import { Range } from "../provers/range.js";
import { CipherBalance, GeneralPrefixData, ProjectivePoint } from "../types.js";
export declare const WITHDRAW_CAIRO_STRING = 8604536554778681719n;
/**
 * Public inputs of the verifier for the withdraw operation.
 * @interface InputsWithdraw
 * @property {ProjectivePoint} y - The Tongo account to withdraw from
 * @property {bigint} nonce - The nonce of the Tongo account
 * @property {bigint} to - The starknet contract address to send the funds to
 * @property {bigint} amount - The amount of tongo to withdraw
 * @property {CipherBalance} currentBalance - The current CipherBalance stored for the account
 * @property {number} bit_size - The bit size for range proofs
 * @property {GeneralPrefixData} prefix_data - General prefix data for the operation
 */
export interface InputsWithdraw {
    y: ProjectivePoint;
    nonce: bigint;
    to: bigint;
    amount: bigint;
    currentBalance: CipherBalance;
    auxiliarCipher: CipherBalance;
    bit_size: number;
    prefix_data: GeneralPrefixData;
}
/**
 * Proof of withdraw operation.
 * @interface ProofOfWithdraw
 * @property {ProjectivePoint} A_x - The proof point A_x
 * @property {ProjectivePoint} A_r - The proof point A_r
 * @property {ProjectivePoint} A - The proof point A
 * @property {ProjectivePoint} A_v - The proof point A_v
 * @property {bigint} sx - The proof scalar sx
 * @property {bigint} sb - The proof scalar sb
 * @property {bigint} sr - The proof scalar sr
 * @property {Range} range - The range proof
 * @todo Remove the _ from property names?
 */
export interface ProofOfWithdraw {
    A_x: ProjectivePoint;
    A_r: ProjectivePoint;
    A: ProjectivePoint;
    A_v: ProjectivePoint;
    sx: bigint;
    sb: bigint;
    sr: bigint;
    range: Range;
}
export declare function proveWithdraw(private_key: bigint, initial_balance: bigint, amount: bigint, to: bigint, initial_cipherbalance: CipherBalance, nonce: bigint, bit_size: number, prefix_data: GeneralPrefixData): {
    inputs: InputsWithdraw;
    proof: ProofOfWithdraw;
    newBalance: CipherBalance;
};
/**
 * Verifies the withdraw operation. First, users have to show knowledge of the private key. Then, users have to provide
 * a cleartext of the amount b to withdraw. The contract will construct a cipher balance (L2, R2) = (g**b y**r2, g**r2)
 * with randomness r2='withdraw'. The contract will subtract (L2,R2) to the stored balance of the user. The user have
 * to provide a zk proof that the final cipher balance is encrypting a positive (a value in (0, u**32)) amount b_left. To do
 * this when the RangeProof is verified, it returns a V = g**b_left h**r, with b_left positive. V is used as an L part of
 * a cipher balance, users have to prove that the cipher balance (V, R_aux = g**r) is encrypting the same amount
 * that the final cipher balance.
 *
 * Complexity:
 * - EC_MUL: 12 + n*5 = 172 for u32
 * - EC_ADD: 8 + n*4  = 136 for u32
 *
 * @param {InputsWithdraw} inputs - The withdraw operation inputs
 * @param {ProofOfWithdraw} proof - The proof to verify
 * @returns {boolean} True if the proof is valid, false otherwise
 */
export declare function verifyWithdraw(inputs: InputsWithdraw, proof: ProofOfWithdraw): void;