Aleo algorithms: the power of privacy-preserving computation

The intersection of privacy and computation has been revolutionized by Aleo, a blockchain platform dedicated to privacy-centric solutions. Aleo’s innovative approach to blockchain development introduces a world of possibilities, and one of the most intriguing facets is the realm of algorithms. In this article, we’ll embark on a journey to explore the fascinating world of 6 Aleo algorithms, showcasing their potential and significance within this burgeoning field.

1. fixed-point numbers: precision in privacy

In the world of computation, precision is key. Aleo’s implementation of fixed-point numbers and associated calculations in Leo provides a method to perform arithmetic with a predetermined number of decimal places. These fixed-point numbers are invaluable in various financial applications, particularly when privacy is paramount.

Build guide: to compile this Leo program, run:

leo build

To test this Leo program, run:

leo test

Development: to output the number of constraints, run:

leo build -d

GitHub - zeroknowledgetutorials/leo-fixed-point-numbers: Fixed-point number implementation and…

2. is_prime: tokenizing primes

is_prime is an Aleo program designed to issue prime tokens, an innovation with both theoretical and practical applications. With the ability to confirm prime numbers privately, this algorithm plays a critical role in cryptographic protocols and digital signatures. Aleo’s approach to prime numbers demonstrates the platform’s commitment to privacy and secure computation.

Build guide: to compile this Aleo program, run:

aleo build

To run it:

aleo run mint_prime_token aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4 5u32

The output:

"{
  owner: aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4.private,
  gates: 0u64.private,
  number: 5u32.private,
  iterations: 1u32.private,
  canary: true.public,
  is_prime: false.public,
  _nonce: 603339317380415816314570888404126663464436332980512234750917908760393090867group.public
}"

Next steps, verify:

aleo run prove_prime_token "{
  owner: aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4.private,
  gates: 0u64.private,
  number: 5u32.private,
  iterations: 1u32.private,
  canary: true.public,
  is_prime: false.public,
  _nonce: 603339317380415816314570888404126663464436332980512234750917908760393090867group.public
}"
aleo run prove_prime_token "{
  owner: aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4.private,
  gates: 0u64.private,
  number: 5u32.private,
  iterations: 2u32.private,
  canary: true.public,
  is_prime: false.public,
  _nonce: 6328869172842952576813143067373849549188650736300757547383240395187818915446group.public
}"
aleo run prove_prime_token "{
  owner: aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4.private,
  gates: 0u64.private,
  number: 5u32.private,
  iterations: 3u32.private,
  canary: true.public,
  is_prime: false.public,
  _nonce: 248329312141775632021658271280856324179595097992133796740743937862232527036group.public
}"
aleo run prove_prime_token "{
  owner: aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4.private,
  gates: 0u64.private,
  number: 5u32.private,
  iterations: 4u32.private,
  canary: true.public,
  is_prime: false.public,
  _nonce: 7879508746557493898655206073250219079880128488601554336586527098259605947701group.public
}"

Output:

"{
  owner: aleo1lr6ap3ed4q823wek3kk9eha3e8e98wv40x578zhl6afmds2twqxs8szyj4.private,
  gates: 0u64.private,
  number: 5u32.private,
  iterations: 5u32.private,
  canary: true.public,
  is_prime: true.public,
  _nonce: 5713367399487472733591011170776859178690336536443012147369880313874690987675group.public
}"

GitHub - arosboro/is_prime: A prime token Aleo program

3. leo/bubblesort: sorting privately

bubblesort is a classic sorting algorithm, but Aleo’s implementation within the Leo language takes this concept a step further. It allows for sorting data privately and securely, a feat that has wide-ranging implications for various data-driven applications. Whether it’s sensitive financial data or confidential user information, Aleo’s bubblesort ensures privacy while maintaining the integrity of the data.

Run guide: to run this program, use:

leo run bubble_sort

Execute guide: to execute this program, run:

leo execute bubble_sort

leo/examples/bubblesort at testnet3 · AleoHQ/leo

4. leo/groups: privacy in mathematical operations

group operations are foundational in mathematics, and Aleo’s implementation in the Leo language facilitates private and secure mathematical operations. The ability to perform operations on encrypted data while maintaining privacy is a game-changer in fields such as secure multi-party computation, data sharing, and collaborative research.

Run guide: to run this program, use:

leo run main

Execute guide: to execute this program, run:

leo execute main

Documentation group element: the set of affine points on the elliptic curve passed into the Leo compiler forms a group. A subset of those points, defined by a chosen generator point, forms a subgroup of the group. Leo supports the set of points in this subgroup as a primitive data type. Group elements are special since their values can be defined as coordinate pairs (x, y)group. The group type keyword group must be used when specifying a pair of group coordinates since implicit syntax would collide with normal tuple (a, b) values.

let a = 0group; // the zero of the group
let b = group::GEN; // the group generator
let c = (0, 1)group; // coordinate notation

leo/examples/groups at testnet3 · AleoHQ/leo

5. leo/twoadicity: private number analysis

Two-adicity is a concept in number theory that explores the divisibility of integers by powers of two. Aleo’s implementation of computing two-adicity in the Leo language enables private number analysis. This is crucial in various applications, including cryptographic protocols and confidential data sharing, where understanding the structure of numbers is essential.

Run guide: to run this program, use:

leo run main

Execute guide: to execute this program, run:

leo execute main

leo/examples/twoadicity at testnet3 · AleoHQ/leo

6. Leo-ElGamal: homomorphic encryption

Multiplicative homomorphic encryption using ElGamal is a cryptographic innovation implemented in Aleo’s Leo language. Homomorphic encryption enables computations on encrypted data without decrypting it, preserving privacy while performing operations. This opens doors to secure cloud computing, confidential data analysis, and more.

Conclusion

These Aleo algorithms, spanning from fixed-point numbers to advanced cryptographic concepts like homomorphic encryption, showcase the platform’s dedication to privacy-preserving computation. They offer developers and users the tools needed to work with sensitive data and perform operations privately, making Aleo a pioneering force in the realm of privacy-focused blockchain technology. As Aleo continues to push the boundaries of what’s possible in the field of algorithms, it’s clear that the future of privacy-centric computation holds immense promise.

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Prepared by Colliseum