplication instructions, reduction strategy, and desired performance.

Choosing the wrong bounds can cause an intermediate result to exceed the range of its machine type.

Fiat Crypto calculates and proves bounds for arithmetic values as they move through the generated routine.

What Is Modular Reduction?

Modular reduction converts a large intermediate number into an equivalent value within the expected modular range.

Multiplying two 256-bit values can produce an intermediate value requiring up to 512 bits.

The implementation must reduce that value modulo the selected prime.

A general division operation can be slow and may not offer suitable timing behavior.

Cryptographic implementations therefore use specialized reduction methods based on the structure of the modulus.

Fiat Crypto supports several implementation strategies for producing efficient reduction code.

Supported Arithmetic Strategies

Saturated Solinas Arithmetic

A saturated representation uses limbs that fill most or all of the available machine-word range.

Solinas-style arithmetic takes advantage of primes that can be expressed using powers of two and a small number of additional terms.

This structure can make reduction faster than general division.

Unsaturated Solinas Arithmetic

An unsaturated representation leaves unused bits at the top of each limb.

The extra space allows several arithmetic operations to occur before a full carry or reduction is required.

Curve25519 field arithmetic commonly uses five approximately 51-bit limbs on 64-bit machines.

Word-by-Word Montgomery Arithmetic

Montgomery arithmetic represents values in a special domain that allows modular multiplication without ordinary division by the modulus.

Word-by-word Montgomery reduction processes the result in machine-sized portions.

This approach can support general odd moduli that do not have a convenient Solinas form.

Dettman Multiplication

Dettman-style multiplication is an implementation technique associated with efficient arithmetic for certain prime-field representations.

It organizes multiplication and reduction to take advantage of the modulus and limb structure.

Solinas Reduction

Solinas reduction uses special relationships between powers of two and the selected prime.

High parts of an intermediate number can be folded back into lower positions using those relationships.

Base Conversion

Base conversion changes how a field value is divided among limbs.

It can be required when two parts of a cryptographic system use different internal representations.

The current repository documents these strategies through the unified

code-generation interface.

What Operations Can Fiat Crypto Generate?

Fiat Crypto can generate modular addition and subtraction routines.

It can generate multiplication and squaring routines.

It can generate carry and reduction functions that place values into an acceptable range.

It can generate negation and multiplication by selected constants.

It can generate conditional selection functions designed to avoid ordinary secret-dependent branches.

It can generate conversion functions between internal limbs and standardized byte strings.

The exact available functions depend on the selected strategy and command-line options.

A complete signature or key-exchange implementation requires additional group operations, hashing, nonce generation, protocol validation, and application logic beyond these field routines.

Which Cryptographic Primes Does Fiat Crypto Support?

Fiat Crypto is designed to generate arithmetic for many prime moduli rather than supporting only one fixed curve.

The official repository includes generation examples for the prime

, which is used by Curve25519-family cryptography.

It includes examples for the NIST P-256 field prime.

Its codebase also contains support and proof work related to the secp256k1 field used in major blockchain signature systems.

Bedrock2 generation examples include the prime

used by Poly1305 authentication.

Support for a field prime does not automatically provide a complete implementation of every protocol that uses that field.

Developers must still integrate the generated arithmetic with correctly implemented point operations, signatures, hashes, serialization, validation, and key management.

Why Is secp256k1 Relevant to Fiat Crypto?

secp256k1 is an elliptic curve used by several major cryptocurrency protocols.

Wallets use secp256k1 private keys to generate signatures authorizing blockchain transactions.

Nodes verify those signatures before accepting the transactions as valid.

The curve’s coordinate calculations depend on arithmetic modulo a specific 256-bit prime.

An error in this field arithmetic could produce incorrect points, signatures, or verification results.

Fiat Crypto’s support for secp256k1-related arithmetic makes the project relevant to blockchain implementation research and high-assurance wallet software.

The related CryptOpt research project has also connected Fiat Cryptography’s verified intermediate code to optimized assembly generation, including work involving secp256k1 arithmetic.

Fiat Crypto and Elliptic-Curve Cryptography

Elliptic-curve cryptography uses points satisfying an algebraic equation over a finite field.

Public keys are derived by multiplying a curve point by a secret scalar.

Signature generation and verification use repeated point additions, doublings, scalar multiplications, and field operations.

Fiat Crypto provides verified foundations for some of the arithmetic underneath these higher-level algorithms.

The repository also contains proofs and definitions for Edwards, Montgomery, and Weierstrass curve representations.

Correct field arithmetic alone does not prove that a complete elliptic-curve protocol is secure.

The curve, point validation, scalar handling, nonce generation, signature construction, and surrounding software must also be correct.

What Programming Languages Does Fiat Crypto Support?

The current repository maintains a primary C backend.

It also supports a Bedrock2/C path with stronger proof coverage for the relationship between the internal syntax tree and Bedrock2.

Community-maintained or externally maintained backends include Go, Rust, and Zig.

A JSON backend is described as experimental.

The repository identifies its Java backend as unmaintained and known to have problems.

Backend status can change, so developers should review the current backend status table before selecting generated code.

The project explicitly avoids giving identical quality guarantees for every backend.

How Is the Compiler Produced?

The verified definitions and transformations are written inside Coq.

Fiat Crypto can extract executable compiler code into OCaml or Haskell.

The resulting command-line program accepts parameters describing the arithmetic implementation.

It writes generated source code to standard output.

This approach allows users to run code generation without loading the full proof assistant for every generation request.

The proof development establishes properties of the transformations from which the executable compiler is extracted.

Users building the full repository still need the documented Coq, OCaml, build-system, and package dependencies.

What Does Fiat Crypto Prove?

Fiat Crypto is designed to prove functional correctness of generated arithmetic relative to its formal specifications.

Functional correctness means that the generated operation calculates the mathematically intended result for inputs satisfying the documented preconditions.

The system also reasons about numeric ranges so intermediate values fit within selected machine integer sizes.

Verified rewriting and compilation passes are intended to preserve the meaning of expressions.

The exact end-to-end proof boundary depends on the backend and integration path.

The repository states that the Bedrock2 backend includes a proof connecting the Bedrock2 abstract syntax tree to the internal abstract syntax tree.

Other language stringification backends do not currently have the same proof coverage.

This distinction is important when evaluating claims that generated source code is completely verified.

What Does Fiat Crypto Not Prove?

Fiat Crypto does not prove that every surrounding wallet, blockchain node, smart contract, or application is secure.

It does not automatically prove the security of a cryptographic protocol against every mathematical attack.

It does not prove that a private key was generated with sufficient randomness.

It does not prevent a developer from passing invalid parameters or using generated functions incorrectly.

It does not guarantee that every compiler, linker, operating system, processor, or hardware device preserves every intended property.

Most output backends do not have a fully proven conversion from their internal representation to the final source-code text.

The repository also notes that ordinary C compiler integer-expression behavior remains part of the trusted or separately reviewed environment.

Formal verification should therefore be understood as a strong, precisely scoped assurance rather than a universal guarantee.

Does Fiat Crypto Guarantee Constant-Time Execution?

Cryptographic code often needs to avoid control flow and memory access patterns that depend on secret values.

This programming discipline is commonly described as constant-time coding.

Generated straight-line arithmetic and conditional-selection primitives can support constant-time implementations.

However, actual timing behavior depends on the generated backend, compiler, target processor, surrounding code, and microarchitecture.

A functional-correctness proof is not automatically a complete proof against every timing, cache, power, electromagnetic, speculative-execution, or fault-injection attack.

Developers must review the specific assurance provided by the selected pipeline and conduct appropriate side-channel testing and analysis.

Fiat Crypto vs. Handwritten Cryptographic Code

Handwritten cryptographic code can be extremely fast when created by an experienced specialist.

It can also contain mistakes that are difficult to identify through ordinary review.

A manual implementation often requires separate work for every prime, word size, processor, and arithmetic representation.

Fiat Crypto automates much of this specialization from a reusable mathematical framework.

Its generated code may be easier to regenerate when assumptions or targets change.

Performance still needs to be measured on the actual target platform.

For some specialized environments, carefully written assembly may remain faster than ordinary generated C.

Projects such as CryptOpt explore how Fiat Crypto’s verified foundations can be extended into highly optimized assembly.

Fiat Crypto vs. Traditional Testing

Testing compares actual outputs with expected outputs for a finite collection of examples.

Formal verification proves a defined property for the complete input range covered by the theorem.

Testing remains valuable because it can detect integration, build, platform, serialization, and performance problems outside the formal proof.

The Fiat Crypto repository tests generated C code using an established cryptographic test suite.

Its Rust output is tested against a separate cryptographic library test suite.

Formal proofs and practical testing therefore complement rather than replace each other.

Fiat Crypto vs. Fiat Currency

Fiat currency is government-issued money such as dollars, euros, or yen.

Fiat Crypto is a software-verification and code-generation project.

The project does not issue money or connect a token to a national currency.

It does not provide bank payments, card payments, fiat deposits, or crypto purchases.

A search for “fiat crypto” may return information about converting government currency into cryptocurrency.

That financial meaning is unrelated to the Fiat-Crypto software project.

Fiat Crypto vs. Fiat-to-Crypto

Fiat-to-crypto describes converting government-issued currency into a cryptocurrency or digital asset.

A fiat-to-crypto on-ramp may process a bank transfer, payment card, identity check, currency conversion, and blockchain delivery.

Fiat Crypto instead generates cryptographic arithmetic implementations.

It does not operate an on-ramp or off-ramp.

The distinction is important because the terms appear similar while referring to completely different parts of the crypto ecosystem.

Fiat Crypto vs. the Fiat–Shamir Transformation

The Fiat–Shamir transformation converts certain interactive proof protocols into non-interactive proofs or signatures.

Its name comes from cryptographers Amos Fiat and Adi Shamir.

Fiat Crypto is a separate formal-methods project for synthesizing cryptographic arithmetic code.

Both topics belong to cryptography, but they solve different problems.

Fiat–Shamir concerns protocol interaction and challenge generation.

Fiat Crypto concerns verified implementation of low-level mathematical operations.

Fiat Crypto vs. a Cryptographic Library

A complete cryptographic library offers ready-to-use APIs for signatures, encryption, hashing, key exchange, certificates, and other protocols.

Fiat Crypto is mainly a generator and proof framework for arithmetic components.

Its output can be integrated into a broader library.

The broader library remains responsible for protocol logic, public interfaces, memory management, randomness, input validation, error handling, and secure key storage.

A developer should not treat one generated multiplication routine as a complete signature implementation.

Fiat Crypto vs. a General-Purpose Compiler

A general-purpose compiler accepts programs covering many types of computation.

Fiat Crypto is a domain-specific system focused on cryptographic arithmetic.

This narrow focus allows it to use mathematical knowledge about prime fields, limbs, carries, and modular reduction.

It can specialize code using details that a general compiler may not infer from ordinary source code.

The generated C or other source code may still be compiled by a general-purpose compiler afterward.

The complete trusted path therefore includes both the Fiat Crypto generation pipeline and the later build toolchain.

Why Fiat Crypto Matters to Blockchain Security

Blockchain protocols place valuable assets under the control of cryptographic keys.

A field-arithmetic error can undermine digital signatures even when the blockchain’s economic rules are correct.

Nodes may process untrusted public keys, signatures, proofs, and transaction data received from the network.

Cryptographic implementations must therefore handle every permitted edge case correctly.

Formal methods can provide stronger evidence than ordinary testing for arithmetic routines with enormous input spaces.

Fiat Crypto also makes it easier to generate consistent implementations for different processor sizes and prime fields.

This can help reduce dependence on a small number of experts manually rewriting delicate arithmetic code.

How Crypto Wallets Could Benefit From Fiat Crypto

Wallets generate public keys and signatures using cryptographic arithmetic.

A mobile wallet may need safe and efficient code on 32-bit or 64-bit processors.

A hardware wallet may have strict memory, timing, and processor limitations.

Generated field routines can provide a verified foundation for key and signature operations.

The wallet developer must still validate public keys, protect secret keys, generate nonces securely, and prevent side-channel leakage.

User-interface and transaction-parsing errors also remain outside the arithmetic proof.

How Blockchain Nodes Could Benefit From Fiat Crypto

Blockchain nodes may verify thousands of signatures or cryptographic proofs.

Performance is important because inefficient verification can reduce transaction throughput and increase hardware requirements.

Correctness is equally important because different nodes must reach the same validity result.

A rare arithmetic disagreement can create a consensus failure when some implementations accept a transaction and others reject it.

Verified arithmetic can reduce one source of implementation disagreement.

Nodes still require consensus tests, protocol specifications, networking security, database safety, and complete implementation review.

How Zero-Knowledge Systems Could Benefit

Zero-knowledge proof systems perform large amounts of finite-field arithmetic.

Provers and verifiers may use several different prime fields.

Incorrect field operations can produce invalid proofs, false rejections, or serious security failures.

A code generator that specializes arithmetic for the proof system’s modulus can improve portability and assurance.

Fiat Crypto does not automatically generate a complete zero-knowledge proving system.

Polynomial commitments, transcript construction, proof equations, circuit logic, and cryptographic assumptions require separate implementations and proofs.

How to Use Fiat Crypto Safely

Developers should begin with the official repository and read the current build and backend documentation.

They should select a supported arithmetic strategy suitable for the modulus and target architecture.

Generated code should be inspected, compiled with supported settings, and tested against independent known-answer vectors.

The project’s proof boundary and backend limitations should be documented in the consuming application’s security review.

Developers should test malformed inputs, boundary values, maximum carries, zero values, and non-canonical encodings.

Side-channel behavior should be evaluated on the actual compiler and hardware combination.

Updates to the generator, proof assistant, compiler, or backend should trigger new testing and review.

Production teams should avoid treating the words “formally verified” as permission to skip integration audits.

Advantages of Fiat Crypto

Fiat Crypto provides machine-checked functional-correctness proofs for important arithmetic transformations.

It can generate implementations for multiple prime moduli and machine-word sizes.

It reduces repetitive manual work when creating optimized field arithmetic.

Its high-level specifications are easier to reason about than thousands of handwritten low-level operations.

The project is open source and can be independently examined.

It supports reproducible code generation rather than relying only on copied arithmetic files with uncertain origins.

Its generated routines have been connected with widely deployed cryptographic software and extensive test suites.

Limitations of Fiat Crypto

Fiat Crypto covers only part of a complete cryptographic software stack.

Its proof guarantees differ between backends.

Building and modifying the proof development requires specialized knowledge of Coq, formal methods, compilers, and cryptographic arithmetic.

Generated source code must still pass through ordinary compilers and platform toolchains.

Functional correctness does not automatically prove resistance to every side channel.

Performance can vary by processor and compiler.

Unsupported parameters or unmaintained backends can create additional risk.

A formally correct implementation of an insecure cryptographic design remains insecure.

Common Misconceptions About Fiat Crypto

Fiat Crypto is not a cryptocurrency.

It is not connected to government-issued fiat money.

It does not convert cash into digital assets.

It is not the Fiat–Shamir transformation.

It does not generate complete blockchain applications automatically.

It does not prove that every program using its output is secure.

It does not eliminate the need for testing and code review.

It does not provide identical proof guarantees for every supported language backend.

It does not make weak keys, insecure protocols, or unsafe wallet interfaces secure.

Frequently Asked Questions

What is Fiat Crypto?

Fiat Crypto is an open-source project that generates efficient cryptographic arithmetic code from high-level specifications with machine-checked correctness proofs.

Is Fiat Crypto a cryptocurrency?

No, it is a software-verification and code-generation project rather than a digital asset.

Is Fiat Crypto related to fiat money?

No, it does not issue, process, or convert government currencies.

Is Fiat Crypto the same as Fiat Cryptography?

Yes, Fiat-Crypto and Fiat Cryptography are commonly used names for the same project and research effort.

Who developed Fiat Crypto?

The project grew from formal-verification and cryptographic implementation research associated with MIT’s Programming Languages and Verification group and external contributors.

What proof assistant does Fiat Crypto use?

It uses Coq to define specifications, implement transformations, and check correctness proofs.

What type of code does Fiat Crypto generate?

It primarily generates low-level modular arithmetic routines for cryptographic finite fields.

Does Fiat Crypto generate C code?

Yes, C is one of its principal maintained output targets.

Does Fiat Crypto support Rust?

The repository includes an externally maintained Rust backend with generated-code testing.

Does Fiat Crypto support Go?

Yes, its repository lists an externally maintained Go backend.

Does Fiat Crypto support Zig?

Yes, Zig is listed as an externally maintained backend with generated code used in testing.

Is the Java backend recommended?

The current repository identifies the Java backend as unmaintained and known to have problems.

What is a finite field?

A finite field is a finite set of values with arithmetic operations used by many cryptographic algorithms.

What is a limb?

A limb is one machine-sized piece of a larger cryptographic integer.

What is modular reduction?

Modular reduction converts an arithmetic result into an equivalent value relative to a selected modulus.

What is Montgomery arithmetic?

Montgomery arithmetic uses a special number representation to perform modular multiplication efficiently without ordinary division by the modulus.

What is Solinas arithmetic?

Solinas arithmetic takes advantage of prime moduli that have forms allowing efficient reduction through powers of two and small constants.

Does Fiat Crypto support Curve25519 arithmetic?

Yes, the official repository includes generation examples for the prime used by Curve25519-family cryptography.

Does Fiat Crypto support secp256k1?

The project contains secp256k1-related field and elliptic-curve work relevant to blockchain signature implementations.

Does Fiat Crypto create digital signatures?

It generates arithmetic components that can be used inside signature implementations, but it is not by itself a complete signing application.

Does Fiat Crypto prove that a signature scheme is secure?

No, functional correctness of arithmetic is different from proving the full mathematical security of a signature scheme.

Does Fiat Crypto prevent arithmetic overflow?

Its verified pipeline reasons about bounds and selects integer sizes intended to hold the intermediate values covered by its specifications.

Does Fiat Crypto guarantee constant-time code?

Its design supports fixed-control-flow cryptographic arithmetic, but complete side-channel security depends on the backend, compiler, processor, and surrounding application.

Can testing replace Fiat Crypto’s proofs?

No, testing and formal proof provide different forms of assurance and are most useful when applied together.

Can formal verification replace a security audit?

No, an audit must also review protocol logic, integration, randomness, memory safety, key handling, side channels, and application behavior.

Is every Fiat Crypto backend formally verified?

No, the repository documents different proof, maintenance, and testing levels for its output backends.

What is the strongest documented backend path?

The Bedrock2 backend includes an additional proof connecting its abstract syntax tree with Fiat Crypto’s internal representation.

Why is Fiat Crypto useful for blockchains?

It can reduce arithmetic implementation errors in signatures, keys, proofs, and other cryptographic operations used by blockchain software.

Can Fiat Crypto be used in wallets?

Generated arithmetic can be integrated into wallet cryptography, but the complete wallet still requires separate security engineering.

Is Fiat Crypto the same as fiat-to-crypto conversion?

No, fiat-to-crypto conversion is a financial service for purchasing digital assets with government currency.

Is Fiat Crypto the same as Fiat–Shamir?

No, Fiat–Shamir transforms interactive proofs, while Fiat Crypto synthesizes verified arithmetic implementations.

Is Fiat Crypto open source?

Yes, the project is publicly available under several permissive open-source license choices documented in its repository.

Conclusion

Fiat Crypto is a formal-verification and code-generation system for producing efficient cryptographic arithmetic.

It allows developers to describe modular operations at a high level and derive lower-level implementations through machine-checked transformations.

The project is especially relevant to cryptocurrency because blockchain signatures, public keys, wallets, nodes, and zero-knowledge systems depend on correct finite-field arithmetic.

Fiat Crypto can generate operations for important prime fields and implementation strategies such as Solinas and Montgomery arithmetic.

Its support includes maintained C and Bedrock2/C paths as well as externally maintained language backends.

The exact assurance depends on the selected backend and the boundary of the formal proof.

Formal verification reduces the risk of arithmetic errors but does not prove every property of a complete cryptographic application.

Developers must still review protocol security, private-key handling, randomness, serialization, compiler behavior, hardware behavior, and side-channel resistance.

Fiat Crypto should therefore be understood as a powerful foundation for high-assurance cryptographic software rather than a complete replacement for testing, auditing, and secure system design.